scholarly journals Faithful measure of quantum non-Gaussianity via quantum relative entropy

2019 ◽  
Vol 100 (1) ◽  
Author(s):  
Jiyong Park ◽  
Jaehak Lee ◽  
Kyunghyun Baek ◽  
Se-Wan Ji ◽  
Hyunchul Nha
Keyword(s):  
Relative Entropy ◽  
Quantum Relative Entropy

scholarly journals Superadditivity of Quantum Relative Entropy for General States

2018 ◽  
Vol 64 (7) ◽  
pp. 4758-4765 ◽  
Author(s):  
Angela Capel ◽  
Angelo Lucia ◽  
David Perez-Garcia
Keyword(s):  
Relative Entropy ◽  
Quantum Relative Entropy

scholarly journals On quantum quasi-relative entropy

2019 ◽  
Vol 31 (07) ◽  
pp. 1950022
Author(s):  
Anna Vershynina
Keyword(s):  
Relative Entropy ◽  
Logarithmic Function ◽  
Operator Inequalities ◽  
Operator Convex Function ◽  
Strong Subadditivity ◽  
Entropy Formula ◽  
Quantum Relative Entropy ◽  
Skew Information ◽  
Explicit Bounds ◽  
Joint Convexity

We consider a quantum quasi-relative entropy [Formula: see text] for an operator [Formula: see text] and an operator convex function [Formula: see text]. We show how to obtain the error bounds for the monotonicity and joint convexity inequalities from the recent results for the [Formula: see text]-divergences (i.e. [Formula: see text]). We also provide an error term for a class of operator inequalities, that generalizes operator strong subadditivity inequality. We apply those results to demonstrate explicit bounds for the logarithmic function, that leads to the quantum relative entropy, and the power function, which gives, in particular, a Wigner–Yanase–Dyson skew information. In particular, we provide the remainder terms for the strong subadditivity inequality, operator strong subadditivity inequality, WYD-type inequalities, and the Cauchy–Schwartz inequality.

scholarly journals An Ergodic Theorem for the Quantum Relative Entropy

2004 ◽  
Vol 247 (3) ◽  
pp. 697-712 ◽  
Author(s):  
Igor Bjelakovic ◽  
Rainer Siegmund-Schultze
Keyword(s):  
Ergodic Theorem ◽  
Relative Entropy ◽  
Quantum Relative Entropy

scholarly journals MONOTONICITY OF QUANTUM RELATIVE ENTROPY REVISITED

2003 ◽  
Vol 15 (01) ◽  
pp. 79-91 ◽  
Author(s):  
DÉNES PETZ
Keyword(s):  
Relative Entropy ◽  
Coarse Graining ◽  
Von Neumann Entropy ◽  
Trace Inequality ◽  
Von Neumann ◽  
Quantum Relative Entropy ◽  
Crucial Property

Monotonicity under coarse-graining is a crucial property of the quantum relative entropy. The aim of this paper is to investigate the condition of equality in the monotonicity theorem and in its consequences as the strong sub-additivity of von Neumann entropy, the Golden–Thompson trace inequality and the monotonicity of the Holevo quantitity. The relation to quantum Markov states is briefly indicated.

scholarly journals Monotonicity of the Quantum Relative Entropy Under Positive Maps

2017 ◽  
Vol 18 (5) ◽  
pp. 1777-1788 ◽  
Author(s):  
Alexander Müller-Hermes ◽  
David Reeb
Keyword(s):  
Relative Entropy ◽  
Quantum Relative Entropy ◽  
Positive Maps

scholarly journals Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy

2018 ◽  
Vol 19 (10) ◽  
pp. 2955-2978 ◽  
Author(s):  
Marius Junge ◽  
Renato Renner ◽  
David Sutter ◽  
Mark M. Wilde ◽  
Andreas Winter
Keyword(s):  
Relative Entropy ◽  
Quantum Relative Entropy

scholarly journals Quantum Relative Entropy of Tagging and Thermodynamics

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 138
Author(s):  
Jose Diazdelacruz
Keyword(s):  
Angular Momentum ◽  
Relative Entropy ◽  
Physical System ◽  
Total Angular Momentum ◽  
Quantum States ◽  
Restricted Class ◽  
Physical Systems ◽  
Quantum Relative Entropy ◽  
Heat Engines ◽  
Labeling System

Thermodynamics establishes a relation between the work that can be obtained in a transformation of a physical system and its relative entropy with respect to the equilibrium state. It also describes how the bits of an informational reservoir can be traded for work using Heat Engines. Therefore, an indirect relation between the relative entropy and the informational bits is implied. From a different perspective, we define procedures to store information about the state of a physical system into a sequence of tagging qubits. Our labeling operations provide reversible ways of trading the relative entropy gained from the observation of a physical system for adequately initialized qubits, which are used to hold that information. After taking into account all the qubits involved, we reproduce the relations mentioned above between relative entropies of physical systems and the bits of information reservoirs. Some of them hold only under a restricted class of coding bases. The reason for it is that quantum states do not necessarily commute. However, we prove that it is always possible to find a basis (equivalent to the total angular momentum one) for which Thermodynamics and our labeling system yield the same relation.

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