The Experts below are selected from a list of 56799 Experts worldwide ranked by ideXlab platform
Mark M. Wilde - One of the best experts on this subject based on the ideXlab platform.
-
geometric distinguishability measures limit Quantum Channel estimation and discrimination
Quantum Information Processing, 2021Co-Authors: Vishal Katariya, Mark M. WildeAbstract:Quantum Channel estimation and discrimination are fundamentally related information processing tasks of interest in Quantum information science. In this paper, we analyze these tasks by employing the right logarithmic derivative Fisher information and the geometric Renyi relative entropy, respectively, and we also identify connections between these distinguishability measures. A key result of our paper is that a chain-rule property holds for the right logarithmic derivative Fisher information and the geometric Renyi relative entropy for the interval $$\alpha \in (0,1) $$ of the Renyi parameter $$\alpha $$ . In Channel estimation, these results imply a condition for the unattainability of Heisenberg scaling, while in Channel discrimination, they lead to improved bounds on error rates in the Chernoff and Hoeffding error exponent settings. More generally, we introduce the amortized Quantum Fisher information as a conceptual framework for analyzing general sequential protocols that estimate a parameter encoded in a Quantum Channel. We then use this framework, beyond the aforementioned application, to show that Heisenberg scaling is not possible when a parameter is encoded in a classical–Quantum Channel. We then identify a number of other conceptual and technical connections between the tasks of estimation and discrimination and the distinguishability measures involved in analyzing each. As part of this work, we present a detailed overview of the geometric Renyi relative entropy of Quantum states and Channels, as well as its properties, which may be of independent interest.
-
Amortized Channel divergence for asymptotic Quantum Channel discrimination
Letters in Mathematical Physics, 2020Co-Authors: Mark M. Wilde, Mario Berta, Christoph Hirche, Eneet KaurAbstract:It is well known that for the discrimination of classical and Quantum Channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive strategies. However, Hayashi (IEEE Trans Inf Theory 55(8):3807–3820, 2009. arXiv:0804.0686 ) showed that in the asymptotic regime, the exponential error rate for the discrimination of classical Channels is not improved in the adaptive setting. We extend this result in several ways. First, we establish the strong Stein’s lemma for classical–Quantum Channels by showing that asymptotically the exponential error rate for classical–Quantum Channel discrimination is not improved by adaptive strategies. Second, we recover many other classes of Channels for which adaptive strategies do not lead to an asymptotic advantage. Third, we give various converse bounds on the power of adaptive protocols for general asymptotic Quantum Channel discrimination. Intriguingly, it remains open whether adaptive protocols can improve the exponential error rate for Quantum Channel discrimination in the asymmetric Stein setting. Our proofs are based on the concept of amortized distinguishability of Quantum Channels, which we analyse using data-processing inequalities.
-
geometric distinguishability measures limit Quantum Channel estimation and discrimination
arXiv: Quantum Physics, 2020Co-Authors: Vishal Katariya, Mark M. WildeAbstract:Quantum Channel estimation and discrimination are fundamentally related information processing tasks of interest in Quantum information science. In this paper, we analyze these tasks by employing the right logarithmic derivative Fisher information and the geometric Renyi relative entropy, respectively, and we also identify connections between these distinguishability measures. A key result of our paper is that a chain-rule property holds for the right logarithmic derivative Fisher information and the geometric Renyi relative entropy for the interval $\alpha\in(0,1) $ of the Renyi parameter $\alpha$. In Channel estimation, these results imply a condition for the unattainability of Heisenberg scaling, while in Channel discrimination, they lead to improved bounds on error rates in the Chernoff and Hoeffding error exponent settings. More generally, we introduce the amortized Quantum Fisher information as a conceptual framework for analyzing general sequential protocols that estimate a parameter encoded in a Quantum Channel, and we use this framework, beyond the aforementioned application, to show that Heisenberg scaling is not possible when a parameter is encoded in a classical-Quantum Channel. We then identify a number of other conceptual and technical connections between the tasks of estimation and discrimination and the distinguishability measures involved in analyzing each. As part of this work, we present a detailed overview of the geometric Renyi relative entropy of Quantum states and Channels, as well as its properties, which may be of independent interest.
-
Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback
2019 IEEE International Symposium on Information Theory (ISIT), 2019Co-Authors: Dawei Ding, Peter W Shor, Yihui Quek, Mark M. WildeAbstract:We prove that the classical capacity of an arbitrary Quantum Channel assisted by a free classical feedback Channel is bounded from above by the maximum average output entropy of the Quantum Channel. As a consequence of this bound, we conclude that a classical feedback Channel does not improve the classical capacity of a Quantum erasure Channel, and by taking into account energy constraints, we conclude the same for a pure-loss bosonic Channel. The method for establishing the aforementioned entropy bound involves identifying an information measure having two key properties: 1) it does not increase under a one-way local operations and classical communication Channel from the receiver to the sender and 2) a Quantum Channel from sender to receiver cannot increase the information measure by more than the maximum output entropy of the Channel. This information measure can be understood as the sum of two terms, with one corresponding to classical correlation and the other to entanglement.
-
Quantum Channel capacities per unit cost
IEEE Transactions on Information Theory, 2019Co-Authors: Dawei Ding, Dmitri S Pavlichin, Mark M. WildeAbstract:Communication over a noisy Channel is often conducted in a setting in which different input symbols to the Channel incur a certain cost. For example, for bosonic Quantum Channels, the cost associated with an input state is the number of photons, which is proportional to the energy consumed. In such a setting, it is often useful to know the maximum amount of information that can be reliably transmitted per cost incurred. This is known as the capacity per unit cost. In this paper, we generalize the capacity per unit cost to various communication tasks involving a Quantum Channel, such as classical communication, entanglement-assisted classical communication, private communication, and Quantum communication. For each task, we define the corresponding capacity per unit cost and derive a formula for it analogous to that of the usual capacity. Furthermore, for the special and natural cases in which there is a zero-cost state, we obtain expressions in terms of an optimized relative entropy involving the zero-cost state. For each communication task, we construct an explicit pulse-position-modulation coding scheme that achieves the capacity per unit cost. Finally, we compute capacities per unit cost for various bosonic Gaussian Channels and introduce the notion of a blocklength constraint as a proposed solution to the long-standing issue of infinite capacities per unit cost. This motivates the idea of a blocklength-cost duality on which we elaborate in depth.
H Nagaoka - One of the best experts on this subject based on the ideXlab platform.
-
Making Good Codes for Classical-Quantum Channel Coding via Quantum Hypothesis Testing
IEEE Transactions on Information Theory, 2007Co-Authors: Tomohiro Ogawa, H NagaokaAbstract:In this correspondence, we give an alternative proof of the direct part of the classical-Quantum Channel coding theorem (the Holevo-Schumacher-Westmoreland (HSW) theorem), using ideas of Quantum hypothesis testing. In order to show the existence of good codes, we invoke a limit theorem, relevant to the Quantum Stein's lemma, in Quantum hypothesis testing as the law of large numbers used in the classical case. We also apply a greedy construction of good codes using a packing procedure of noncommutative operators. Consequently we derive an upper bound on the coding error probability, which is used to give an alternative proof of the HSW theorem. This approach elucidates how the Holevo information applies to the classical-Quantum Channel coding problems
-
a general formula for the classical capacity of a general Quantum Channel
International Symposium on Information Theory, 2002Co-Authors: Masahito Hayashi, H NagaokaAbstract:We derive a general formula of the Channel capacity for any (classical-) Quantum Channel. It can be regarded as a Quantum version of Verdu and Han's result (see IEEE Trans. Inform. Theory, vol.40, p.1147-57, 1994). Our results contain Holevo's (see IEEE Trans. Inform. Theory, vol.44, p.269-73, 1998) and Schumacher and Westmoreland's (see Phys. Rev. A, vol.56, p.131-8, 1997) results as the stationary and memoryless case.
-
Strong converse to the Quantum Channel coding theorem
IEEE Transactions on Information Theory, 1999Co-Authors: H NagaokaAbstract:A lower bound on the probability of decoding error for a Quantum communication Channel is presented, from which the strong converse to the Quantum Channel coding theorem is immediately shown. The results and their derivations are mostly straightforward extensions of the classical counterparts which were established by Arimoto (1973), except that more careful treatment is necessary here due to the noncommutativity of operators.
-
strong converse to the Quantum Channel coding theorem
arXiv: Quantum Physics, 1998Co-Authors: Tomohiro Ogawa, H NagaokaAbstract:A lower bound on the probability of decoding error of Quantum communication Channel is presented. The strong converse to the Quantum Channel coding theorem is shown immediately from the lower bound. It is the same as Arimoto's method exept for the difficulty due to non-commutativity.
Peter W Shor - One of the best experts on this subject based on the ideXlab platform.
-
Entropy Bound for the Classical Capacity of a Quantum Channel Assisted by Classical Feedback
2019 IEEE International Symposium on Information Theory (ISIT), 2019Co-Authors: Dawei Ding, Peter W Shor, Yihui Quek, Mark M. WildeAbstract:We prove that the classical capacity of an arbitrary Quantum Channel assisted by a free classical feedback Channel is bounded from above by the maximum average output entropy of the Quantum Channel. As a consequence of this bound, we conclude that a classical feedback Channel does not improve the classical capacity of a Quantum erasure Channel, and by taking into account energy constraints, we conclude the same for a pure-loss bosonic Channel. The method for establishing the aforementioned entropy bound involves identifying an information measure having two key properties: 1) it does not increase under a one-way local operations and classical communication Channel from the receiver to the sender and 2) a Quantum Channel from sender to receiver cannot increase the information measure by more than the maximum output entropy of the Channel. This information measure can be understood as the sum of two terms, with one corresponding to classical correlation and the other to entanglement.
-
the capacity of a Quantum Channel for simultaneous transmission of classical and Quantum information
Communications in Mathematical Physics, 2005Co-Authors: Igor Devetak, Peter W ShorAbstract:An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and Quantum information over a given Quantum Channel, generalizing both the classical and Quantum capacities of the Channel. Although our formula involves regularization, i.e. taking a limit over many copies of the Channel, it reduces to a single-letter expression in the case of generalized dephasing Channels. Analogous formulas are conjectured for the simultaneous public-private capacity of a Quantum Channel and for the simultaneously 1-way distillable common randomness and entanglement of a bipartite Quantum state.
-
equivalence of additivity questions in Quantum information theory
Communications in Mathematical Physics, 2004Co-Authors: Peter W ShorAbstract:We reduce the number of open additivity problems in Quantum information theory by showing that four of them are equivalent. Namely, we show that the conjectures of additivity of the minimum output entropy of a Quantum Channel, additivity of the Holevo expression for the classical capacity of a Quantum Channel, additivity of the entanglement of formation, and strong superadditivity of the entanglement of formation, are either all true or all false.
-
the capacity of a Quantum Channel for simultaneous transmission of classical and Quantum information
arXiv: Quantum Physics, 2003Co-Authors: Igor Devetak, Peter W ShorAbstract:An expression is derived characterizing the set of admissible rate pairs for simultaneous transmission of classical and Quantum information over a given Quantum Channel, generalizing both the classical and Quantum capacities of the Channel. Although our formula involves regularization, i.e. taking a limit over many copies of the Channel, it reduces to a single-letter expression in the case of generalized dephasing Channels. Analogous formulae are conjectured for the simultaneous public-private capacity of a Quantum Channel and for the simultaneously 1-way distillable common randomness and entanglement of a bipartite Quantum state.
-
equivalence of additivity questions in Quantum information theory
arXiv: Quantum Physics, 2003Co-Authors: Peter W ShorAbstract:We reduce the number of open additivity problems in Quantum information theory by showing that four of them are equivalent. We show that the conjectures of additivity of the minimum output entropy of a Quantum Channel, additivity of the Holevo expression for the classical capacity of a Quantum Channel, additivity of the entanglement of formation, and strong superadditivity of the entanglement of formation, are either all true or all false.
Aram W. Harrow - One of the best experts on this subject based on the ideXlab platform.
-
strengthened monotonicity of relative entropy via pinched petz recovery map
International Symposium on Information Theory, 2016Co-Authors: David Sutter, Marco Tomamichel, Aram W. HarrowAbstract:The Quantum relative entropy between two states satisfies a monotonicity property, meaning that applying the same Quantum Channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a “recovery map” that exactly reverses the effects of the Quantum Channel on both states. In this paper we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination of rotated Petz recovery maps and perfectly reverses the Quantum Channel on the second state. As a special case we reproduce recent lower bounds on the conditional mutual information such as the one proved in [Fawzi and Renner, Commun. Math. Phys., 2015]. Our proof only relies on elementary properties of pinching maps and the operator logarithm.
-
strengthened monotonicity of relative entropy via pinched petz recovery map
IEEE Transactions on Information Theory, 2016Co-Authors: David Sutter, Marco Tomamichel, Aram W. HarrowAbstract:The Quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same Quantum Channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a recovery map that exactly reverses the effects of the Quantum Channel on both states. In this paper, we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination of rotated Petz recovery maps and perfectly reverses the Quantum Channel on the second state. As a special case, we reproduce recent lower bounds on the conditional mutual information, such as the one proved by Fawzi and Renner. Our proof only relies on the elementary properties of pinching maps and the operator logarithm.
-
superactivation of the asymptotic zero error classical capacity of a Quantum Channel
IEEE Transactions on Information Theory, 2011Co-Authors: Toby S Cubitt, Jianxin Chen, Aram W. HarrowAbstract:The zero-error classical capacity of a Quantum Channel is the asymptotic rate at which it can be used to send classical bits perfectly so that they can be decoded with zero probability of error. We show that there exist pairs of Quantum Channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the Channels are available), but such that access to even a single copy of both Channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a Quantum Channel.
-
adaptive versus nonadaptive strategies for Quantum Channel discrimination
Physical Review A, 2010Co-Authors: Aram W. Harrow, Avinatan Hassidim, Debbie Leung, John WatrousAbstract:We provide a simple example that illustrates the advantage of adaptive over nonadaptive strategies for Quantum Channel discrimination. In particular, we give a pair of entanglement-breaking Channels that can be perfectly discriminated by means of an adaptive strategy that requires just two Channel evaluations, but for which no nonadaptive strategy can give a perfect discrimination using any finite number of Channel evaluations.
Mario Berta - One of the best experts on this subject based on the ideXlab platform.
-
Amortized Channel divergence for asymptotic Quantum Channel discrimination
Letters in Mathematical Physics, 2020Co-Authors: Mark M. Wilde, Mario Berta, Christoph Hirche, Eneet KaurAbstract:It is well known that for the discrimination of classical and Quantum Channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive strategies. However, Hayashi (IEEE Trans Inf Theory 55(8):3807–3820, 2009. arXiv:0804.0686 ) showed that in the asymptotic regime, the exponential error rate for the discrimination of classical Channels is not improved in the adaptive setting. We extend this result in several ways. First, we establish the strong Stein’s lemma for classical–Quantum Channels by showing that asymptotically the exponential error rate for classical–Quantum Channel discrimination is not improved by adaptive strategies. Second, we recover many other classes of Channels for which adaptive strategies do not lead to an asymptotic advantage. Third, we give various converse bounds on the power of adaptive protocols for general asymptotic Quantum Channel discrimination. Intriguingly, it remains open whether adaptive protocols can improve the exponential error rate for Quantum Channel discrimination in the asymmetric Stein setting. Our proofs are based on the concept of amortized distinguishability of Quantum Channels, which we analyse using data-processing inequalities.
-
Quantum Channel simulation and the Channel s smooth max information
IEEE Transactions on Information Theory, 2020Co-Authors: Kun Fang, Marco Tomamichel, Xin Wang, Mario BertaAbstract:We study the general framework of Quantum Channel simulation, that is, the ability of a Quantum Channel to simulate another one using different classes of codes. First, we show that the minimum error of simulation and the one-shot Quantum simulation cost under no-signalling assisted codes are given by semidefinite programs. Second, we introduce the Channel’s smooth max-information, which can be seen as a one-shot generalization of the mutual information of a Quantum Channel. We provide an exact operational interpretation of the Channel’s smooth max-information as the one-shot Quantum simulation cost under no-signalling assisted codes, which significantly simplifies the study of Channel simulation and provides insights and bounds for the case under entanglement-assisted codes. Third, we derive the asymptotic equipartition property of the Channel’s smooth max-information; i.e., it converges to the Quantum mutual information of the Channel in the independent and identically distributed asymptotic limit. This implies the Quantum reverse Shannon theorem in the presence of no-signalling correlations. Finally, we explore the simulation cost of various Quantum Channels.
-
Quantum Channel simulation and the Channel s smooth max information
International Symposium on Information Theory, 2018Co-Authors: Kun Fang, Marco Tomamichel, Xin Wang, Mario BertaAbstract:We study the general framework of Quantum Channel simulation, that is, the ability of a Quantum Channel to simulate another one using different classes of codes. Our main results are as follows. First, we show that the minimum error of simulation under non-signalling assisted codes is efficiently computable via semidefinite programming. The cost of simulating a Channel via noiseless Quantum Channels under non-signalling assisted codes can also be characterized as a semidefinite program. Second, we introduce the Channel's smooth max-information, which can be seen as a one-shot generalization of the Channel's mutual information. We show that the one-shot Quantum simulation cost under non-signalling assisted codes is exactly equal to the Channel's smooth max-information. Due to the Quantum reverse Shannon theorem, the Channel's smooth max-information converges to the Channel's mutual information in the independent and identically distributed asymptotic limit. Together with earlier findings on the (activated) non-signalling assisted one-shot capacity of Channels [Wang et al., arXiv:1709.05258], this suggest that the operational min- and max-type one-shot analogues of the Channel's mutual information are the Channel's hypothesis testing relative entropy and the Channel's smooth max-information, respectively.
