首页/论文/quant-ph/0407147

arXiv quant-ph/04071472004-07-19quant-ph

Jensen-Shannon divergence, Fisher information, and Wootters' hypothesis

M. Casas, P. W. Lamberti, A. Plastino, A. R. Plastino

英文摘要：

We discuss different statistical distances in probability space, with emphasis on the Jensen-Shannon divergence, vis-a-vis {\it metrics} in Hilbert space and their relationship with Fisher's information measure. This study provides further reconfirmation of Wootters' hypothesis concerning the possibility that statistical fluctuations in the outcomes of measurements be regarded (at least partly) as responsible for the Hilbert-space structure of quantum mechanics.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

利用Jensen-Shannon散度对量子生成序列进行分割

Segmentation of quantum generated sequences by using the Jensen-Shannon divergence

本文提出一种基于Jensen-Shannon散度的方法，用于分割由测量量子系统生成的符号序列，并在单量子比特和双量子比特系统上验证了其有效性。

2023-04-18quant-ph

Jensen Shannon divergence as a measure of the degree of entanglement

The notion of distance in Hilbert space is relevant in many scenarios. In particular, distances between quantum states play a central role in quantum information theory. An appropriate measure of distance is the quantum Jensen Shannon divergence (QJSD) between quantum states. Here we study this distance as a geometrical measure of entanglement and apply it to different families of states.

2008-04-23quant-ph

On the metric character of the quantum Jensen-Shannon divergence

In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (Phys. Rev. A 72, 052310 (2005)). This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of simulations for mixed states, that its square root verifies the triangle inequality.

2008-05-06quant-ph

Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence

The Holevo quantity provides an upper bound for the mutual information between the sender of a classical message encoded in quantum carriers and the receiver. Applying the strong sub-additivity of entropy we prove that the Holevo quantity associated with an initial state and a given quantum operation represented in its Kraus form is not larger than the exchange entropy. This implies upper bounds for the coherent information and for the quantum Jensen--Shannon divergence. Restricting our attention to classical information we bound the transmission distance between any two probability distributi…

2010-04-27quant-ph

Jensen-Shannon divergence as a measure of distinguishability between mixed quantum states

We discuss an alternative to relative entropy as a measure of distance between mixed quantum states. The proposed quantity is an extension to the realm of quantum theory of the Jensen-Shannon divergence (JSD) between probability distributions. The JSD has several interesting properties. It arises in information theory and, unlike the Kullback-Leibler divergence, it is symmetric, always well defined and bounded. We show that the quantum JSD (QJSD) shares with the relative entropy most of the physically relevant properties, in particular those required for a "good" quantum distinguishability mea…

2005-10-18quant-ph

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…

2004-11-18quant-ph

更多相关论文收起更多论文

Properties of Classical and Quantum Jensen-Shannon Divergence

Jensen-Shannon divergence (JD) is a symmetrized and smoothed version of the most important divergence measure of information theory, Kullback divergence. As opposed to Kullback divergence it determines in a very direct way a metric; indeed, it is the square of a metric. We consider a family of divergence measures (JD_alpha for alpha>0), the Jensen divergences of order alpha, which generalize JD as JD_1=JD. Using a result of Schoenberg, we prove that JD_alpha is the square of a metric for alpha lies in the interval (0,2], and that the resulting metric space of probability distributions can be i…

2009-04-14quant-ph

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。

2026-04-08quant-ph

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.

2021-01-22math-phmath.FAmath.MP

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…

2019-12-16cs.ITmath.ITquant-ph

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。

2026-04-09quant-ph

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…

2005-09-26physics.atom-phquant-ph

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。

2023-04-24quant-ph

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…

2005-06-06cond-mat.othernucl-thphysics.atom-ph

Entropic bounds on information backflow

In the dynamics of open quantum systems, the backflow of information to the reduced system under study has been suggested as the actual physical mechanism inducing memory and thus leading to non-Markovian quantum dynamics. To this aim, the trace-distance or Bures-distance revivals between distinct evolved system states have been shown to be subordinated to the establishment of system-environment correlations or changes in the environmental state. We show that this interpretation can be substantiated also for a class of entropic quantifiers. We exploit a suitably regularized version of Umegaki'…

2021-01-07math-phmath.MPquant-ph