On the metric character of the quantum Jensen-Shannon divergence

通过量子(α,β) Jensen-Shannon散度量化魔性

Quantifying magic via quantum $(α,β)$ Jensen-Shannon divergence

本文提出两种新的魔性量化器，基于量子(α,β)熵和量子(α,β)-相对熵，展示了其在低维希尔伯特空间中的高效计算性及在特定量子门类中提升魔性生成能力的特性。

The metric property of the quantum Jensen-Shannon divergence

In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space.

Metrics Induced by Jensen-Shannon and Related Divergences on Positive Definite Matrices

We study metric properties of symmetric divergences on Hermitian positive definite matrices. In particular, we prove that the square root of these divergences is a distance metric. As a corollary we obtain a proof of the metric property for Quantum Jensen-Shannon-(Tsallis) divergences (parameterized by $α\in [0,2]$), which in turn (for $α=1$) yields a proof of the metric property of the Quantum Jensen-Shannon divergence that was conjectured by Lamberti \emph{et al.} a decade ago (\emph{Metric character of the quantum Jensen-Shannon divergence}, Phy.\ Rev.\ A, \textbf{79}, (2008).) A somewhat m…

基于Jensen-Shannon和Jeffreys分歧的量子速度限制：一般物理过程

Quantum speed limits based on Jensen-Shannon and Jeffreys divergences for general physical processes

本文研究了有限维量子系统在一般物理过程中的量子速度限制，利用Jensen-Shannon和Jeffreys分歧的平方根作为距离度量，并通过数值模拟验证了速度限制的紧性及与以往结果的对比。

联合凸量子Jensen散度

Jointly convex quantum Jensen divergences

本研究从联合凸性角度探究量子Jensen散度，证明生成正定矩阵上联合凸量子Jensen散度的函数集等价于Chen和Tropp近期提出的矩阵熵类。

Maps on quantum states preserving Bregman and Jensen divergences

We describe the structure of the bijective transformations on the set of density operators which preserve the Bregman $f$-divergence for an arbitrary differentiable strictly convex function $f.$ Furthermore, we determine the preservers of the Jensen $f$-divergence in the case when the generating function $f$ belongs to a recently introduced function class called Matrix Entropy Class.

Information Entropy, Information Distances and Complexity in Atoms

Shannon information entropies in position and momentum spaces and their sum are calculated as functions of Z (Z=2-54) in atoms. Roothaan-Hartree-Fock electron wave functions are used. The universal property S=a+b lnZ is verified. In addition, we calculate the Kullback-Leibler relative entropy, the Jensen-Shannon divergence, Onicescu's information energy and a complexity measure recently proposed. Shell effects at closed shells atoms are observed. The complexity measure shows local minima at the closed shells atoms indicating that for the above atoms complexity decreases with respect to neighbo…

量子信道空间中的传输距离

Transmission distance in the space of quantum channels

本研究利用量子Jensen-Shannon散度平方根提出量子信道传输距离与熵信道散度两种可区分性度量，推导其数学性质与物理意义，建立熵信道散度链式法则并验证摊销坍缩，还分析了Pauli信道可区分性与退相干下的哈密顿动力学。

Wootters' distance revisited: a new distinguishability criterium

The notion of distinguishability between quantum states has shown to be fundamental in the frame of quantum information theory. In this paper we present a new distinguishability criterium by using a information theoretic quantity: the Jensen-Shannon divergence (JSD). This quantity has several interesting properties, both from a conceptual and a formal point of view. Previous to define this distinguishability criterium, we review some of the most frequently used distances defined over quantum mechanics' Hilbert space. In this point our main claim is that the JSD can be taken as a unifying dista…

Distance between quantum states in presence of initial qubit-environment correlations: a comparative study

The time evolution of the trace distance between two states of an open quantum system may increase due to initial system-environment correlations, thus exhibiting a breakdown of distance contractivity of the reduced dynamics. We analyze how the time evolution of the distance depends on the chosen distance measure. Here we elucidate the behavior of the trace distance, the Hilbert- Schmidt distance, the Bures distance, the Hellinger distance and the quantum Jensen-Shannon divergence for two system-environment setups, namely a qubit bi-linearly coupled to an infinite and a finite size environment…

Rényi divergence inequalities via interpolation, with applications to generalised entropic uncertainty relations

We investigate quantum Rényi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed Rényi generalisations of the quantum relative entropy. We may define Rényi generalisations of the quantum conditional entropy and mutual information in terms of this divergence, from which they inherit many desirable properties. However, these quantities lack some of the convenient structure of their Shannon and von Neumann counterparts. We attempt to bridge this gap by establishing divergence inequalities for valid combinations of Rényi order wh…

Quantum-Information Theoretic Properties of Nuclei and Trapped Bose Gases

Fermionic (atomic nuclei) and bosonic (correlated atoms in a trap) systems are studied from an information-theoretic point of view. Shannon and Onicescu information measures are calculated for the above systems comparing correlated and uncorrelated cases as functions of the strength of short range correlations. One-body and two-body density and momentum distributions are employed. Thus the effect of short-range correlations on the information content is evaluated. The magnitude of distinguishability of the correlated and uncorrelated densities is also discussed employing suitable measures of d…

Shannon and Rényi mutual information in quantum critical spin chains

We study the Shannon mutual information in one-dimensional critical spin chains, following a recent conjecture (Phys. Rev. Lett. 111, 017201 (2013)), as well as Rényi generalizations of it. We combine conformal field theory arguments with numerical computations in lattice discretizations with central charge $c=1$ and $c=1/2$. For a periodic system of length $L$ cut into two parts of length $\ell$ and $L-\ell$, all our results agree with the general shape-dependence $I_n(\ell,L)=(b_n/4)\ln \left(\frac{L}π\sin \frac{π\ell}{L}\right)$, where $b_n$ is a universal coefficient. For the free boson CF…