UNCERTAINTY RELATIONS AND INFORMATION LOSS FOR SPIN-1/2 MEASUREMENTS

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2023-11-01 DOI:10.1142/9789811275999_0007

Alberto Barchielli, Matteo Gregoratti

引用次数: 2

Abstract

We formulate entropic measurements uncertainty relations (MURs) for a spin-1/2 system. When incompatible observables are approximatively jointly measured, we use relative entropy to quantify the information lost in approximation and we prove positive lower bounds for such a loss: there is an unavoidable information loss. Firstly we allow only for covariant approximate joint measurements and we find state-dependent MURs for two or three orthogonal spin-1/2 components. Secondly we consider any possible approximate joint measurement and we find state-independent MURs for two or three spin-1/2 components. In particular we study how MURs depend on the angle between two spin directions. Finally, we extend our approach to infinitely many incompatible observables, namely to the spin components in all possible directions. In every scenario, we always consider also the characterization of the optimal approximate joint measurements.

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自旋-1/2测量的不确定关系和信息损失

我们建立了自旋为1/2的系统的熵测量不确定关系(MURs)。当不相容的观测值被近似地联合测量时，我们使用相对熵来量化近似中丢失的信息，并且我们证明了这种损失的正下界:存在不可避免的信息损失。首先，我们只允许协变近似联合测量，我们找到了两个或三个正交自旋1/2分量的状态相关的mrs。其次，我们考虑任何可能的近似联合测量，我们找到了两个或三个自旋1/2分量的状态无关的mrs。特别地，我们研究了自旋方向间的夹角对模量的影响。最后，我们将我们的方法扩展到无限多个不相容的可观测值，即所有可能方向上的自旋分量。在每种情况下，我们总是考虑最优近似关节测量的表征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.