中国科学院软件研究所机构知识库
Advanced  
ISCAS OpenIR  > 软件所图书馆  > 期刊论文
Title:
Uniqueness of quantum states compatible with given measurement results
Author: Chen, Jianxin ; Dawkins, Hillary ; Ji, Zhengfeng ; Johnston, Nathaniel ; Kribs, David ; Shultz, Frederic ; Zeng, Bei
Source: PHYSICAL REVIEW A
Issued Date: 2013
Volume: 88, Issue:1
Indexed Type: SCI
Department: [Chen, Jianxin; Dawkins, Hillary; Johnston, Nathaniel; Kribs, David; Zeng, Bei] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada. [Chen, Jianxin; Ji, Zhengfeng; Johnston, Nathaniel; Kribs, David; Zeng, Bei] Univ Waterloo, Inst Quantum Comp, Waterloo, ON N2L 3G1, Canada. [Ji, Zhengfeng] Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing, Peoples R China. [Shultz, Frederic] Wellesley Coll, Dept Math, Wellesley, MA 02481 USA.
Abstract: We discuss the uniqueness of quantum states compatible with given measurement results for a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it was known that for a d-dimensional Hilbert space, there exists a set of 4d - 5 observables that uniquely determines any pure state. We show that for case (2), 5d - 7 observables suffice to uniquely determine any pure state. Thus, there is a gap between the results for (1) and (2), and we give some examples to illustrate this. Unique determination of a pure state by its reduced density matrices (RDMs), a special case of determination by observables, is also discussed. We improve the best-known bound on local dimensions in which almost all pure states are uniquely determined by their RDMs for case (2). We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low-rank quantum states.
English Abstract: We discuss the uniqueness of quantum states compatible with given measurement results for a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it was known that for a d-dimensional Hilbert space, there exists a set of 4d - 5 observables that uniquely determines any pure state. We show that for case (2), 5d - 7 observables suffice to uniquely determine any pure state. Thus, there is a gap between the results for (1) and (2), and we give some examples to illustrate this. Unique determination of a pure state by its reduced density matrices (RDMs), a special case of determination by observables, is also discussed. We improve the best-known bound on local dimensions in which almost all pure states are uniquely determined by their RDMs for case (2). We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low-rank quantum states.
Language: 英语
WOS ID: WOS:000321833000002
Citation statistics:
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16924
Appears in Collections:软件所图书馆_期刊论文

Files in This Item:

There are no files associated with this item.


Recommended Citation:
Chen, Jianxin,Dawkins, Hillary,Ji, Zhengfeng,et al. Uniqueness of quantum states compatible with given measurement results[J]. PHYSICAL REVIEW A,2013-01-01,88(1).
Service
Recommend this item
Sava as my favorate item
Show this item's statistics
Export Endnote File
Google Scholar
Similar articles in Google Scholar
[Chen, Jianxin]'s Articles
[Dawkins, Hillary]'s Articles
[Ji, Zhengfeng]'s Articles
CSDL cross search
Similar articles in CSDL Cross Search
[Chen, Jianxin]‘s Articles
[Dawkins, Hillary]‘s Articles
[Ji, Zhengfeng]‘s Articles
Related Copyright Policies
Null
Social Bookmarking
Add to CiteULike Add to Connotea Add to Del.icio.us Add to Digg Add to Reddit
所有评论 (0)
暂无评论
 
评注功能仅针对注册用户开放,请您登录
您对该条目有什么异议,请填写以下表单,管理员会尽快联系您。
内 容:
Email:  *
单位:
验证码:   刷新
您在IR的使用过程中有什么好的想法或者建议可以反馈给我们。
标 题:
 *
内 容:
Email:  *
验证码:   刷新

Items in IR are protected by copyright, with all rights reserved, unless otherwise indicated.

 

 

Valid XHTML 1.0!
Copyright © 2007-2020  中国科学院软件研究所 - Feedback
Powered by CSpace