具有已知约化态的无限维量子系统态的秩

数学物理学报 ›› 2022, Vol. 42 ›› Issue (1): 1-8.

• 论文 • 下一篇

具有已知约化态的无限维量子系统态的秩

杨舒媛^1,³(),贺衎^2,^3,*()

¹ 太原理工大学信息与计算机学院太原 030024
² 中国科学院量子信息重点实验室合肥 230026
³ 太原理工大学数学学院太原 030024

收稿日期:2021-01-27 出版日期:2022-02-01 发布日期:2022-02-23
通讯作者: 贺衎 E-mail:yangshuyuan2000@163.com;hekanquantum@163.com
作者简介:杨舒媛, E-mail: yangshuyuan2000@163.com
基金资助:
国家自然科学基金(11771011);国家自然科学基金(12071336);中国科学院量子信息重点实验室开放课题

Ranks of Quantum States with Prescribed Reduced States in an Infinite Dimensional Quantum System

Shuyuan Yang^1,³(),Kan He^2,^3,*()

¹ College of Information and Computer, Taiyuan University of Technology, Taiyuan 030024
² Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei 230026
³ College of Mathematics, Taiyuan University of Technology, Taiyuan 030024

Received:2021-01-27 Online:2022-02-01 Published:2022-02-23
Contact: Kan He E-mail:yangshuyuan2000@163.com;hekanquantum@163.com
Supported by:
the NSFC(11771011);the NSFC(12071336);the Key Laboratory of Quantum Information, University of Science and Technology of China

摘要/Abstract

摘要：

若 $H$ 和 $K$ 为两个无限维量子系统（即无限维复Hilbert空间）.令 $\rho$ 是 $H\otimes K$ 上的量子态，在已知其两个约化态 $tr_H（\rho）$ 与 $tr_K（\rho）$ 的情况下，该文确定 $\rho$ 所有可能的秩.

关键词: 量子态, 约化态, 偏迹, 秩

Abstract:

Suppose that $H$ and $K$ are two infinite dimensional quantum systems (i.e. infinite dimensional complex Hilbert space). Let $\rho$ be a quantum state on $H\otimes K$ with two reduced states $tr_H(\rho)$ and $tr_K(\rho)$ . Then all possible ranks of $\rho$ are determined in this paper.

Key words: Quantum state, Reduced state, Partial trace, Rank

中图分类号:

O177.1

杨舒媛,贺衎. 具有已知约化态的无限维量子系统态的秩[J]. 数学物理学报, 2022, 42(1): 1-8.

Shuyuan Yang,Kan He. Ranks of Quantum States with Prescribed Reduced States in an Infinite Dimensional Quantum System[J]. Acta mathematica scientia,Series A, 2022, 42(1): 1-8.

参考文献 7

1	Von Neumann J . Mathematical Foundations of Quantum Mechanics. United States: Princeton University Press, 1932
2	Klyachko A . Quantum marginal problem and N-representability. J Phys Conf Ser, 2006, 36: 72- 86 doi: 10.1088/1742-6596/36/1/014
3	Li C K , Poon Y T , Wang X . Ranks of quantum states with prescribed reduced states. Electron J Linear Algebra, 2017, 34: 331- 342
4	Li C K , Poon Y T , Wang X . Ranks and eigenvalues of states with prescribed reduced states. Electron J Linear Algebra, 2014, 27: 935- 950
5	Fulton W . Eigenvalues, invariant factors, highest weights, and Schubert calculus. Bull Amer Math Soc, 2000, 37: 209- 249 doi: 10.1090/S0273-0979-00-00865-X
6	Horn A . Eigenvalues of sums of Hermitian matrices. Pac J Math, 1962, 12 (1): 225- 241 doi: 10.2140/pjm.1962.12.225
7	Bercovici H , Li W S , Timotin D . The Horn conjecture for sums of compact selfadjoint operators. Am J Math, 2009, 131: 1543- 1567

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具有已知约化态的无限维量子系统态的秩

Ranks of Quantum States with Prescribed Reduced States in an Infinite Dimensional Quantum System

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