Universal recovery map for approximate Markov chains
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TLDR
It is proved that the conditional mutual information I(A:C|B) of a tripartite quantum state ρABC can be bounded from below by its distance to the closest recovered state RB→BC(ρAB), where the C-part is reconstructed from the B-part only and the recovery map RB→ BC merely depends on ρBC.Abstract:
A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the quantum conditional mutual information measures the performance of such recovery operations. More precisely, we prove that the conditional mutual information $I(A:C|B)$ of a tripartite quantum state $\rho_{ABC}$ can be bounded from below by its distance to the closest recovered state $\mathcal{R}_{B \to BC}(\rho_{AB})$, where the $C$-part is reconstructed from the $B$-part only and the recovery map $\mathcal{R}_{B \to BC}$ merely depends on $\rho_{BC}$. One particular application of this result implies the equivalence between two different approaches to define topological order in quantum systems.read more
Citations
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Multivariate Trace Inequalities
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Recoverability in quantum information theory
TL;DR: In this article, the Renyi generalization of the relative entropy difference between two quantum states after a quantum physical evolution is shown to provide physically meaningful improvements to many known entropy inequalities.
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Quantum stochastic processes and quantum non-Markovian phenomena
Simon Milz,Kavan Modi +1 more
TL;DR: In this paper, the authors discuss the structure of quantum stochastic processes, in terms of the modern language of quantum combs, and provide a tutorial aimed at students in quantum physics and quantum information theory.
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On Variational Expressions for Quantum Relative Entropies
TL;DR: In this article, it was shown that the Renyi relative entropy is strictly smaller than Umegaki's quantum relative entropy whenever the states do not commute, and this result remains true for general positive operator valued measures.
Journal Article
Recoverability in quantum information theory
TL;DR: In this paper, the Renyi generalization of the relative entropy difference between two quantum states after a quantum physical evolution is shown to provide physically meaningful improvements to many known entropy inequalities.
References
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Book
Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Journal ArticleDOI
Quantum computation and quantum information
TL;DR: This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing, with a focus on entanglement.
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Topological entanglement entropy
TL;DR: The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity.
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