How much symmetry do symmetric measurements need for efficient operational applications?

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-08-14 DOI:10.1088/1751-8121/ad6cb8
Katarzyna Siudzińska
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Abstract

We introduce a generalization of symmetric measurements to collections of unequinumerous positive, operator-valued measures (POVMs). This provides a uniform description of objects that are more general than symmetric, informationally complete POVMs and mutually unbiased bases, but at the same time less destructive and more noise tolerant. For informationally complete sets, we propose construction methods from orthonormal Hermitian operator bases. The correspondence between operator bases and measurements can be as high as one-to-four, with a one-to-one correspondence following only under additional assumptions. Importantly, it turns out that some of the symmetry properties, lost in the process of generalization, can be recovered without fixing the same number of elements for all POVMs. In particular, for a wide class of unequinumerous symmetric measurements that are conical 2-designs, we derive the index of coincidence, entropic uncertainty relations, and separability criteria for bipartite quantum states.
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对称测量需要多大的对称性才能实现高效的操作应用?
我们将对称测量推广到不等量的正算子值测量(POVMs)集合。这提供了对对象的统一描述,它比对称、信息完整的 POVMs 和互不偏倚基更为通用,但同时破坏性更小,对噪声的容忍度更高。对于信息完全集,我们提出了正交赫米特算子基的构造方法。算子基与测量之间的对应关系可高达一比四,只有在额外的假设条件下才能实现一一对应。重要的是,事实证明,在泛化过程中丢失的一些对称特性可以在不固定所有 POVM 的相同元素数的情况下恢复。特别是,对于一大类锥形 2 设计的不等量对称测量,我们推导出了重合指数、熵不确定性关系以及双方量子态的可分性准则。
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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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