Related papers: A chain rule for the quantum relative entropy
The uncertainty relation reveals the intrinsic difference between the classical world and the quantum world. We investigate the quantum uncertainty relation of quantum channel in qubit systems. Under two general measurement bases, we first…
We give a simple proof of the uncertainty principle with quantum side information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the monotonicity of the relative entropy. Our proof shows that the entropic uncertainty principle…
Quantum networks play a key role in many scenarios of quantum information theory. Here we consider the quantum causal networks in the manner of entropy. First we present a revised smooth max-relative entropy of quantum combs, then we…
We introduce a new operational technique for deriving chain rules for general information theoretic quantities. This technique is very different from the popular (and in some cases fairly involved) methods like SDP formulation and operator…
The chain rule for the Shannon and von Neumann entropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here we consider the chain rule for the more general smooth…
Uncertainty principle reveals the intrinsic differences between the classical and quantum worlds, which plays a significant role in quantum information theory. By using $\rho$-absolute variance, we introduce the uncertainty of quantum…
The classical randomization criterion is an important result of statistical decision theory. Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum…
Given two pairs of quantum states, we want to decide if there exists a quantum channel that transforms one pair into the other. The theory of quantum statistical comparison and quantum relative majorization provides necessary and sufficient…
We derive generalization and excess risk bounds for neural nets using a family of complexity measures based on a multilevel relative entropy. The bounds are obtained by introducing the notion of generated hierarchical coverings of neural…
If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum…
We study the problem of binary composite channel discrimination in the asymmetric setting, where the hypotheses are given by fairly arbitrary sets of channels, and samples do not have to be identically distributed. In the case of quantum…
We extend the definition of the conditional min-entropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an…
The quantum relative entropy is known to play a key role in determining the asymptotic convertibility of quantum states in general resource-theoretic settings, often constituting the unique monotone that is relevant in the asymptotic…
We review the properties of the quantum relative entropy function and discuss its application to problems of classical and quantum information transfer and to quantum data compression. We then outline further uses of relative entropy to…
Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…
We study asymmetric binary channel discrimination, for qantum channels acting on separable Hilbert spaces. We establish quantum Stein's lemma for channels for both adaptive and parallel strategies, and show that under finiteness of the…
We argue that a fundamental (conjectured) property of memoryless quantum channels, namely the strong superadditivity, is intimately related to the decreasing property of the quantum relative entropy. Using the latter we first give, for a…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…
Probabilistic quantum filtering is proposed to properly adapt sequential independent quantum channels in order to stop sudden death of entanglement. In the adaptation, the quantum filtering does not distill or purify more entanglement, it…