quantum Shannon theory Research Papers (original) (raw)

2025, arXiv (Cornell University)

We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only... more

We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only non-classical properties of a quantum channel E, i.e., they leave invariant the transition probabilities induced by E in the distinguished basis. We prove that such superchannels ΞC form a particular subclass of Schur-product supermaps that act on the Jamio lkowski state J(E) of a channel E via a Schur product, J = J • C. We also find physical realizations of general ΞC through a pre-and post-processing employing dephasing channels with memory, and show that memory plays a non-trivial role for quantum systems of dimension d > 2. Moreover, we prove that coherence generating power of a general quantum channel is a monotone under dephasing superchannels. Finally, we analyse the effect dephasing noise can have on a quantum channel E by investigating the number of distinguishable channels that E can be mapped to by a family of dephasing superchannels. More precisely, we upper bound this number in terms of hypothesis testing channel divergence between E and its fully dephased version, and also relate it to the robustness of coherence of E.

2025, Information Sciences

New entropy measures such as higher order fuzzy entropy and hybrid e:ntropy of a set have been introduced. Various properties along with their proofs have: been included. Applicability of these new measures to various problems has been... more

New entropy measures such as higher order fuzzy entropy and hybrid e:ntropy of a set have been introduced. Various properties along with their proofs have: been included. Applicability of these new measures to various problems has been highlighted.

2025, Bulletin of the American Physical Society

Using a channel similar to one side of a Bell inequality experiment, we show how the auxiliary resources of shared sender:receiver entanglement and classical back communication, neither of which increases the forward capacity of any... more

Using a channel similar to one side of a Bell inequality experiment, we show how the auxiliary resources of shared sender:receiver entanglement and classical back communication, neither of which increases the forward capacity of any classical channel, can greatly increase both the quantum and classical capacities of some quantum channels. Joint work with

2024

Orientador: Mario Noboru TamashiroDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb WataghinResumo: Obtivemos a energia livre eletrostática de íons próximos a uma interface dielétrica planar e esférica... more

Orientador: Mario Noboru TamashiroDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb WataghinResumo: Obtivemos a energia livre eletrostática de íons próximos a uma interface dielétrica planar e esférica entre fluidos imiscíveis utilizando a teoria de dielétrico contínuo. Para a geometria planar, o íon foi modelado como uma esfera dielétrica com densidade de carga superficial uniforme e fixa. Para evitar a polarização de cargas na interface iônica, consideramos não haver contraste dielétrico entre o interior do íon e o meio dielétrico externo em que ele está presente (aproximação de dielétrico misto), permitindo uma solução exata do problema eletrostático utilizando o método de carga imagem. Mostramos que resultados publicados anteriormente na literatura para este modelo subestimam a energia livre eletrostática associada a íons não-polarizáveis por uma ordem de magnitude, especialmente quando há penetração iônica parcial na interface. Para a geometri...

2024, IEEE Transactions on Information Theory

Effective complexity measures the information content of the regularities of an object. It has been introduced by M. Gell-Mann and S. Lloyd to avoid some of the disadvantages of Kolmogorov complexity, also known as algorithmic information... more

Effective complexity measures the information content of the regularities of an object. It has been introduced by M. Gell-Mann and S. Lloyd to avoid some of the disadvantages of Kolmogorov complexity, also known as algorithmic information content. In this paper, we give a precise formal definition of effective complexity and rigorous proofs of its basic properties. In particular, we show that incompressible binary strings are effectively simple, and we prove the existence of strings that have effective complexity close to their lengths. Furthermore, we show that effective complexity is related to Bennett's logical depth: If the effective complexity of a string x exceeds a certain explicit threshold then that string must have astronomically large depth; otherwise, the depth can be arbitrarily small.

2024

O problema de estados ligados em um potencial delta duplo é revisto com o uso do método das transformadas seno e cosseno de Fourier. Palavras-chave: duplo delta, estado ligado, transformadas seno e cosseno de Fourier. The problem of bound... more

O problema de estados ligados em um potencial delta duplo é revisto com o uso do método das transformadas seno e cosseno de Fourier. Palavras-chave: duplo delta, estado ligado, transformadas seno e cosseno de Fourier. The problem of bound states in a double delta potential is revisited by means of Fourier sine and cosine transforms.

2024, arXiv (Cornell University)

Let G be a finite subgroup of unitary matrices acting on the space of Nqubits. We associate with G a uniform quantum channel QU from the space on N-qubits to itself. We give a quantum algorithm to approximate this channel by considering a... more

Let G be a finite subgroup of unitary matrices acting on the space of Nqubits. We associate with G a uniform quantum channel QU from the space on N-qubits to itself. We give a quantum algorithm to approximate this channel by considering a set of generators on G. Under suitable assumptions this approximation is BPQ. We then apply this approximation to study the orbit equivalence of two density matrices under the action of G. We show that for some special cases of G and two pure states the orbit equivalence in BPQ, if a specific quantum observation can be implemented efficiently. We discuss the application of our problem to the graph isomorphism problem.

2024

This thesis addresses two known quantities in quantum information science: (1) entanglement cost, and (2) Holevo capacity. These quantities will be crucial values when teleportation becomes common in daily life, perhaps centuries from... more

This thesis addresses two known quantities in quantum information science: (1) entanglement cost, and (2) Holevo capacity. These quantities will be crucial values when teleportation becomes common in daily life, perhaps centuries from now. Assume that Alice desires to send a singing Japanese cricket to her friend Bob in America, and that Alice and Bob already share a quantum entanglement. First, Alice sends Bob a mass of information bits resulting from the interaction between the cricket she holds in her hand and half of the entanglement. Subsequently, Bob receives the information bits and manipulates the other half of the entanglement, transforming them back into the original cricket. Examining this situation from an instrumental engineering viewpoint, quantifying the amount of the quantum entanglement and the number of information bits is crucial for this transmission. If both values are enough, Alice could even send herself to Bob's place instead of the tiny cricket. The topics of this thesis therefore are: (1) the mathematical properties of the entanglement cost, such as whether it is an additive measure similar to normal length or weight; and (2) how to calculate the Holevo capacity, an ultimately achievable limit of the information conveyance capacity of an information channel, such as of a single photon passing through an optical fiber or space. These two distinct quantities are magically tied together by several "additive or not" hypotheses, which await mathematical proof.

2024

The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some... more

The Schmidt decomposition is an important tool in the study of quantum systems especially for the quantification of the entanglement of pure states. However, the Schmidt decomposition is only unique for bipartite pure states, and some multipartite pure states. Here a generalized Schmidt decomposition is given for a class of mixed quantum states. It is shown that it shares some desirable properties with its pure-state counterpart, but lacks some properties which make the pure-state decomposition so important. Experimental methods for the identification of this class of mixed states are provided and some examples are discussed which show the utility of this description.

2024

Quantum channels can be described via a unitary coupling of system and environment, followed by a trace over the environment state space. Taking the trace instead over the system state space produces a different mapping which we call the... more

Quantum channels can be described via a unitary coupling of system and environment, followed by a trace over the environment state space. Taking the trace instead over the system state space produces a different mapping which we call the conjugate channel. We explore the properties of conjugate channels and describe several different methods of construction. In general, conjugate channels map M d → M d with d < d , and different constructions may differ by conjugation with a partial isometry. We show that a channel and its conjugate have the same minimal output entropy and maximal output p-norm. It then follows that the additivity and multiplicativity conjectures for these measures of optimal output purity hold for a product of channels if and only if they also hold for the product of their conjugates. This allows us to reduce these conjectures to the special case of maps taking M d → M d 2 with a minimal representation of dimension at most d. We find explicit expressions for the conjugates for a number of well-known examples, including entanglement-breaking channels, unital qubit channels, the depolarizing channel, and a subclass of random unitary channels. For the entanglement-breaking channels, channels this yields a new class of channels for which additivity and multiplicativity of optimal output purity can be established. For random unitary channels using the generalized Pauli matrices, we obtain a new formulation of the multiplicativity conjecture. The conjugate of the completely noisy channel plays a special role and suggests a mechanism for using noise to transmit information.

2024, arXiv: Quantum Physics

In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the... more

In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the system-environment interaction. When the experimenter takes into account certain known features of the interaction such as its invariant subspaces or its non-local content, it may not be possible to consistently model the system evolution over a certain time interval using a standard Stinespring dilation, which assumes the system and environment to be initially uncorrelated. Simple examples demonstrating how restrictions can emerge are presented below. When the system and environment are qubits, we completely characterize the set of unitaries that always generate reduced dynamics capable of being modeled using a consistent Stinespring dilation. Finally, we show how any initial correlations between the system and environment can be certified by observing the system transformation alone during certain joint evolutions.

2024, The European Physical Journal E - Soft Matter

Assume in a sample of size M one finds Mi representatives of species i with i = 1. .. N *. The normalized frequency p * i ≡ Mi/M , based on the finite sample, may deviate considerably from the true probabilities pi. We propose a method to... more

Assume in a sample of size M one finds Mi representatives of species i with i = 1. .. N *. The normalized frequency p * i ≡ Mi/M , based on the finite sample, may deviate considerably from the true probabilities pi. We propose a method to infer rank-ordered true probabilities ri from measured frequencies Mi. We show that the rank-ordered probabilities provide important informations on the system, e.g., the true number of species, the Shannon-and the Renyi-entropies.

2024, IEEE Transactions on Information Theory

In this work new achievable rates are derived, for the uplink channel of a cellular network with joint multicell processing, where unlike previous results, the ideal backhaul network has finite capacity per-cell. Namely, the cell sites... more

In this work new achievable rates are derived, for the uplink channel of a cellular network with joint multicell processing, where unlike previous results, the ideal backhaul network has finite capacity per-cell. Namely, the cell sites are linked to the central joint processor via lossless links with finite capacity. The cellular network is abstracted by symmetric models, which render analytical treatment plausible. For this idealistic model family, achievable rates are presented for cell-sites that use compress-and-forward schemes combined with local decoding, for both Gaussian and fading channels. The rates are given in closed form for the classical Wyner model and the soft-handover model. These rates are then demonstrated to be rather close to the optimal unlimited backhaul joint processing rates, already for modest backhaul capacities, supporting the potential gain offered by the joint multicell processing approach. Particular attention is also given to the low-SNR characterization of these rates through which the effect of the limited backhaul network is explicitly revealed. In addition, the rate at which the backhaul capacity should scale in order to maintain the original high-SNR characterization of an unlimited backhaul capacity system is found.

2024

Rate-distortion theory is considered for the Shannon cipher system (SCS). The admissible region of cryptogram rate R, key rate R k , legitimate receiver's distortion D, and wiretapper's uncertainty h is determined for the SCS with a noisy... more

Rate-distortion theory is considered for the Shannon cipher system (SCS). The admissible region of cryptogram rate R, key rate R k , legitimate receiver's distortion D, and wiretapper's uncertainty h is determined for the SCS with a noisy channel. Furthermore, inner and outer bounds of the admissible region of R, R k , D, and wiretapper's attainable minimum distortionD are derived for the SCS with a finite discrete source and a noiseless channel.

2024, Journal of the Optical Society of America

It is demonstrated that, given a finite number of samples of a function, the constraints of square integrability and band limitation are not sufficient to determine that function uniquely. Hence existing algorithms for band-limited... more

It is demonstrated that, given a finite number of samples of a function, the constraints of square integrability and band limitation are not sufficient to determine that function uniquely. Hence existing algorithms for band-limited interpolation and extrapolation (e.g., for super resolution) require additional constraints such as those provided by an appropriate model.

2024, Physical Review A

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent... more

The performance of a quantum information processing protocol is ultimately judged by distinguishability measures that quantify how distinguishable the actual result of the protocol is from the ideal case. The most prominent distinguishability measures are those based on the fidelity and trace distance, due to their physical interpretations. In this paper, we propose and review several algorithms for estimating distinguishability measures based on trace distance and fidelity, and we evaluate their performance using simulators of quantum computers. The algorithms can be used for distinguishing quantum states, channels, and strategies (the last also known in the literature as "quantum combs"). The fidelity-based algorithms offer novel physical interpretations of these distinguishability measures in terms of the maximum probability with which a single prover (or competing provers) can convince a verifier to accept the outcome of an associated computation. We simulate these algorithms by using a variational approach with parameterized quantum circuits and find that they converge well for the examples that we consider. CONTENTS References 28 A. Approximate fixed points and Deutschian closed timelike curves 31

2024, Physical Review A

We construct the unique optimal quantum device for turning a finite number of d-level quantum systems in the same unknown pure state σ into M systems of the same kind, in an approximation of the M-fold tensor product of the state σ.

2024, Physical Review A

We show how to simplify the computation of the entanglement of formation and the relative entropy of entanglement for states, which are invariant under a group of local symmetries. For several examples of groups we characterize the state... more

We show how to simplify the computation of the entanglement of formation and the relative entropy of entanglement for states, which are invariant under a group of local symmetries. For several examples of groups we characterize the state spaces, which are invariant under these groups. For specific examples we calculate the entanglement measures. In particular, we derive an explicit formula for the entanglement of formation for U ⊗U -invariant states, and we find a counterexample to the additivity conjecture for the relative entropy of entanglement.

2024, Journal of Physics A: Mathematical and General

We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the... more

We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert-Schmidt scalar product, and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation and dense coding schemes are assumed to be "tight" in the sense that all Hilbert spaces involved have the same finite dimension d, and the classical channel involved distinguishes d 2 signals. A general construction procedure for orthonormal bases of unitaries, involving Latin Squares and complex Hadamard Matrices is also presented.

2024, Journal of Modern Optics

FIG. 1: The basic correction scheme. The noisy channel T’ is represented by the shaded shape, and consists of a unitary coupling U of the system to an environment in state po. The result a of the measurement M on the environment is used to select the recovery operation R., resulting in the overall corrected channel Torr.

2024, Journal of Mathematical Physics

We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian... more

We consider the problem of correcting the errors incurred from sending quantum information through a noisy quantum environment by using classical information obtained from a measurement on the environment. For discrete time Markovian evolutions, in the case of fixed measurement on the environment, we give criteria for quantum information to be perfectly corrigible and characterize the related feedback. Then we analyze the case when perfect correction is not possible and, in the qubit case, we find optimal feedback maximizing the channel fidelity.

2024, Journal of Mathematical Physics

We analyze some special properties of a system of two qubits, and in particular of the so-called Bell basis for this system, and discuss the possibility of extending these properties to higher dimensional systems. We give a general... more

We analyze some special properties of a system of two qubits, and in particular of the so-called Bell basis for this system, and discuss the possibility of extending these properties to higher dimensional systems. We give a general construction for orthonormal bases of maximally entangled vectors, which works in any dimension, and is based on Latin squares and complex Hadamard matrices. However, for none of these bases the special properties of the operation of complex conjugation in Bell basis hold, namely that maximally entangled vectors have up-to-a-phase real coefficients and that factorizable unitaries have real matrix elements.

2024, Statistical Methodology

The problem of filtering of finite-alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set has the following properties. First, it... more

The problem of filtering of finite-alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set has the following properties. First, it includes the unknown signal with probability γ , where γ is a parameter supplied to the filter. Second, the size of the confidence sets grows exponentially with a rate that is asymptotically equal to the conditional entropy of the signal given the data. Moreover, it is shown that this rate is optimal. We also show that the described construction of the confidence set can be applied to the case where the signal is corrupted by an erasure channel with unknown statistics.

2024, arXiv (Cornell University)

The problem of filtering of finite-alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set has the following properties: First, it... more

The problem of filtering of finite-alphabet stationary ergodic time series is considered. A method for constructing a confidence set for the (unknown) signal is proposed, such that the resulting set has the following properties: First, it includes the unknown signal with probability γ, where γ is a parameter supplied to the filter. Second, the size of the confidence sets grows exponentially with the rate that is asymptotically equal to the conditional entropy of the signal given the data. Moreover, it is shown that this rate is optimal. We also show that the described construction of the confidence set can be applied for the case where the signal is corrupted by an erasure channel with unknown statistics.

2024, arXiv (Cornell University)

Quantum coherence is a prime resource in quantum computing and quantum communication. Quantum coherence of an arbitrary qubit can be created at a remote location using maximally entangled state, local operation and classical... more

Quantum coherence is a prime resource in quantum computing and quantum communication. Quantum coherence of an arbitrary qubit can be created at a remote location using maximally entangled state, local operation and classical communication. However, if there is a noisy channel acting on one side of the shared resource, then, it is not possible to create perfect quantum coherence remotely. Here, we present a method for the creation of quantum coherence at a remote location via the use of entangled state and indefinite causal order. We show this specifically for the superposition of two completely depolarizing channels, two partially depolarizing channels and one completely depolarizing channel along with a unitary operator. We find that when the indefinite causal order of channels act on one-half of the entangled pair, then the shared state looses entanglement, but can retain non-zero quantum discord. This finding may have some interesting applications on its own where discord can be consumed as a resource. Our results suggest that the indefinite causal order along with a tiny amount of quantum discord can act as a resource in creating non-zero quantum coherence in the absence of entanglement.

2024, Quantum Information Processing

A generic behavior of quantum correlations during any quantum process taking place in a noisy environment is that they are non-increasing. We have shown that mitigation of these decreases providing relative enhancements in correlations is... more

A generic behavior of quantum correlations during any quantum process taking place in a noisy environment is that they are non-increasing. We have shown that mitigation of these decreases providing relative enhancements in correlations is possible by means of quantum memory channels which model correlated environmental quantum noises. For two-qubit systems subject to mixtures of two-use actions of different decoherence channels we point out that improvement in correlations can be achieved in such way that the input-output fidelity is also as high as possible. These make it possible to create the optimal conditions in realizing any quantum communication task in a noisy environment.

2024, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.

This paper considers the entropy of the highly correlated quantized samples resulting from sampling at high rate. Two results are shown. The first concerns sampling and identically scalar quantizing a stationary random process over a... more

This paper considers the entropy of the highly correlated quantized samples resulting from sampling at high rate. Two results are shown. The first concerns sampling and identically scalar quantizing a stationary random process over a finite interval. It is shown that if the process crosses a quantization threshold with positive probability, then the joint entropy of the quantized samples tends to infinity as the sampling interval goes to zero. The second result provides an upper bound to the rate at which the joint entropy tends to infinity, in the case of infinite-level uniform threshold scalar quantizers and a stationary Gaussian random process whose mean lies at a midpoint of some quantization cell. Specifically, an asymptotic formula for the conditional entropy of one quantized sample conditioned on another quantized sample is derived.

2024, 2017 IEEE 30th Computer Security Foundations Symposium (CSF)

More and more quantum algorithms have been designed for solving problems in machine learning, database search and data analytics. An important problem then arises: how privacy can be protected when these algorithms are used on private... more

More and more quantum algorithms have been designed for solving problems in machine learning, database search and data analytics. An important problem then arises: how privacy can be protected when these algorithms are used on private data? For classical computing, the notion of differential privacy provides a very useful conceptual framework in which a great number of mechanisms that protect privacy by introducing certain noises into algorithms have been successfully developed. This paper defines a notion of differential privacy for quantum information processing. We carefully examine how the mechanisms using three important types of quantum noise, the amplitude/phase damping and depolarizing, can protect differential privacy. A composition theorem is proved that enables us to combine multiple privacy-preserving operations in quantum information processing.

2024, Research, Society and Development

O que é entropia?reflexões para o ensino de ciências What is entropy?reflections for science teaching ¿Qué es la entropía?reflexiones para la enseñanza de las ciências

2024, Research, Society and Development

Diferente da pressão ou da temperatura, o conceito de entropia, embora compartilhe de abstração e importância semelhante ao conceito de energia, destoa desse último por não ser intuitivo, além da ambiguidade historicamente atrelada ao... more

Diferente da pressão ou da temperatura, o conceito de entropia, embora compartilhe de abstração e importância semelhante ao conceito de energia, destoa desse último por não ser intuitivo, além da ambiguidade historicamente atrelada ao mesmo por conta dos desenvolvimentos relativos à segunda Lei da Termodinâmica. Neste trabalho, buscamos promover uma reflexão sobre as discrepâncias existentes em torno da conceituação de entropia em termos de desordem e seus impactos no processo de aprendizagem em todos os níveis de ensino, elencando outras possibilidades conceituais, dentre as quais a entropia de Shannon, tida como mais adequada para representar todo o corpo de conhecimento multidisciplinar advindo da teoria da informação, incluindo a computação quântica. O trabalho leva em conta as publicações do químico israelense Arieh Ben Naim e, aproveitando-se da inexistência de outras possíveis analogias para a entropia na literatura brasileira, propõe uma exposição que contemple as diferentes...

2024, SIAM Journal on Computing

We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and it will be of importance... more

We study the problem of simulating protocols in a quantum communication setting over noisy channels. This problem falls at the intersection of quantum information theory and quantum communication complexity, and it will be of importance for eventual real-world applications of interactive quantum protocols, which can be proved to have exponentially lower communication costs than their classical counterparts for some problems. These are the first results concerning the quantum version of this problem, originally studied by Schulman in a classical setting (FOCS '92, STOC '93). We simulate a length N quantum communication protocol by a length O(N) protocol with arbitrarily small error. Under adversarial noise, our strategy can withstand, for arbitrarily small ε > 0, error rates as high as 1/2 − ε when parties pre-share perfect entanglement, but the classical channel is noisy. We show that this is optimal. We provide extension of these results in several other models of communication, including when also the entanglement is noisy, and when there is no pre-shared entanglement but communication is quantum and noisy. We also study the case of random noise, for which we provide simulation protocols with positive communication rates and no pre-shared entanglement over some quantum channels with quantum capacity C Q = 0, proving that C Q is in general not the right characterization of a channel's capacity for interactive quantum communication. Our results are stated for a general quantum communication protocol in which Alice and Bob collaborate, and these results hold in particular in the quantum communication complexity settings of the Yao and Cleve-Buhrman models.

2024, arXiv (Cornell University)

We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for... more

We consider the communication complexity of the binary inner product function in a variation of the two-party scenario where the parties have an a priori supply of particles in an entangled quantum state. We prove linear lower bounds for both exact protocols, as well as for protocols that determine the answer with bounded-error probability. Our proofs employ a novel kind of "quantum" reduction from a quantum information theory problem to the problem of computing the inner product. The communication required for the former problem can then be bounded by an application of Holevo's theorem. We also give a specific example of a probabilistic scenario where entanglement reduces the communication complexity of the inner product function by one bit. The communication complexity of a function f : {0, 1} n × {0, 1} n → {0, 1} is defined as the minimum amount of communication necessary among two parties, conventionally referred to as Alice and Bob, in order for, say, Bob to acquire the value of f (x, y), where, initially, Alice is given x and Bob is given y. This scenario was introduced by Yao [16] and has been widely studied (see [13] for a survey). There are a number of technical choices in the model, such as: whether the communication cost is taken as the worst-case (x, y), or the average-case (x, y) with respect to some probability distribution; whether the protocols are ⋆ Research initiated while visiting the Université de Montréal and supported in part by Canada's NSERC.

2024, Physical Review Letters

Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be... more

Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be transmitted. We show that the asymptotic classical communication cost of RSP is one bit per qubit-half that of teleportation-and even less when transmitting part of a known entangled state. We explore the tradeoff between entanglement and classical communication required for RSP, and discuss RSP capacities of general quantum channels.

FIG. 1. Entanglement (e) and forward classical communi- cation (b) costs of remotely preparing qubit states in vari- ous ways, including teleportation (T), our high-entanglement method with entanglement recycling (R), and convex com- binations (solid line between T and R). The shaded region b < 1 is inaccessible because it would violate causality. Solid curve below and right of T is our low-entanglement method and convex combinations with teleportation. Dashed curve is Devetak-Berger method.  states, even ones maliciously chosen to avoid successes with the particular rotations {D(i,j)} Alice and Bob are using, Alice divides the states into subblocks of size s & ./n, and applies the above protocol separately to each subblock, but before doing so applies a set of s random prerotations r1,...7; which Bob removes after- ward, to the states in each subblock. Then, even if the original states 7; are awkwardly located, the random- ized states Tj mods; will be random within each sub- block. Reusing the prerotations causes the deviations of the actual mixed-state output from the ideal 7 1...W, to be correlated between subblocks, but because of the exponentially fast convergence of Schumacher compres- sion with increasing subblock size, the full n-fold fidelity still approaches unity in the limit n— oo, for any se- quence w 1...W, of states to be remotely prepared. Of course Alice must tell Bob the prerotations 1 ...r, so he can remove them at the end. If the prerotations are described with precision, say, \/s bits, the finite- precision errors will vanish exponentially rapidly, while keeping the communication overhead sublinear in n.

2024, IEEE Transactions on Information Theory

Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally... more

Dual to the usual noisy channel coding problem, where a noisy (classical or quantum) channel is used to simulate a noiseless one, reverse Shannon theorems concern the use of noiseless channels to simulate noisy ones, and more generally the use of one noisy channel to simulate another. For channels of nonzero capacity, this simulation is always possible, but for it to be efficient, auxiliary resources of the proper kind and amount are generally required. In the classical case, shared randomness between sender and receiver is a sufficient auxiliary resource, regardless of the nature of the source, but in the quantum case the requisite auxiliary resources for efficient simulation depend on both the channel being simulated, and the source from which the channel inputs are coming. For tensor power sources (the quantum generalization of classical IID sources), entanglement in the form of standard ebits (maximally entangled pairs of qubits) is sufficient, but for general sources, which may be arbitrarily correlated or entangled across channel inputs, additional resources, such as entanglement-embezzling states or backward communication, are generally needed. Combining existing and new results, we establish the amounts of communication and auxiliary resources needed in both the classical and quantum cases, the tradeoffs among them, and the loss of simulation efficiency when auxiliary resources are absent or insufficient. In particular we find a new single-letter expression for the excess forward communication cost of coherent feedback simulations of quantum channels (i.e. simulations in which the sender retains what would escape into the environment in an ordinary simulation), on nontensor-power sources in the presence of unlimited ebits but no other auxiliary resource. Our results on tensor power sources establish a strong converse to the entanglement-assisted capacity theorem.

2024, arXiv (Cornell University)

The entanglement-assisted classical capacity of a noisy quantum channel (C E) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver... more

The entanglement-assisted classical capacity of a noisy quantum channel (C E) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that the capacity C E is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs ρ, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of ρ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel, alone or in the presence of ancillary resources such as prior entanglement. In the classical analog of entanglement assisted communication-communication over a discrete memoryless channel (DMC) between parties who share prior random information-we show that one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMC's of equal capacity can simulate one another with unit asymptotic efficiency.

2024, Springer eBooks

We consider the problem of trying to send a single classical bit through a noisy quantum channel when two transmissions through the channel are available as a resource. Classically, two transmissions add nothing to the receiver's... more

We consider the problem of trying to send a single classical bit through a noisy quantum channel when two transmissions through the channel are available as a resource. Classically, two transmissions add nothing to the receiver's capability of inferring the bit. In the quantum world, however, one has the possible further advantage of entangling the two transmissions. We demonstrate that, for certain noisy channels, such entangled transmissions enhance the receiver's capability of a correct inference.

2024, arXiv (Cornell University)

We exhibit discrete memoryless quantum channels whose quantum capacity assisted by two-way classical communication, Q2, exceeds their unassisted one-shot Holevo capacity CH. These channels may be thought of as having a data input and... more

We exhibit discrete memoryless quantum channels whose quantum capacity assisted by two-way classical communication, Q2, exceeds their unassisted one-shot Holevo capacity CH. These channels may be thought of as having a data input and output, along with a control input that partly influences, and a control output that partly reveals, which of a set of unitary evolutions the data undergoes en route from input to output. The channel is designed so that the data's evolution can be exactly inferred by a classically coordinated processing of 1) the control output, and 2) a reference system entangled with the control input, but not from either of these resources alone. Thus a twoway classical side channel allows the otherwise noisy evolution of the data to be corrected, greatly increasing the capacity. The same family of channels provides examples where the classical capacity assisted by classical feedback, CB, and the quantum capacity assisted by classical feedback QB, both exceed CH. A related channel, whose data input undergoes dephasing before interacting with the control input, has a classical capacity C = CH strictly less than its C2, the classical capacity assisted by independent classical communication.

2024

The entanglement-assisted classical capacity of a noisy quantum channel (CE) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver... more

The entanglement-assisted classical capacity of a noisy quantum channel (CE) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that the capacity CE is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs ρ, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of ρ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to complete...

2024, arXiv (Cornell University)

Random access code (RAC) is an important communication protocol to obtain information about a randomly specified substring of an n-bit string, while only having limited information about the n-bit string. Quantum RACs usually utilise... more

Random access code (RAC) is an important communication protocol to obtain information about a randomly specified substring of an n-bit string, while only having limited information about the n-bit string. Quantum RACs usually utilise either communication of quantum bits or a shared-in-advance quantum state used in conjunction with classical communication. Here we consider the latter version of the quantum protocols under the constraint of single-bit communication and with shared arbitrary state of two qubits. Taking the worst-case success probability as the figure of merit, we demonstrate that any state with invertible correlation matrix can be used to outperform the best classical RAC for n = 3. We derive an additional condition sufficient to beat the best classical performance in the case of n = 2. In particular, separable states turn out to be a useful resource behind the quantum advantage for n = 2, 3. For n ≥ 4 RACs assisted with a single copy of a quantum state do not outperform the classical RACs.

2024, Physical Review A

Random access code (RAC) is an important communication protocol to obtain information about a randomly specified substring of an n-bit string, while only having limited information about the n-bit string. Quantum RACs usually utilise... more

Random access code (RAC) is an important communication protocol to obtain information about a randomly specified substring of an n-bit string, while only having limited information about the n-bit string. Quantum RACs usually utilise either communication of quantum bits or a shared-in-advance quantum state used in conjunction with classical communication. Here we consider the latter version of the quantum protocols under the constraint of single-bit communication and with shared arbitrary state of two qubits. Taking the worst-case success probability as the figure of merit, we demonstrate that any state with invertible correlation matrix can be used to outperform the best classical RAC for n = 3. We derive an additional condition sufficient to beat the best classical performance in the case of n = 2. In particular, separable states turn out to be a useful resource behind the quantum advantage for n = 2, 3. For n ≥ 4 RACs assisted with a single copy of a quantum state do not outperform the classical RACs.

2024, arXiv (Cornell University)

Random access code (RAC) is a strategy to access remote data even if one has limited information about it. We derive here the conditions for the optimal performance of two most basic RAC protocols implemented using two-qubit states. The... more

Random access code (RAC) is a strategy to access remote data even if one has limited information about it. We derive here the conditions for the optimal performance of two most basic RAC protocols implemented using two-qubit states. The conditions derived are valid for any set of decoding operations. This allows a meaningful comparison between quantum and classical resources in RAC and leads to identifying the condition for quantum advantage. It turns out that the necessary resource is quantum discord of the assisting state, but, importantly, the non-vanishing value of quantum discord in itself does not guarantee quantum advantage for any choice of decoding operations. We argued that simultaneous correlation in mutually unbiased bases as well as a particular notion of nonclassicality based on quantum steering can capture efficiency of the optimal RAC for orthogonal decoding operations.

2024, Physics Letters A

Too much noise kills entanglement. This is the main problem in its production and transmission. We use a handy approach to indicate noise resistance of entanglement of a bi-partite system described by d × d Hilbert space. Our analysis... more

Too much noise kills entanglement. This is the main problem in its production and transmission. We use a handy approach to indicate noise resistance of entanglement of a bi-partite system described by d × d Hilbert space. Our analysis uses a geometric approach based on the fact that if a scalar product of a vector s with a vector e is less than the square of the norm of e, then s = e. We use such concepts for correlation tensors of separable and entangled states. As a general form correlation tensors for pairs of qudits, for d > 2, is very difficult to obtain, because one does not have a Bloch sphere for pure one qudit states, we use a simplified approach. The criterion reads: if the largest Schmidt eigenvalue of a correlation tensor is smaller than the square of its norm, then the state is entangled. this criterion is applied in the case of various types of noise admixtures to the initial (pure) state. These include white noise, colored noise, local depolarizing noise and amplitude damping noise. A broad set of numerical and analytical results is presented. As the other simple criterion for entanglement is violation of Bell's inequalities, we also find critical noise parameters to violate specific family of Bell inequalities (CGLMP), for maximally entangled states. We give analytical forms of our results for d approaching infinity.

2024, International Journal for Research in Applied Science and Engineering Technology

We are Currently in the NISQ(noisy intermediate scale quantum) era. Current Quantum computers have a high noise error rate. With the increasing number of qubits every year we can develop fault tolerant quantum systems which have immense... more

We are Currently in the NISQ(noisy intermediate scale quantum) era. Current Quantum computers have a high noise error rate. With the increasing number of qubits every year we can develop fault tolerant quantum systems which have immense power to change our current computing power. Current quantum systems have shown to have the potential to break the classical RSA algorithm using shors algorithm. With more development and increase in number of qubits available it could easily break the current security systems of our computing. In future we could transmit data safely using the same quantum principles in the post quantum cryptography era. Quantum key distribution could be the future protocol used to transfer our secure information without getting hacked even by using quantum computing and break other quantum principles like shors algorithm which can break current encryption techniques like the RSA algorithms. We need to develop Quantum network infrastructure so we can implement the quantum key distribution algorithm in the future to enable secure transmission of data.

2024, International Journal for Research in Applied Science and Engineering Technology

We are Currently in the NISQ(noisy intermediate scale quantum) era. Current Quantum computers have a high noise error rate. With the increasing number of qubits every year we can develop fault tolerant quantum systems which have immense... more

We are Currently in the NISQ(noisy intermediate scale quantum) era. Current Quantum computers have a high noise error rate. With the increasing number of qubits every year we can develop fault tolerant quantum systems which have immense power to change our current computing power. Current quantum systems have shown to have the potential to break the classical RSA algorithm using shors algorithm. With more development and increase in number of qubits available it could easily break the current security systems of our computing. In future we could transmit data safely using the same quantum principles in the post quantum cryptography era. Quantum key distribution could be the future protocol used to transfer our secure information without getting hacked even by using quantum computing and break other quantum principles like shors algorithm which can break current encryption techniques like the RSA algorithms. We need to develop Quantum network infrastructure so we can implement the quantum key distribution algorithm in the future to enable secure transmission of data.

2024, 2022 IEEE International Symposium on Information Theory (ISIT)

There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected... more

There are various ways to quantify the communication capabilities of a quantum channel. In this work we study the communication value (cv) of channel, which describes the optimal success probability of transmitting a randomly selected classical message over the channel. The cv also offers a dual interpretation as the classical communication cost for zero-error channel simulation using non-signaling resources. We first provide an entropic characterization of the cv as a generalized conditional minentropy over the cone of separable operators. Additionally, the logarithm of a channel's cv is shown to be equivalent to its max-Holevo information, which can further be related to channel capacity. We evaluate the cv exactly for all qubit channels and the Werner-Holevo family of channels. While all classical channels are multiplicative under tensor product, this is no longer true for quantum channels in general. We provide a family of qutrit channels for which the cv is non-multiplicative. On the other hand, we prove that any pair of qubit channels have multiplicative cv when used in parallel. Even stronger, all entanglement-breaking channels and the partially depolarizing channel are shown to have multiplicative cv when used in parallel with any channel. We then turn to the entanglement-assisted cv and prove that it is equivalent to the conditional min-entropy of the Choi matrix of the channel. Combining with previous work on zero-error channel simulation, this implies that the entanglement-assisted cv is the classical communication cost for perfectly simulating a channel using quantum nonsignaling resources. A final component of this work investigates relaxations of the channel cv to other cones such as the set of operators having a positive partial transpose (PPT). The PPT cv is analytically and numerically investigated for well-known channels such as the Werner-Holevo family and the dephrasure family of channels.

2024

Yves Francois Meyer was born July 19th, 1939 in Paris, but he grew up in Tunisia. After his studies at the École Normale Supérieure he was a teacher for three years at the school Prytanée Militaire in La Flèche (Loire Valley) and obtained... more

Yves Francois Meyer was born July 19th, 1939 in Paris, but he grew up in Tunisia. After his studies at the École Normale Supérieure he was a teacher for three years at the school Prytanée Militaire in La Flèche (Loire Valley) and obtained a position in Strasbourg afterwards. During this period he prepared his PhD which he presented in 1966. Formally Jean-Pierre Kahane was his advisor, but he considers himself a ”self-made man”. From that time on he spentF all of his active time in Paris at different schools, such as Université Paris-Sud, École Polytechnique, Université Paris-Dauphine and École Normale Supérieure de Cachan. His extensive work has many facets, covering number theory ([38]), harmonic analysis, quasi-crystals, operator theory and of course wavelets, as is nicely described in the article [11] by Ingrid Daubechies, We will focus in our presentation on the last two topics, because they have been the reason for awarding him the Abel Prize 2017. The interview with Yves Meyer...

2024, Journal of Chemical Sciences

A study of quantum teleportation using two and three-particle correlated density matrix is presented. A criterion based on standard quantum statistical correlations employed in the many-body virial expansion is used to determine the... more

A study of quantum teleportation using two and three-particle correlated density matrix is presented. A criterion based on standard quantum statistical correlations employed in the many-body virial expansion is used to determine the extent of entanglement for a 2N-particle system. A relation between the probability and statistical parameters is established using the correlated density matrices for the particles.