Compressing continuous variable quantum measurements

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
Pauli Jokinen, Sophie Egelhaaf, Juha-Pekka Pellonpää and Roope Uola
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引用次数: 0

Abstract

We generalize the notion of joint measurability to continuous variable systems by extending a recently introduced compression algorithm of quantum measurements to this realm. The extension results in a property that asks for the minimal dimensional quantum system required for representing a given set of quantum measurements. To illustrate the concept, we show that the canonical pair of position and momentum is completely incompressible. We translate the concept of measurement compression to the realm of quantum correlations, where it results in a generalization of continuous variable quantum steering. In contrast to the steering scenario, which detects entanglement, the generalization detects the dimensionality of entanglement. We illustrate the bridge between the concepts by showing that an analogue of the original EPR argument is genuinely infinite-dimensional with respect to our figure of merit, and that a fundamental discrete variable result on preparability of unsteerable state assemblages with separable states does not directly carry over to the continuous variable setting. We further prove a representation result for partially entanglement breaking channels that can be of independent interest.
压缩连续可变量子测量
我们通过将最近引入的量子测量压缩算法扩展到连续变量系统,将联合可测性的概念推广到这一领域。这一扩展产生了一个特性,即要求用最小维度的量子系统来表示一组给定的量子测量值。为了说明这一概念,我们展示了位置和动量的典型对是完全不可压缩的。我们将测量压缩的概念转化到量子相关性领域,并在此基础上对连续变量量子转向进行了概括。与检测纠缠的转向方案不同,广义方案检测的是纠缠的维度。我们通过证明原始 EPR 论证的一个类似物就我们的优点图而言确实是无穷维的,以及一个关于具有可分离状态的不可转向状态集合的可准备性的基本离散变量结果并不能直接套用到连续变量环境中,来说明这两个概念之间的桥梁。我们还进一步证明了部分纠缠断裂通道的表征结果,这可能与我们的兴趣无关。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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