Related papers: Bounding relative entropy for non-unitary excitati…
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…
Quantum states that possess negative conditional von Neumann entropy provide quantum advantage in several information-theoretic protocols including superdense coding, state merging, distributed private randomness distillation and one-way…
Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy…
In effective field theory, the positivity bounds of higher derivative operators are derived from analyticity, causality, and unitarity. We show that the positivity bounds on some operators of the effective field theory, e.g.,…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
We compare the entropy-energy inequality and the von Neumann entropic inequality for three level atom implemented on superconducting circuits with Josephson junction. The positivity of entropy and energy relations for the qutrit system are…
We compute the local second variation of the von Neumann entropy of a region in theories with a gravity dual. For null variations our formula says that the diagonal part of the Quantum Null Energy Condition is saturated in every state, thus…
Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of…
This work explores connections between the quantum relative entropy of two faithful states $\rho,\sigma$ (i.e. full-rank density matrices) and the Kullback-Leibler divergences of classical measures $\mu,\nu$. Here, $\mu$ and $\nu$ are…
The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the non-analyticity of this entropy at disorder-dominated quantum phase transitions in non-interacting electronic systems.…
The relative entropy of a correlated state and an uncorrelated reference state is a reasonable measure for the degree of correlations. A key question is however which uncorrelated state to compare to. The relative entropy becomes minimal…
For pure states of multi-dimensional quantum lattice systems, which in a convenient computational basis have amplitude and phase structure of sufficiently rapid decorrelation, we construct high fidelity approximations of relatively low…
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of…
Standard entropy calculations in quantum field theory, when applied to a subsystem of definite volume, exhibit area-dependent UV divergences that make a thermodynamic interpretation troublesome. In this paper we define a renormalized…
Relative entropy (divergence) of Bregman type recently proposed by T. D. Frank and Jan Naudts is considered and its quantum counterpart is used to calculate purity of the Werner state in nonextensive formalism. It has been observed that two…
Energy bounds which are uniform in the background metric are obtained from upper bounds for entropy-like quantities. The argument is based on auxiliary Monge-Amp\`ere equations involving sublevel sets, and bypasses the…
We construct a complete set of Wannier functions which are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability…
We prove a bound on the entropy dissipation for the Boltzmann collision operator from below by a weighted $L^p$-Norm. The estimate holds for a wide range of potentials including soft potentials as well as very soft potentials. As an…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
Given an arbitrary quantum state ($\sigma$), we obtain an explicit construction of a state $\rho^*_\varepsilon(\sigma)$ (resp. $\rho_{*,\varepsilon}(\sigma)$) which has the maximum (resp. minimum) entropy among all states which lie in a…