arXiv subjects

Cai-Hong Wang

Publications and source records attributed to Cai-Hong Wang.

5 recordsLinked to original sources

arXiv2025

Classical representation of local Clifford operators

It is known that every (single-qudit) Clifford operator maps the full set of generalized Pauli matrices (GPMs) to itself under unitary conjugation, which is an important quantum operation and plays a crucial role in quantum computation and information. However, in many quantum information processing tasks, it is required that a specific set of GPMs be mapped to another such set under conjugation, instead of the entire set. We formalize this by introducing local Clifford operator, which maps a given $n$-GPM set to another such set under unitary conjugation. We establish necessary and sufficient conditions for such an operator to transform a pair of GPMs, showing that these local Clifford operators admit a classical matrix representation, analogous to the classical (or symplectic) representation of standard (single-qudit) Clifford operators. Furthermore, we demonstrate that any local Clifford operator acting on an $n$-GPM ($n\geq 2$) set can be decomposed into a product of standard Clifford operators and a local Clifford operator acting on a pair of GPMs. This decomposition provides a complete classical characterization of unitary conjugation mappings between $n$-GPM sets. As a key application, we use this framework to address the local unitary equivalence (LU-equivalence) of sets of generalized Bell states (GBSs). We prove that the 31 equivalence classes of $4$-GBS sets in bipartite system $\mathbb{C}^{6}\otimes \mathbb{C}^{6}$ previously identified via Clifford operators are indeed distinct under LU-equivalence, confirming that this classification is complete.

quant-ph↗

arXiv2025

Detectors for local discrimination of sets of generalized Bell states

A fundamental problem in quantum information processing is the discrimination among a set of orthogonal quantum states of a composite system under local operations and classical communication (LOCC). Corresponding to the LOCC indistinguishable sets of four ququad-ququad orthogonal maximally entangled states (MESs) constructed by Yu et al. [Phys. Rev. Lett. 109, 020506 (2012)], the maximum commutative sets (MCSs) were introduced as detectors for the local distinguishability of the set of generalized Bell states (GBSs), for which the detectors are sufficient to determine the LOCC distinguishability. In this work, we show how to determine all the detectors for a given GBS set. We construct also several 4-GBS sets without detectors, most of which are one-way LOCC indistinguishable and only one is one-way LOCC distinguishable, indicating that the detectors are not necessary for LOCC distinguishability. Furthermore, we show that for 4-GBS sets in quantum system $\mathbb{C}^{6}\otimes\mathbb{C}^{6}$, the detectors are almost necessary for one-way LOCC distinguishability, except for one set in the sense of local unitary equivalence. The problem of one-way LOCC discrimination of 4-GBS sets in $\mathbb{C}^{6}\otimes\mathbb{C}^{6}$ is completely resolved.

quant-ph↗

arXiv2025

Local unitary classification of sets of generalized Bell states in $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$

Two sets of quantum entangled states that are equivalent under local unitary transformations may exhibit identical effectiveness and versatility in various quantum information processing tasks. Consequently, classification under local unitary transformations has become a fundamental issue in the theory of quantum entanglement. The primary objective of this work is to establish a complete LU-classification of all sets of generalized Bell states (GBSs) in bipartite quantum systems $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$ with $d\geq 3$. Based on this classification, we determine the minimal cardinality of indistinguishable GBS sets in $\mathbb{C}^{6}\otimes \mathbb{C}^{6}$ under one-way local operations and classical communication (one-way LOCC). We propose first two classification methods based on LU-equivalence for all $l$-GBS sets for $l\geq 2$. We then establish LU-classification for all 2-GBS, 3-GBS, 4-GBS and 5-GBS sets in $\mathbb{C}^{6}\otimes \mathbb{C}^{6}$. Since LU-equivalent sets share identical local distinguishability, it suffices to examine representative GBS sets from equivalent classes. Notably, we identify a one-way LOCC indistinguishable 4-GBS set among these representatives, thereby resolving the case of $d = 6$ for the problem of determining the minimum cardinality of one-way LOCC indistinguishable GBS sets in [Quant. Info. Proc. 18, 145 (2019)] or [Phys. Rev. A 91, 012329 (2015)].

quant-ph↗

arXiv2023

Finding out all locally indistinguishable sets of generalized Bell states

In general, for a bipartite quantum system $\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ and an integer $k$ such that $4\leq k\le d$,there are few necessary and sufficient conditions for local discrimination of sets of $k$ generalized Bell states (GBSs) and it is difficult to locally distinguish $k$-GBS sets.The purpose of this paper is to completely solve the problem of local discrimination of GBS sets in some bipartite quantum systems.Firstly three practical and effective sufficient conditions are given,Fan$^{,}$s and Wang et al.$^{,}$s results [Phys Rev Lett 92, 177905 (2004); Phys Rev A 99, 022307 (2019)] can be deduced as special cases of these conditions.Secondly in $\mathbb{C}^{4}\otimes\mathbb{C}^{4}$, a necessary and sufficient condition for local discrimination of GBS sets is provided, and a list of all locally indistinguishable 4-GBS sets is provided,and then the problem of local discrimination of GBS sets is completely solved.In $\mathbb{C}^{5}\otimes\mathbb{C}^{5}$, a concise necessary and sufficient condition for one-way local discrimination of GBS sets is obtained,which gives an affirmative answer to the case $d=5$ of the problem proposed by Wang et al.

quant-ph↗

arXiv2018

Construnctions of LOCC indistinguishable set of generalized Bell states

In this paper, we mainly consider the local indistinguishability of the set of mutually orthogonal bipartite generalized Bell states (GBSs). We construct small sets of GBSs with cardinality smaller than $d$ which are not distinguished by one-way local operations and classical communication (1-LOCC) in $d\otimes d$. The constructions, based on linear system and Vandermonde matrix, is simple and effective. The results give a unified upper bound for the minimum cardinality of 1-LOCC indistinguishable set of GBSs, and greatly improve previous results in [Zhang \emph{et al.}, Phys. Rev. A 91, 012329 (2015); Wang \emph{et al.}, Quantum Inf. Process. 15, 1661 (2016)]. The case that $d$ is odd of the results also shows that the set of 4 GBSs in $5\otimes 5$ in [Fan, Phys. Rev. A 75, 014305 (2007)] is indeed a 1-LOCC indistinguishable set which can not be distinguished by Fan's method.

quant-ph↗