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Uniqueness of quantum states compatible with given measurement results
文献类型：期刊论文
| 作者 | Chen, Jianxin ; Dawkins, Hillary ; Ji, Zhengfeng ; Johnston, Nathaniel ; Kribs, David ; Shultz, Frederic ; Zeng, Bei |
| 刊名 | PHYSICAL REVIEW A
 |
| 出版日期 | 2013 |
| 卷号 | 88期号:1 |
| ISSN号 | 1050-2947 |
| 中文摘要 | 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. |
| 英文摘要 | 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. |
| 收录类别 | SCI |
| 语种 | 英语 |
| WOS记录号 | WOS:000321833000002 |
| 公开日期 | 2014-12-16 |
| 源URL | [http://ir.iscas.ac.cn/handle/311060/16924]  |
| 专题 | 软件研究所_软件所图书馆_期刊论文 |
| 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). |
入库方式： OAI收割
来源：软件研究所
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