Quantum Key Distribution Based on Arbitrarily Weak Distillable Entangled States (original) (raw)
IEEE Transactions on Information Theory, 2000
We prove unconditional security for a quantum key distribution (QKD) protocol based on distilling pbits (twisted ebits) [1] from an arbitrary untrusted state that is claimed to contain distillable key. Our main result is that we can verify security using only public communication -via parameter estimation of the given untrusted state. The technique applies even to bound entangled states, thus extending QKD to the regime where the available quantum channel has zero quantum capacity. We also show how to convert our purification-based QKD schemes to prepare-measure schemes.
Provable entanglement and information cost for qubit-based quantum key-distribution protocols
European Physical Journal D, 2006
Provable entanglement has been shown to be a necessary precondition for unconditionally secure key generation in the context of quantum cryptographic protocols. We estimate the maximal threshold disturbance up to which the two legitimate users can prove the presence of quantum correlations in their data, in the context of the four- and six-state quantum key-distribution protocols, under the assumption of coherent attacks. Moreover, we investigate the conditions under which an eavesdropper can saturate these bounds, by means of incoherent and two-qubit coherent attacks. A direct connection between entanglement distillation and classical advantage distillation is also presented.
Low-Dimensional Bound Entanglement With One-Way Distillable Cryptographic Key
IEEE Transactions on Information Theory, 2008
We provide a class of bound entangled states that have positive distillable secure key rate. The smallest state of this kind is 4 ⊗ 4, which shows that peculiar security contained in bound entangled states does not need high dimensional systems. We show, that for these states a positive key rate can be obtained by one-way Devetak-Winter protocol. Subsequently the volume of bound entangled keydistillable states in arbitrary dimension is shown to be nonzero. We provide a scheme of verification of cryptographic quality of experimentally prepared state in terms of local observables. Proposed set of 7 collective settings is proven to be optimal in number of settings.
Unconditional Privacy over Channels which Cannot Convey Quantum Information
Physical Review Letters, 2008
By sending systems in specially prepared quantum states, two parties can communicate without an eavesdropper being able to listen. The technique, called quantum cryptography, enables one to verify that the state of the quantum system has not been tampered with, and thus one can obtain privacy regardless of the power of the eavesdropper. All previous protocols relied on the ability to faithfully send quantum states. In fact, until recently, they could all be reduced to a single protocol where security is ensured though sharing maximally entangled states. Here we show this need not be the case -one can obtain verifiable privacy even through some channels which cannot be used to reliably send quantum states.
Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels
Physical Review Letters, 1996
Existing quantum cryptographic schemes are not, as they stand, operable in the presence of noise on the quantum communication channel. Although they become operable if they are supplemented by classical privacy-amplification techniques, the resulting schemes are difficult to analyse and have not been proved secure. We introduce the concept of quantum privacy amplification and a cryptographic scheme incorporating it which is provably secure over a noisy channel. The scheme uses an 'entanglement purification' procedure which, because it requires only a few quantum Controlled-Not and singlequbit operations, could be implemented using technology that is currently being developed. The scheme allows an arbitrarily small bound to be placed on the information that any eavesdropper may extract from the encrypted 1 message. 89.70.+c, 03.65.Bz, 89.80.+h Typeset using REVT E X
Security of Quantum Key Distribution with entangled quNits
2003
We consider a generalisation of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by qu$N$its (i.e., N-dimensional systems). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf's formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of quNit generalisations of the Ekert's protocol for qubits.
Secret-Key Distillation across a Quantum Wiretap Channel under Restricted Eavesdropping
Physical Review Applied
The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an allpowerful adversary is excessive and can be relaxed considerably. In this paper we study secret-key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret-key-distillation capacity against an unrestricted eavesdropper in the quantum wiretap channel. Furthermore, we show upper bounds on the key rates based on the relative entropy of entanglement. This simple restricted eavesdropping model is widely applicable, for example, to free-space quantum optical communication, where realistic collection of light by Eve is limited by the finite size of her optical aperture. Future work will include calculating bounds on the amount of light Eve can collect under various realistic scenarios.
Quantum key distribution using intra-particle entanglement
We propose the use of intra-particle entanglement to enhance the security of a practical implementation of the Bennett-Brassard-1984 (BB84) quantum key distribution scheme. Intra-particle entanglement is an attractive resource since it can be easily generated using only linear optics. Security is studied under a simple model of incoherent attack for protocols involving two or all five mutually unbiased bases. In terms of efficiency of secret key generation and tolerable error rate, the latter is found to be superior to the former. We find that states that allow secrecy distillation are necessarily entangled, though they may be local. Since more powerful attacks by Eve obviously exist, our result implies that security is a strictly stronger condition than entanglement for these protocols.
Security of quantum key distributions with entangled qudits
Physical Review A, 2004
We consider a generalisation of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by quN its (i.e., N -dimensional systems). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf's formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of quN it generalisations of the Ekert's protocol for qubits.
Quantum cryptography using partially entangled states
Optics Communications, 2010
We show that non-maximally entangled states can be used to build a quantum key distribution (QKD) scheme where the key is probabilistically teleported from Alice to Bob. This probabilistic aspect of the protocol ensures the security of the key without the need of non-orthogonal states to encode it, in contrast to other QKD schemes. Also, the security and key transmission rate of the present protocol is nearly equivalent to those of standard QKD schemes and these aspects can be controlled by properly harnessing the new free parameter in the present proposal, namely, the degree of partial entanglement. Furthermore, we discuss how to build a controlled QKD scheme, also based on partially entangled states, where a third party can decide whether or not Alice and Bob are allowed to share a key.
Detecting two-party quantum correlations in quantum-key-distribution protocols
2005
A necessary precondition for secure quantum key distribution (QKD) is that sender and receiver can prove the presence of entanglement in a quantum state that is effectively distributed between them. In order to deliver this entanglement proof one can use the class of entanglement witness (EW) operators that can be constructed from the available measurements results. This class of EWs can be used to provide a necessary and sufficient condition for the existence of quantum correlations even when a quantum state cannot be completely reconstructed. The set of optimal EWs for two well-known entanglement based (EB) schemes, the 6-state and the 4-state EB protocols, has been obtained recently [M. Curty et al., Phys. Rev. Lett. 92, 217903 (2004)]. Here we complete these results, now showing specifically the analysis for the case of prepare&measure (P&M) schemes. For this, we investigate the signal states and detection methods of the 4-state and the 2-state P&M schemes. For each of these protocols we obtain a reduced set of EWs. More importantly, each set of EWs can be used to derive a necessary and sufficient condition to prove that quantum correlations are present in these protocols.
Entangled-coherent-state quantum key distribution with entanglement witnessing
Physical Review A, 2014
An entanglement-witness approach to quantum coherent-state key distribution and a system for its practical implementation are described. In this approach, eavesdropping can be detected by a change in sign of either of two witness functions: an entanglement witness S or an eavesdropping witness W. The effects of loss and eavesdropping on system operation are evaluated as a function of distance. Although the eavesdropping witness W does not directly witness entanglement for the system, its behavior remains related to that of the true entanglement witness S. Furthermore, W is easier to implement experimentally than S. W crosses the axis at a finite distance, in a manner reminiscent of entanglement sudden death. The distance at which this occurs changes measurably when an eavesdropper is present. The distance dependence of the two witnesses due to amplitude reduction and due to increased variance resulting from both ordinary propagation losses and possible eavesdropping activity is provided. Finally, the information content and secure key rate of a continuous variable protocol using this witness approach are given.
Long-distance practical quantum key distribution by entanglement swapping
Optics Express, 2011
We develop a model for practical, entanglement-based longdistance quantum key distribution employing entanglement swapping as a key building block. Relying only on existing off-the-shelf technology, we show how to optimize resources so as to maximize secret key distribution rates. The tools comprise lossy transmission links, such as telecom optical fibers or free space, parametric down-conversion sources of entangled photon pairs, and threshold detectors that are inefficient and have dark counts. Our analysis provides the optimal trade-off between detector efficiency and dark counts, which are usually competing, as well as the optimal source brightness that maximizes the secret key rate for specified distances (i.e. loss) between sender and receiver. Practical decoy state for quantum key distribution," Phys. Rev. A 72, 012326 (2005). 21. X.-B. Wang, "Decoy-state protocol for quantum cryptography with four different intensities of coherent light," Phys. Rev. A 72, 012322 (2005). 22. Y. Zhao, B. Qi, X. Ma, H.-K. Lo, and L. Qian, "Experimental Quantum Key Distribution with Decoy States," Phys. Rev. Lett. 96, 070502 (2006). 23. N. Lütkenhaus, "Security against individual attacks for realistic quantum key distribution," Phys. Rev. A 61, 052304 (2000). 24. l.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, "Long-distance quantum communication with atomic ensembles and linear optics," Nature 414, 413-418, 2001. 25. J. B. Brask and A. S. Sørensen, "Memory imperfections in atomic-ensemble-based quantum repeaters," Phys. Rev. A 78, 012350 (2008). 26. L. Jiang, J. M. Taylor, and M. D. Lukin, "Fast and robust approach to long-distance quantum communication with atomic ensembles," Phys. Rev. A 76, 012301 (2007). -W. Pan, "Robust creation of entanglement between remote memory qubits," Phys. Rev. Lett. 98, 240502 (2007). 28. J. B. Brask, L. Jiang, A. V. Gorshkov, V. Vuletic, A. S. Sørensen, and M. D. Lukin "Fast entanglement distribution with atomic ensembles and fluorescent detection," Phys. Rev. A 81, 020303(R) (2010). 29. J. Amirloo, M. Razavi, and A. H. Majedi, "
Security of quantum key distribution with entangled qutrits
Physical Review A, 2003
The study of quantum cryptography and quantum entanglement have traditionally been based on two-level quantum systems ͑qubits͒. In this paper, we consider a generalization of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by three-level systems ͑qutrits͒. In order to investigate the security against the optimal individual attack, we derive the information gained by a potential eavesdropper applying a cloning-based attack. We exhibit the explicit form of this cloner, which is distinct from the previously known cloners, and conclude that the protocol is more robust than those based on entangled qubits as well as unentangled qutrits.
Secure direct communication using entanglement
A novel communication protocol based on an entangled pair of qubits is presented, allowing secure direct communication from one party to another without the need for a shared secret key. Since the information is transferred in a deterministic manner, no qubits have to be discarded and every qubit carries message information. The security of the transfer against active and passive eavesdropping attacks is provided. The detection rate of active attacks is at least 25%. The protocol works with a quantum efficiency of 1 bit per qubit transmitted. I. INTRODUCTION What is secure direct communication? Traditionally, secure communication schemes based on quantum mechanics are non-deterministic [1-5]: Alice, the sender, cannot determine which bit value Bob receives through the secure quantum channel. Such non-deterministic communication can be used to establish a secret key between Alice and Bob. Whenever an eavesdropper tries to extract information from the quantum channel, he influences the transmitted state and can be detected with some probability. If Alice and Bob are virtually sure that a certain random subsequence of bits has been transmitted secretely, Alice can use the remaining subsequence as a shared secret key to encrypt her message, send the encrypted message to Bob through a non-secret channel and then Bob uses the shared key to decrypt the message. It is a common belief that every secure quantum communication protocol should work that way. Recently, however, a deterministic quantum cryptographic protocol has been presented [6,7], which I will refer to as the BEKW protocol. Against the paradigm of quantum cryptography, the information is sent directly from Alice to Bob. Alice uses a secret key to encrypt her message before sending it through a quantum channel. If she is virtually sure that no eavesdropper was in the line, Alice publishes the secret key so Bob can read the message. This is a different concept of quantum cryptography, and I will refer to it as secure direct communication as opposed to quantum key distribution. In the present paper, another deterministic cryptographic scheme is presented which has significant advantages against other schemes:
A generic security proof for quantum key distribution
2004
Quantum key distribution allows two parties, traditionally known as Alice and Bob, to establish a secure random cryptographic key if, firstly, they have access to a quantum communication channel, and secondly, they can exchange classical public messages which can be monitored but not altered by an eavesdropper, Eve. Quantum key distribution provides perfect security because, unlike its classical counterpart, it relies on the laws of physics rather than on ensuring that successful eavesdropping would require excessive computational effort. However, security proofs of quantum key distribution are not trivial and are usually restricted in their applicability to specific protocols. In contrast, we present a general and conceptually simple proof which can be applied to a number of different protocols. It relies on the fact that a cryptographic procedure called privacy amplification is equally secure when an adversary's memory for data storage is quantum rather than classical [1].
Establishing a Private Shared Reference Frame via the Distillation of Entanglement
International Journal of Theoretical Physics, 2009
We show how a collection of N ebits can be used to establish a private shared reference frame, in the sense that a relative orientation of the x and y axes with respect to a publicly-known z axis is unconditionally private to Alice and Bob. Our protocol relies on the distillation protocol of entanglement. The scheme is based on tensor product states of spin pairs. We implicitly assume a shared reference frame (which is not guaranteed to be private) at the beginning of the protocol. It turns out that the entanglement distillation protocol implies the construction of a private shared reference frame.
Device-independent quantum key distribution based on measurement inputs
2013
We provide an analysis of a new family of device independent quantum key distribution (QKD) protocols with several novel features: (a) The bits used for the secret key do not come from the results of the measurements on an entangled state but from the choices of settings; (b) Instead of a single security parameter (a violation of some Bell inequality) a set of them is used to estimate the level of trust in the secrecy of the key. The main advantage of these protocols is a smaller vulnerability to imperfect random number generators made possible by feature (a). We prove the security and the robustness of such protocols. We show that using our method it is possible to construct a QKD protocol which retains its security even if the source of randomness used by communicating parties is strongly biased. As a proof of principle, an explicit example of a protocol based on the Hardy's paradox is presented. Moreover, in the noiseless case, the protocol is secure in a natural way against ...
Key distillation from quantum channels using two-way communication protocols
Physical Review A, 2007
We provide a general formalism to characterize the cryptographic properties of quantum channels in the realistic scenario where the two honest parties employ prepare and measure protocols and the known two-way communication reconciliation techniques. We obtain a necessary and sufficient condition to distill a secret key using this type of schemes for Pauli qubit channels and generalized Pauli channels in higher dimension. Our results can be applied to standard protocols such as BB84 or six-state, giving a critical error rate of 20% and 27.6%, respectively. We explore several possibilities to enlarge these bounds, without any improvement. These results suggest that there may exist weakly entangling channels useless for key distribution using prepare and measure schemes.