Uniqueness of quantum states compatible with given measurement results

ISCAS OpenIR

	Uniqueness of quantum states compatible with given measurement results
	Chen, Jianxin; Dawkins, Hillary; Ji, Zhengfeng; Johnston, Nathaniel; Kribs, David; Shultz, Frederic; Zeng, Bei
	2013
发表期刊	PHYSICAL REVIEW A
ISSN	1050-2947
卷号	88 期号:1
摘要	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.; 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.
收录类别	SCI
部门归属	[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.
语种	英语
WOS记录号	WOS:000321833000002
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/16924
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	Chen, Jianxin,Dawkins, Hillary,Ji, Zhengfeng,et al. Uniqueness of quantum states compatible with given measurement results[J]. PHYSICAL REVIEW A,2013,88(1).
APA	Chen, Jianxin.,Dawkins, Hillary.,Ji, Zhengfeng.,Johnston, Nathaniel.,Kribs, David.,...&Zeng, Bei.(2013).Uniqueness of quantum states compatible with given measurement results.PHYSICAL REVIEW A,88(1).
MLA	Chen, Jianxin,et al."Uniqueness of quantum states compatible with given measurement results".PHYSICAL REVIEW A 88.1(2013).