Estimating quantum entropy

被引：16
作者：
Acharya J. [1 ,3 ]
Issa I. [1 ,2 ,3 ]
Shende N.V. [3 ,4 ]
Wagner A.B. [1 ,3 ]
机构：
[1] School of Electrical and Computer Engineering, Cornell University, Ithaca, 14853, NY
[2] School of Electrical and Computer Engineering, American University of Beirut, Beirut
[3] Cornell University, Ithaca, 14853, NY
[4] Marvell Semiconductor, Santa Clara, 95054, CA
来源：
Acharya, Jayadev (acharya@cornell.edu) | 1600年 / Institute of Electrical and Electronics Engineers Inc.卷 / 01期
关键词：
Copy complexity; Entropy estimation; Quantum information; Renyi entropy; Von Neumann entropy; Weak Schur sampling;
D O I：
10.1109/JSAIT.2020.3015235
中图分类号：
学科分类号：
摘要：
The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of estimating the von Neumann entropy, S(p), and Rényi entropy, Sα(p) of an unknown mixed quantum state p in d dimensions, given access to independent copies of p. We provide algorithms with copy complexity O(d2/α) for estimating Sα(p) for α < 1, and copy complexity O(d2) for estimating S(p), and Sα(p) for non-integral α > 1. These bounds are at least quadratic in d, which is the order dependence on the number of copies required for estimating the entire state p. For integral α > 1, on the other hand, we provide an algorithm for estimating Sα(p) with a sub-quadratic copy complexity of O(d2-2/α), and we show the optimality of the algorithms by providing a matching lower bound. © 2020 IEEE Journal on Selected Areas in Information Theory.All right reserved.
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页码：454 / 468
页数：14
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