Aditya Nema - Academia.edu (original) (raw)
Papers by Aditya Nema
arXiv (Cornell University), Feb 2, 2021
We prove the first non-trivial one-shot inner bounds for sending quantum information over an enta... more We prove the first non-trivial one-shot inner bounds for sending quantum information over an entanglement unassisted two-sender quantum multiple access channel (QMAC) and an unassisted two-sender two-receiver quantum interference channel (QIC). Previous works only studied the unassisted QMAC in the limit of many independent and identical uses of the channel also known as the asymptotic iid limit, and did not study the unassisted QIC at all. We employ two techniques, rate splitting and successive cancellation, in order to obtain our inner bound. Rate splitting was earlier used to obtain inner bounds, avoiding time sharing, for classical channels in the asymptotic iid setting. Our main technical contribution is to extend rate splitting from the classical asymptotic iid setting to the quantum one-shot setting. In the asymptotic iid limit our one-shot inner bound for QMAC approaches the rate region of Yard et al. [YDH05]. For the QIC we get novel non-trivial rate regions in the asymptotic iid setting. All our results also extend to the case where limited entanglement assistance is provided, in both one-shot and asymptotic iid settings. The limited entanglement results for one-setting for both QMAC and QIC are new. For the QIC the limited entanglement results are new even in the asymptotic iid setting.
arXiv (Cornell University), May 13, 2021
We provide the first inner bounds for sending private classical information over a quantum multip... more We provide the first inner bounds for sending private classical information over a quantum multiple access channel. We do so by using three powerful information theoretic techniques: rate splitting, quantum simultaneous decoding for multiple access channels, and a novel smoothed distributed covering lemma for classical quantum channels. Our inner bounds are given in the one shot setting and accordingly the three techniques used are all very recent ones specifically designed to work in this setting. The last technique is new to this work and is our main technical advancement. For the asymptotic iid setting, our one shot inner bounds lead to the natural quantum analogue of the best classical inner bounds for this problem.
arXiv (Cornell University), Feb 27, 2019
We follow the geometric functional analytic approach of Aubrun, Szarek and Werner in order to pro... more We follow the geometric functional analytic approach of Aubrun, Szarek and Werner in order to prove our result. More precisely we prove a sharp Dvoretzky-like theorem stating that, with high probability under the choice of a unitary from an approximate t-design, random subspaces of large dimension make a Lipschitz function take almost constant value. Such theorems were known earlier only for Haar random unitaries. We obtain our result by appealing to Low's technique for proving concentration of measure for an approximate t-design, combined with a stratified analysis of the variational behaviour of Lipschitz functions on the unit sphere in high dimension. The stratified analysis is the main technical advance of this work.
2023 IEEE International Symposium on Information Theory (ISIT)
Cornell University - arXiv, Aug 10, 2022
Local pure states represent a fundamental resource in quantum information theory. In this work we... more Local pure states represent a fundamental resource in quantum information theory. In this work we obtain one-shot achievable bounds on the rates for local purity distillation, in the single-party and in the two-party cases. In both situations, local noisy operations are freely available, while in the two-party case also one-way classical communication can be used. In addition, in both situations local pure ancillas can be borrowed, as long as they are discounted from the final net rate of distillation. The one-shot rates that we obtain, written in terms of mutual information-like quantities, are shown to recover in the limit the asymptotic i.i.d. rates of Devetak [PRA, 2005], up to first order analysis.
IEEE Transactions on Information Theory
In a breakthrough, Hastings showed that there exist quantum channels whose classical capacity is ... more In a breakthrough, Hastings showed that there exist quantum channels whose classical capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as compared to unentangled quantum encoding strategies. Hastings' proof used Haar random unitaries to exhibit superadditivity. In this paper we show that a unitary chosen uniformly at random from an approximate n^{2/3}-design gives rise to a quantum channel with superadditive classical capacity, where n is the dimension of the unitary exhibiting the Stinespring dilation of the channel superoperator. We do so by showing that the minimum output von Neumann entropy of a quantum channel arising from an approximate unitary n^{2/3}-design is subadditive, which by Shor's work implies superadditivity of classical capacity of quantum channels. We follow the geometric functional analytic approach of Aubrun, Szarek and Werner in order to prove our result. More precisely we prove a sharp Dvoretzky-like theorem stating that, with high probability under the choice of a unitary from an approximate t-design, random subspaces of large dimension make a Lipschitz function take almost constant value. Such theorems were known earlier only for Haar random unitaries. We obtain our result by appealing to Low's technique for proving concentration of measure for an approximate t-design, combined with a stratified analysis of the variational behaviour of Lipschitz functions on the unit sphere in high dimension. The stratified analysis is the main technical advance of this work.
2021 IEEE International Symposium on Information Theory (ISIT), 2021
We prove the first non-trivial one-shot inner bounds for sending quantum information over an enta... more We prove the first non-trivial one-shot inner bounds for sending quantum information over an entanglement unassisted two-sender quantum multiple access channel (QMAC) and an unassisted two-sender two-receiver quantum interference channel (QIC). Previous works only studied the unassisted QMAC in the limit of many independent and identical uses of the channel also known as the asymptotic iid limit, and did not study the unassisted QIC at all. We employ two techniques, rate splitting and successive cancellation, in order to obtain our inner bound. Rate splitting was earlier used to obtain inner bounds, avoiding time sharing, for classical channels in the asymptotic iid setting. Our main technical contribution is to extend rate splitting from the classical asymptotic iid setting to the quantum one-shot setting. In the asymptotic iid limit our one-shot inner bound for QMAC approaches the rate region of Yard et al. [YDH05]. For the QIC we get novel non-trivial rate regions in the asymptotic iid setting. All our results also extend to the case where limited entanglement assistance is provided, in both one-shot and asymptotic iid settings. The limited entanglement results for one-setting for both QMAC and QIC are new. For the QIC the limited entanglement results are new even in the asymptotic iid setting.
arXiv: Quantum Physics, 2020
Decoupling theorems are an important tool in quantum information theory where they are used as bu... more Decoupling theorems are an important tool in quantum information theory where they are used as building blocks in a host of information transmission protocols. A decoupling theorem takes a bipartite quantum state shared between a system and a reference, applies some local operation on the system, and under suitable constraints, proves that the resulting state is close to a product state between the output system and the untouched reference. The theorem is said to be non-catalytic if it does not require an additional input of a quantum state, in tensor with the given input state, for the decoupling. Dupuis proved an important non-catalytic decoupling theorem where the operation on the system was a Haar random unitary followed by a fixed superoperator, unifying many decoupling results proved earlier. He also showed a concentration result for his decoupling theorem. In this work we give a new concentration result for non-catalytic decoupling by showing that, for suitably large t, a uni...
In a breakthrough, Hastings [Has09] showed that there exist quantum channels whose classical capa... more In a breakthrough, Hastings [Has09] showed that there exist quantum channels whose classical capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as compared to unentangled quantum encoding strategies. Hastings’ proof used Haar random unitaries to exhibit superadditivity. In this paper we show that a unitary chosen uniformly at random from an approximate ndesign gives rise to a quantum channel with superadditive classical capacity, where n is the dimension of the unitary exhibiting the Stinespring dilation of the channel superoperator. We do so by showing that the minimum output von Neumann entropy of a quantum channel arising from an approximate unitary n-design is subadditive, which by Shor’s work [Sho04] implies superadditivity of classical capacity of quantum channels. We follow the geometric functional analytic approach of Aubrun, Szarek andWerner [ASW10a] in order to prove our result....
In a breakthrough, Hastings' showed that there exist quantum channels whose classical capacit... more In a breakthrough, Hastings' showed that there exist quantum channels whose classical capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as compared to unentangled quantum encoding strategies. Hastings' proof used Haar random unitaries to exhibit superadditivity. In this paper we show that a unitary chosen uniformly at random from an approximate n2/3n^{2/3}n2/3-design gives rise to a quantum channel with superadditive classical Holevo capacity, where nnn is the dimension of the unitary exhibiting the Stinespring dilation of the channel superoperator. We prove a sharp Dvoretzky-like theorem (similar to Aubrun, Szarek, Werner, 2010) stating that, with high probability under the choice of a unitary from an approximate ttt-design, random subspaces of large dimension make a Lipschitz function take almost constant value. Such theorems were known earlier only for Haar random unitaries. We obta...
2021 IEEE Information Theory Workshop (ITW), 2021
We provide the first inner bounds for sending private classical information over a quantum multip... more We provide the first inner bounds for sending private classical information over a quantum multiple access channel. We do so by using three powerful information theoretic techniques: rate splitting, quantum simultaneous decoding for multiple access channels, and a novel smoothed distributed covering lemma for classical quantum channels. Our inner bounds are given in the one shot setting and accordingly the three techniques used are all very recent ones specifically designed to work in this setting. The last technique is new to this work and is our main technical advancement. For the asymptotic iid setting, our one shot inner bounds lead to the natural quantum analogue of the best classical inner bounds for this problem.
ArXiv, 2021
In this work, we prove a novel one-shot multi-sender decoupling theorem generalising Dupuis resul... more In this work, we prove a novel one-shot multi-sender decoupling theorem generalising Dupuis result. We start off with a multipartite quantum state, say on A1 A2 R, where A1, A2 are treated as the two sender systems and R is the reference system. We apply independent Haar random unitaries in tensor product on A1 and A2 and then send the resulting systems through a quantum channel. We want the channel output B to be almost in tensor with the untouched reference R. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a k-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard...
arXiv: Quantum Physics, 2019
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of ... more We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous approaches for efficient estimation of average gate fidelity replaced Haar random unitaries in the naive estimation algorithm by approximate unitary 2-designs, and sampled them uniformly and independently. In contrast, in our first algorithm we sample the unitaries of the approximate unitary 2-design uniformly using a limited independence pseudorandom generator, a powerful tool from derandomisation theory. This algorithm uses the same number of basic operations as previous efficient algorithms but much fewer number of random bits. Reducing the requirement of classical random bits increases the reliability of estimation as often, high quality random bits are an expensive computational resource. Our second efficient algorithm, based on a 4-quantum tens...
2021 IEEE International Symposium on Information Theory (ISIT), 2021
In this work, we prove a novel one-shot ‘multi-sender’ decoupling theorem generalising Dupuis'... more In this work, we prove a novel one-shot ‘multi-sender’ decoupling theorem generalising Dupuis' seminal single sender decoupling theorem. We start off with a multipartite quantum state, say on A1A2RA_{1}A_{2}RA1A2R, where A1,A2A_{1}, A_{2}A1,A2 are treated as the two ‘sender’ systems and RRR is the reference system. We apply independent Haar random unitaries in tensor product on A1A_{1}A1 and A2A_{2}A2 and then send the resulting systems through a quantum channel. We want the channel output BBB to be almost in tensor with the untouched reference RRR. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a kkk-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard et al. [20] in the asymptotic iid limit. Our work is the first one to obtain a non-trivial simultaneous decoder for the QMAC with limited entanglement assistance in both one-shot and asymptotic iid settings; previous works used unlimited entanglement assistance.
arXiv (Cornell University), Feb 2, 2021
We prove the first non-trivial one-shot inner bounds for sending quantum information over an enta... more We prove the first non-trivial one-shot inner bounds for sending quantum information over an entanglement unassisted two-sender quantum multiple access channel (QMAC) and an unassisted two-sender two-receiver quantum interference channel (QIC). Previous works only studied the unassisted QMAC in the limit of many independent and identical uses of the channel also known as the asymptotic iid limit, and did not study the unassisted QIC at all. We employ two techniques, rate splitting and successive cancellation, in order to obtain our inner bound. Rate splitting was earlier used to obtain inner bounds, avoiding time sharing, for classical channels in the asymptotic iid setting. Our main technical contribution is to extend rate splitting from the classical asymptotic iid setting to the quantum one-shot setting. In the asymptotic iid limit our one-shot inner bound for QMAC approaches the rate region of Yard et al. [YDH05]. For the QIC we get novel non-trivial rate regions in the asymptotic iid setting. All our results also extend to the case where limited entanglement assistance is provided, in both one-shot and asymptotic iid settings. The limited entanglement results for one-setting for both QMAC and QIC are new. For the QIC the limited entanglement results are new even in the asymptotic iid setting.
arXiv (Cornell University), May 13, 2021
We provide the first inner bounds for sending private classical information over a quantum multip... more We provide the first inner bounds for sending private classical information over a quantum multiple access channel. We do so by using three powerful information theoretic techniques: rate splitting, quantum simultaneous decoding for multiple access channels, and a novel smoothed distributed covering lemma for classical quantum channels. Our inner bounds are given in the one shot setting and accordingly the three techniques used are all very recent ones specifically designed to work in this setting. The last technique is new to this work and is our main technical advancement. For the asymptotic iid setting, our one shot inner bounds lead to the natural quantum analogue of the best classical inner bounds for this problem.
arXiv (Cornell University), Feb 27, 2019
We follow the geometric functional analytic approach of Aubrun, Szarek and Werner in order to pro... more We follow the geometric functional analytic approach of Aubrun, Szarek and Werner in order to prove our result. More precisely we prove a sharp Dvoretzky-like theorem stating that, with high probability under the choice of a unitary from an approximate t-design, random subspaces of large dimension make a Lipschitz function take almost constant value. Such theorems were known earlier only for Haar random unitaries. We obtain our result by appealing to Low's technique for proving concentration of measure for an approximate t-design, combined with a stratified analysis of the variational behaviour of Lipschitz functions on the unit sphere in high dimension. The stratified analysis is the main technical advance of this work.
2023 IEEE International Symposium on Information Theory (ISIT)
Cornell University - arXiv, Aug 10, 2022
Local pure states represent a fundamental resource in quantum information theory. In this work we... more Local pure states represent a fundamental resource in quantum information theory. In this work we obtain one-shot achievable bounds on the rates for local purity distillation, in the single-party and in the two-party cases. In both situations, local noisy operations are freely available, while in the two-party case also one-way classical communication can be used. In addition, in both situations local pure ancillas can be borrowed, as long as they are discounted from the final net rate of distillation. The one-shot rates that we obtain, written in terms of mutual information-like quantities, are shown to recover in the limit the asymptotic i.i.d. rates of Devetak [PRA, 2005], up to first order analysis.
IEEE Transactions on Information Theory
In a breakthrough, Hastings showed that there exist quantum channels whose classical capacity is ... more In a breakthrough, Hastings showed that there exist quantum channels whose classical capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as compared to unentangled quantum encoding strategies. Hastings' proof used Haar random unitaries to exhibit superadditivity. In this paper we show that a unitary chosen uniformly at random from an approximate n^{2/3}-design gives rise to a quantum channel with superadditive classical capacity, where n is the dimension of the unitary exhibiting the Stinespring dilation of the channel superoperator. We do so by showing that the minimum output von Neumann entropy of a quantum channel arising from an approximate unitary n^{2/3}-design is subadditive, which by Shor's work implies superadditivity of classical capacity of quantum channels. We follow the geometric functional analytic approach of Aubrun, Szarek and Werner in order to prove our result. More precisely we prove a sharp Dvoretzky-like theorem stating that, with high probability under the choice of a unitary from an approximate t-design, random subspaces of large dimension make a Lipschitz function take almost constant value. Such theorems were known earlier only for Haar random unitaries. We obtain our result by appealing to Low's technique for proving concentration of measure for an approximate t-design, combined with a stratified analysis of the variational behaviour of Lipschitz functions on the unit sphere in high dimension. The stratified analysis is the main technical advance of this work.
2021 IEEE International Symposium on Information Theory (ISIT), 2021
We prove the first non-trivial one-shot inner bounds for sending quantum information over an enta... more We prove the first non-trivial one-shot inner bounds for sending quantum information over an entanglement unassisted two-sender quantum multiple access channel (QMAC) and an unassisted two-sender two-receiver quantum interference channel (QIC). Previous works only studied the unassisted QMAC in the limit of many independent and identical uses of the channel also known as the asymptotic iid limit, and did not study the unassisted QIC at all. We employ two techniques, rate splitting and successive cancellation, in order to obtain our inner bound. Rate splitting was earlier used to obtain inner bounds, avoiding time sharing, for classical channels in the asymptotic iid setting. Our main technical contribution is to extend rate splitting from the classical asymptotic iid setting to the quantum one-shot setting. In the asymptotic iid limit our one-shot inner bound for QMAC approaches the rate region of Yard et al. [YDH05]. For the QIC we get novel non-trivial rate regions in the asymptotic iid setting. All our results also extend to the case where limited entanglement assistance is provided, in both one-shot and asymptotic iid settings. The limited entanglement results for one-setting for both QMAC and QIC are new. For the QIC the limited entanglement results are new even in the asymptotic iid setting.
arXiv: Quantum Physics, 2020
Decoupling theorems are an important tool in quantum information theory where they are used as bu... more Decoupling theorems are an important tool in quantum information theory where they are used as building blocks in a host of information transmission protocols. A decoupling theorem takes a bipartite quantum state shared between a system and a reference, applies some local operation on the system, and under suitable constraints, proves that the resulting state is close to a product state between the output system and the untouched reference. The theorem is said to be non-catalytic if it does not require an additional input of a quantum state, in tensor with the given input state, for the decoupling. Dupuis proved an important non-catalytic decoupling theorem where the operation on the system was a Haar random unitary followed by a fixed superoperator, unifying many decoupling results proved earlier. He also showed a concentration result for his decoupling theorem. In this work we give a new concentration result for non-catalytic decoupling by showing that, for suitably large t, a uni...
In a breakthrough, Hastings [Has09] showed that there exist quantum channels whose classical capa... more In a breakthrough, Hastings [Has09] showed that there exist quantum channels whose classical capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as compared to unentangled quantum encoding strategies. Hastings’ proof used Haar random unitaries to exhibit superadditivity. In this paper we show that a unitary chosen uniformly at random from an approximate ndesign gives rise to a quantum channel with superadditive classical capacity, where n is the dimension of the unitary exhibiting the Stinespring dilation of the channel superoperator. We do so by showing that the minimum output von Neumann entropy of a quantum channel arising from an approximate unitary n-design is subadditive, which by Shor’s work [Sho04] implies superadditivity of classical capacity of quantum channels. We follow the geometric functional analytic approach of Aubrun, Szarek andWerner [ASW10a] in order to prove our result....
In a breakthrough, Hastings' showed that there exist quantum channels whose classical capacit... more In a breakthrough, Hastings' showed that there exist quantum channels whose classical capacity is superadditive i.e. more classical information can be transmitted by quantum encoding strategies entangled across multiple channel uses as compared to unentangled quantum encoding strategies. Hastings' proof used Haar random unitaries to exhibit superadditivity. In this paper we show that a unitary chosen uniformly at random from an approximate n2/3n^{2/3}n2/3-design gives rise to a quantum channel with superadditive classical Holevo capacity, where nnn is the dimension of the unitary exhibiting the Stinespring dilation of the channel superoperator. We prove a sharp Dvoretzky-like theorem (similar to Aubrun, Szarek, Werner, 2010) stating that, with high probability under the choice of a unitary from an approximate ttt-design, random subspaces of large dimension make a Lipschitz function take almost constant value. Such theorems were known earlier only for Haar random unitaries. We obta...
2021 IEEE Information Theory Workshop (ITW), 2021
We provide the first inner bounds for sending private classical information over a quantum multip... more We provide the first inner bounds for sending private classical information over a quantum multiple access channel. We do so by using three powerful information theoretic techniques: rate splitting, quantum simultaneous decoding for multiple access channels, and a novel smoothed distributed covering lemma for classical quantum channels. Our inner bounds are given in the one shot setting and accordingly the three techniques used are all very recent ones specifically designed to work in this setting. The last technique is new to this work and is our main technical advancement. For the asymptotic iid setting, our one shot inner bounds lead to the natural quantum analogue of the best classical inner bounds for this problem.
ArXiv, 2021
In this work, we prove a novel one-shot multi-sender decoupling theorem generalising Dupuis resul... more In this work, we prove a novel one-shot multi-sender decoupling theorem generalising Dupuis result. We start off with a multipartite quantum state, say on A1 A2 R, where A1, A2 are treated as the two sender systems and R is the reference system. We apply independent Haar random unitaries in tensor product on A1 and A2 and then send the resulting systems through a quantum channel. We want the channel output B to be almost in tensor with the untouched reference R. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a k-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard...
arXiv: Quantum Physics, 2019
We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of ... more We give three new algorithms for efficient in-place estimation, without using ancilla qubits, of average fidelity of a quantum logic gate acting on a d-dimensional system using much fewer random bits than what was known so far. Previous approaches for efficient estimation of average gate fidelity replaced Haar random unitaries in the naive estimation algorithm by approximate unitary 2-designs, and sampled them uniformly and independently. In contrast, in our first algorithm we sample the unitaries of the approximate unitary 2-design uniformly using a limited independence pseudorandom generator, a powerful tool from derandomisation theory. This algorithm uses the same number of basic operations as previous efficient algorithms but much fewer number of random bits. Reducing the requirement of classical random bits increases the reliability of estimation as often, high quality random bits are an expensive computational resource. Our second efficient algorithm, based on a 4-quantum tens...
2021 IEEE International Symposium on Information Theory (ISIT), 2021
In this work, we prove a novel one-shot ‘multi-sender’ decoupling theorem generalising Dupuis'... more In this work, we prove a novel one-shot ‘multi-sender’ decoupling theorem generalising Dupuis' seminal single sender decoupling theorem. We start off with a multipartite quantum state, say on A1A2RA_{1}A_{2}RA1A2R, where A1,A2A_{1}, A_{2}A1,A2 are treated as the two ‘sender’ systems and RRR is the reference system. We apply independent Haar random unitaries in tensor product on A1A_{1}A1 and A2A_{2}A2 and then send the resulting systems through a quantum channel. We want the channel output BBB to be almost in tensor with the untouched reference RRR. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a kkk-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard et al. [20] in the asymptotic iid limit. Our work is the first one to obtain a non-trivial simultaneous decoder for the QMAC with limited entanglement assistance in both one-shot and asymptotic iid settings; previous works used unlimited entanglement assistance.