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Mark M. Wilde - One of the best experts on this subject based on the ideXlab platform.
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polar codes in network Quantum Information Theory
IEEE Transactions on Information Theory, 2016Co-Authors: Christoph Hirche, Ciara Morgan, Mark M. WildeAbstract:Polar coding is a method for communication over noisy classical channels, which is provably capacity achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of Quantum Information processing, for tasks such as classical communication, private classical communication, and Quantum communication. In this paper, we apply the polar coding method to network classical-Quantum Information Theory, by making use of recent advances for related classical tasks. In particular, we consider problems such as the compound multiple access channel and the Quantum interference channel. The main result of our work is that it is possible to achieve the best known inner bounds on the achievable rate regions for these tasks, without requiring a so-called Quantum simultaneous decoder. Thus, this paper paves the way for developing network classical-Quantum Information Theory further without requiring a Quantum simultaneous decoder.
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recoverability in Quantum Information Theory
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2015Co-Authors: Mark M. WildeAbstract:The fact that the Quantum relative entropy is non-increasing with respect to Quantum physical evolutions lies at the core of many optimality theorems in Quantum Information Theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in Quantum relative entropy between two Quantum states after a Quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a Quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in Quantum Information Theory, which have to do with providing physically meaningful improvements to many known entropy inequalities.
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renyi generalizations of the conditional Quantum mutual Information
Journal of Mathematical Physics, 2015Co-Authors: Mario Berta, Kaushik P Seshadreesan, Mark M. WildeAbstract:The conditional Quantum mutual Information I(A; B|C) of a tripartite state ρABC is an Information quantity which lies at the center of many problems in Quantum Information Theory. Three of its main properties are that it is non-negative for any tripartite state, that it decreases under local operations applied to systems A and B, and that it obeys the duality relation I(A; B|C) = I(A; B|D) for a four-party pure state on systems ABCD. The conditional mutual Information also underlies the squashed entanglement, an entanglement measure that satisfies all of the axioms desired for an entanglement measure. As such, it has been an open question to find Renyi generalizations of the conditional mutual Information, that would allow for a deeper understanding of the original quantity and find applications beyond the traditional memoryless setting of Quantum Information Theory. The present paper addresses this question, by defining different α-Renyi generalizations I α (A; B|C) of the conditional mutual Information, some of which we can prove converge to the conditional mutual Information in the limit α → 1. Furthermore, we prove that many of these generalizations satisfy non-negativity, duality, and monotonicity with respect to local operations on one of the systems A or B (with it being left as an open question to prove that monotonicity holds with respect to local operations on both systems). The quantities defined here should find applications in Quantum Information Theory and perhaps even in other areas of physics, but we leave this for future work. We also state a conjecture regarding the monotonicity of the Renyi conditional mutual Informations defined here with respect to the Renyi parameter α. We prove that this conjecture is true in some special cases and when α is in a neighborhood of one.
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polar codes in network Quantum Information Theory
arXiv: Quantum Physics, 2014Co-Authors: Christoph Hirche, Ciara Morgan, Mark M. WildeAbstract:Polar coding is a method for communication over noisy classical channels which is provably capacity-achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of Quantum Information processing, for tasks such as classical communication, private classical communication, and Quantum communication. In the present work, we apply the polar coding method to network Quantum Information Theory, by making use of recent advances for related classical tasks. In particular, we consider problems such as the compound multiple access channel and the Quantum interference channel. The main result of our work is that it is possible to achieve the best known inner bounds on the achievable rate regions for these tasks, without requiring a so-called Quantum simultaneous decoder. Thus, our work paves the way for developing network Quantum Information Theory further without requiring a Quantum simultaneous decoder.
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Quantum Information Theory
2013Co-Authors: Mark M. WildeAbstract:Finally, here is a modern, self-contained text on Quantum Information Theory suitable for graduate-level courses. Developing the subject 'from the ground up' it covers classical results as well as major advances of the past decade. Beginning with an extensive overview of classical Information Theory suitable for the non-expert, the author then turns his attention to Quantum mechanics for Quantum Information Theory, and the important protocols of teleportation, super-dense coding and entanglement distribution. He develops all of the tools necessary for understanding important results in Quantum Information Theory, including capacity theorems for classical, entanglement-assisted, private and Quantum communication. The book also covers important recent developments such as superadditivity of private, coherent and Holevo Information, and the superactivation of Quantum capacity. This book will be warmly welcomed by the upcoming generation of Quantum Information theorists and the already established community of classical Information theorists.
David Sutter - One of the best experts on this subject based on the ideXlab platform.
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pretty good measures in Quantum Information Theory
International Symposium on Information Theory, 2017Co-Authors: Raban Iten, Joseph M. Renes, David SutterAbstract:Quantum generalizations of Renyi's entropies are a useful tool to describe a variety of operational tasks in Quantum Information processing. Two families of such generalizations turn out to be particularly useful: the Petz Quantum Renyi divergence D α and the minimal Quantum Renyi divergence D α . In this paper, we prove a reverse Araki-Lieb-Thirring inequality that implies a new relation between these two families of divergences, namely that αD α (ρ‖σ) for α ∊ [0, 1] and where ρ and σ are density operators. This bound suggests defining a “pretty good fidelity”, whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction.
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pretty good measures in Quantum Information Theory
IEEE Transactions on Information Theory, 2017Co-Authors: Raban Iten, Joseph M. Renes, David SutterAbstract:Quantum generalizations of Renyi’s entropies are a useful tool to describe a variety of operational tasks in Quantum Information processing. Two families of such generalizations turn out to be particularly useful: the Petz Quantum Renyi divergence $\overline {D}_{\alpha }$ and the minimal Quantum Renyi divergence $\widetilde {D}_{\alpha }$ . In this paper, we prove a reverse Araki–Lieb–Thirring inequality that implies a new relation between these two families of divergences, namely, $\alpha \overline {D}_{\alpha }( \varrho \| \sigma ) \leq \widetilde {D}_{\alpha }( \varrho \| \sigma )$ for $\alpha \in [{0,1}]$ and where $ \varrho $ and $\sigma $ are density operators. This bound suggests defining a ”pretty good fidelity,” whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction. We also find a new necessary and sufficient condition for optimality of the pretty good measurement and singlet fraction.
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pretty good measures in Quantum Information Theory
arXiv: Quantum Physics, 2016Co-Authors: Raban Iten, Joseph M. Renes, David SutterAbstract:Quantum generalizations of Renyi's entropies are a useful tool to describe a variety of operational tasks in Quantum Information processing. Two families of such generalizations turn out to be particularly useful: the Petz Quantum Renyi divergence $\bar{D}_{\alpha}$ and the minimal Quantum Renyi divergence $\tilde{D}_{\alpha}$. In this paper, we prove a reverse Araki-Lieb-Thirring inequality that implies a new relation between these two families of divergences, namely that $\alpha \bar{D}_{\alpha}(\rho \| \sigma) \leq \tilde{D}_{\alpha}(\rho \| \sigma)$ for $\alpha \in [0,1]$ and where $\rho$ and $\sigma$ are density operators. This bound suggests defining a "pretty good fidelity", whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction. We also find a new necessary and sufficient condition for optimality of the pretty good measurement and singlet fraction.
Joseph M. Renes - One of the best experts on this subject based on the ideXlab platform.
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pretty good measures in Quantum Information Theory
International Symposium on Information Theory, 2017Co-Authors: Raban Iten, Joseph M. Renes, David SutterAbstract:Quantum generalizations of Renyi's entropies are a useful tool to describe a variety of operational tasks in Quantum Information processing. Two families of such generalizations turn out to be particularly useful: the Petz Quantum Renyi divergence D α and the minimal Quantum Renyi divergence D α . In this paper, we prove a reverse Araki-Lieb-Thirring inequality that implies a new relation between these two families of divergences, namely that αD α (ρ‖σ) for α ∊ [0, 1] and where ρ and σ are density operators. This bound suggests defining a “pretty good fidelity”, whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction.
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pretty good measures in Quantum Information Theory
IEEE Transactions on Information Theory, 2017Co-Authors: Raban Iten, Joseph M. Renes, David SutterAbstract:Quantum generalizations of Renyi’s entropies are a useful tool to describe a variety of operational tasks in Quantum Information processing. Two families of such generalizations turn out to be particularly useful: the Petz Quantum Renyi divergence $\overline {D}_{\alpha }$ and the minimal Quantum Renyi divergence $\widetilde {D}_{\alpha }$ . In this paper, we prove a reverse Araki–Lieb–Thirring inequality that implies a new relation between these two families of divergences, namely, $\alpha \overline {D}_{\alpha }( \varrho \| \sigma ) \leq \widetilde {D}_{\alpha }( \varrho \| \sigma )$ for $\alpha \in [{0,1}]$ and where $ \varrho $ and $\sigma $ are density operators. This bound suggests defining a ”pretty good fidelity,” whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction. We also find a new necessary and sufficient condition for optimality of the pretty good measurement and singlet fraction.
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pretty good measures in Quantum Information Theory
arXiv: Quantum Physics, 2016Co-Authors: Raban Iten, Joseph M. Renes, David SutterAbstract:Quantum generalizations of Renyi's entropies are a useful tool to describe a variety of operational tasks in Quantum Information processing. Two families of such generalizations turn out to be particularly useful: the Petz Quantum Renyi divergence $\bar{D}_{\alpha}$ and the minimal Quantum Renyi divergence $\tilde{D}_{\alpha}$. In this paper, we prove a reverse Araki-Lieb-Thirring inequality that implies a new relation between these two families of divergences, namely that $\alpha \bar{D}_{\alpha}(\rho \| \sigma) \leq \tilde{D}_{\alpha}(\rho \| \sigma)$ for $\alpha \in [0,1]$ and where $\rho$ and $\sigma$ are density operators. This bound suggests defining a "pretty good fidelity", whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction. We also find a new necessary and sufficient condition for optimality of the pretty good measurement and singlet fraction.
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Resource Theory of Quantum states out of thermal equilibrium
Physical Review Letters, 2013Co-Authors: Fernando G. S. L. Brandão, Michał Horodecki, Jonathan Oppenheim, Joseph M. Renes, Robert W SpekkensAbstract:The ideas of thermodynamics have proved fruitful in the setting of Quantum Information Theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The Theory of entanglement is perhaps the best-known and most well-understood resource Theory in this sense. Here we return to the basic questions of thermodynamics using the formalism of resource theories developed in Quantum Information Theory and show that the free energy of thermodynamics emerges naturally from the resource Theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically-many copies of a Quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution.
Raban Iten - One of the best experts on this subject based on the ideXlab platform.
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pretty good measures in Quantum Information Theory
International Symposium on Information Theory, 2017Co-Authors: Raban Iten, Joseph M. Renes, David SutterAbstract:Quantum generalizations of Renyi's entropies are a useful tool to describe a variety of operational tasks in Quantum Information processing. Two families of such generalizations turn out to be particularly useful: the Petz Quantum Renyi divergence D α and the minimal Quantum Renyi divergence D α . In this paper, we prove a reverse Araki-Lieb-Thirring inequality that implies a new relation between these two families of divergences, namely that αD α (ρ‖σ) for α ∊ [0, 1] and where ρ and σ are density operators. This bound suggests defining a “pretty good fidelity”, whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction.
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pretty good measures in Quantum Information Theory
IEEE Transactions on Information Theory, 2017Co-Authors: Raban Iten, Joseph M. Renes, David SutterAbstract:Quantum generalizations of Renyi’s entropies are a useful tool to describe a variety of operational tasks in Quantum Information processing. Two families of such generalizations turn out to be particularly useful: the Petz Quantum Renyi divergence $\overline {D}_{\alpha }$ and the minimal Quantum Renyi divergence $\widetilde {D}_{\alpha }$ . In this paper, we prove a reverse Araki–Lieb–Thirring inequality that implies a new relation between these two families of divergences, namely, $\alpha \overline {D}_{\alpha }( \varrho \| \sigma ) \leq \widetilde {D}_{\alpha }( \varrho \| \sigma )$ for $\alpha \in [{0,1}]$ and where $ \varrho $ and $\sigma $ are density operators. This bound suggests defining a ”pretty good fidelity,” whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction. We also find a new necessary and sufficient condition for optimality of the pretty good measurement and singlet fraction.
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pretty good measures in Quantum Information Theory
arXiv: Quantum Physics, 2016Co-Authors: Raban Iten, Joseph M. Renes, David SutterAbstract:Quantum generalizations of Renyi's entropies are a useful tool to describe a variety of operational tasks in Quantum Information processing. Two families of such generalizations turn out to be particularly useful: the Petz Quantum Renyi divergence $\bar{D}_{\alpha}$ and the minimal Quantum Renyi divergence $\tilde{D}_{\alpha}$. In this paper, we prove a reverse Araki-Lieb-Thirring inequality that implies a new relation between these two families of divergences, namely that $\alpha \bar{D}_{\alpha}(\rho \| \sigma) \leq \tilde{D}_{\alpha}(\rho \| \sigma)$ for $\alpha \in [0,1]$ and where $\rho$ and $\sigma$ are density operators. This bound suggests defining a "pretty good fidelity", whose relation to the usual fidelity implies the known relations between the optimal and pretty good measurement as well as the optimal and pretty good singlet fraction. We also find a new necessary and sufficient condition for optimality of the pretty good measurement and singlet fraction.
Jonathan Oppenheim - One of the best experts on this subject based on the ideXlab platform.
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fundamental limitations for Quantum and nanoscale thermodynamics
Nature Communications, 2013Co-Authors: Michal Horodecki, Jonathan OppenheimAbstract:The usual laws of thermodynamics that are valid for macroscopic systems do not necessarily apply to the nanoscale, where Quantum effects become important. Here, the authors develop a theoretical framework based on Quantum Information Theory to properly treat thermodynamics at the nanoscale.
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Resource Theory of Quantum states out of thermal equilibrium
Physical Review Letters, 2013Co-Authors: Fernando G. S. L. Brandão, Michał Horodecki, Jonathan Oppenheim, Joseph M. Renes, Robert W SpekkensAbstract:The ideas of thermodynamics have proved fruitful in the setting of Quantum Information Theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The Theory of entanglement is perhaps the best-known and most well-understood resource Theory in this sense. Here we return to the basic questions of thermodynamics using the formalism of resource theories developed in Quantum Information Theory and show that the free energy of thermodynamics emerges naturally from the resource Theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically-many copies of a Quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution.
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local versus nonlocal Information in Quantum Information Theory formalism and phenomena
Physical Review A, 2005Co-Authors: Michal Horodecki, Jonathan Oppenheim, Pawel Horodecki, Ryszard Horodecki, Aditi Sen, Ujjwal Sen, Barbara SynakradtkeAbstract:In spite of many results in Quantum Information Theory, the complex nature of compound systems is far from clear. In general the Information is a mixture of local and nonlocal ('Quantum') Information. It is important from both pragmatic and theoretical points of view to know the relationships between the two components. To make this point more clear, we develop and investigate the Quantum-Information processing paradigm in which parties sharing a multipartite state distill local Information. The amount of Information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm in detail, we show that the upper bound for the deficit is given by the relative entropy distance to so-called pseudoclassically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is Informationally nonlocal - i.e., has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other nonlocal phenomena which can be found using themore » paradigm of local Information. For example, we prove the existence of a form of nonlocality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal. We also show that there do not exist states for which the deficit is strictly equal to the whole Informational content (bound local Information). We discuss the relation of the paradigm with measures of classical correlations introduced earlier. It is also proved that in the one-way scenario, the deficit is additive for Bell diagonal states. We then discuss complementary features of Information in distributed Quantum systems. Finally we discuss the physical and theoretical meaning of the results and pose many open questions.« less