线性映射作为多体系统纠缠深度和相容性的充分准则

IF 1.3 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
M. Lewenstein, Guillem Muller-Rigat, Jordi Tura i Brugués, A. Sanpera
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引用次数: 0

摘要

物理变换由完全正的和迹迹保留(CPTP)的线性映射描述。然而,正的(P)而非完全正的(CP)映射有助于推导可分性/纠缠准则。此外,这种映射的属性可以与它们检测到的状态的纠缠属性联系起来。在这里,我们推广了文献[34]中给出的结果,其中给出了二部系统的足够的可分性准则。特别是,我们通过提出线性映射来分析[公式:见文本]-量子比特系统的纠缠深度,当应用于任何状态时,会导致[公式:见文本]分区的可分状态,即[公式:见文本]-纠缠深度。此外,我们推导了检测任意[公式:见文本]的标准-针对完全去极化状态(归一化单位矩阵)附近的状态量身定制的纠缠深度。我们还提供了对称扇区的可分离性(或[公式:见文本]-纠缠深度)条件,包括对角线状态。最后,我们建议如何使用类似的映射技术来推导一组期望值与可分离状态或局部隐藏变量理论相容的充分条件。我们把这篇论文献给已故的安德烈·科萨科夫斯基,他是我们在线性地图领域的精神和智力导师。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Linear Maps as Sufficient Criteria for Entanglement Depth and Compatibility in Many-Body Systems
Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement criteria. Moreover, the properties of such maps can be linked to entanglement properties of the states they detect. Here, we extend the results presented in [34], where sufficient separability criteria for bipartite systems were derived. In particular, we analyze the entanglement depth of an [Formula: see text]-qubit system by proposing linear maps that, when applied to any state, result in a biseparable state for the [Formula: see text] partitions, i.e., [Formula: see text]-entanglement depth. Furthermore, we derive criteria to detect arbitrary [Formula: see text]-entanglement depth tailored to states in close vicinity of the completely depolarized state (the normalized identity matrix). We also provide separability (or [Formula: see text]-entanglement depth) conditions in the symmetric sector, including the diagonal states. Finally, we suggest how similar map techniques can be used to derive sufficient conditions for a set of expectation values to be compatible with separable states or local-hidden-variable theories. We dedicate this paper to the memory of the late Andrzej Kossakowski, our spiritual and intellectual mentor in the field of linear maps.
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来源期刊
Open Systems & Information Dynamics
Open Systems & Information Dynamics 工程技术-计算机:信息系统
CiteScore
1.40
自引率
12.50%
发文量
4
审稿时长
>12 weeks
期刊介绍: The aim of the Journal is to promote interdisciplinary research in mathematics, physics, engineering and life sciences centered around the issues of broadly understood information processing, storage and transmission, in both quantum and classical settings. Our special interest lies in the information-theoretic approach to phenomena dealing with dynamics and thermodynamics, control, communication, filtering, memory and cooperative behaviour, etc., in open complex systems.
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