Unitary-Invariant Witnesses of Quantum Imaginarity

IF 8.1 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Physical review letters Pub Date : 2024-11-08 DOI:10.1103/physrevlett.133.190201
Carlos Fernandes, Rafael Wagner, Leonardo Novo, Ernesto F. Galvão
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Abstract

Quantum theory is traditionally formulated using complex numbers. This imaginarity of quantum theory has been quantified as a resource with applications in discrimination tasks, pseudorandomness generation, and quantum metrology. In the standard formulation, a quantum state is said to have “imaginarity” if the associated density matrix is not real-valued in a given, fixed basis. If instead we consider a set of states, it is possible to devise tests that guarantee imaginarity of some state in the set, independently of the basis chosen. Here we propose such basis-independent witnesses for imaginarity that rely on measurements of unitary-invariant properties of sets of states. For three pure states, we completely characterize the invariant values attainable by quantum theory, and give a partial characterization for four pure states. We show that simple pairwise overlap measurements suffice to witness imaginarity of sets of four states, but not for sets of three. Our witnesses are experimentally friendly, opening up a new path for measuring and using imaginarity as a resource.
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量子想象力的单元不变见证
量子理论传统上使用复数来表述。量子理论的这种意象性被量化为一种资源,应用于辨别任务、伪随机性生成和量子计量学。在标准的表述中,如果相关的密度矩阵在给定的固定基础上不是实值,则称该量子态具有 "意象性"。如果我们考虑的是一组状态,那么就有可能设计出测试方法,保证这组状态中的某些状态具有意象性,而与所选的基础无关。在这里,我们提出了这种与基础无关的意象性证明,它依赖于对状态集合单位不变性质的测量。对于三个纯态,我们完全描述了量子理论可达到的不变值,并给出了四个纯态的部分描述。我们证明,简单的成对重叠测量就足以证明四个态集的意象性,而三个态集则不然。我们的见证是实验友好型的,为测量和利用意象性这一资源开辟了一条新路。
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
Physical review letters
Physical review letters 物理-物理:综合
CiteScore
16.50
自引率
7.00%
发文量
2673
审稿时长
2.2 months
期刊介绍: Physical review letters(PRL)covers the full range of applied, fundamental, and interdisciplinary physics research topics: General physics, including statistical and quantum mechanics and quantum information Gravitation, astrophysics, and cosmology Elementary particles and fields Nuclear physics Atomic, molecular, and optical physics Nonlinear dynamics, fluid dynamics, and classical optics Plasma and beam physics Condensed matter and materials physics Polymers, soft matter, biological, climate and interdisciplinary physics, including networks
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