arXiv subjects

Ying-Hui Yang

Publications and source records attributed to Ying-Hui Yang.

9 recordsLinked to original sources

arXiv2026

Kirkwood-Dirac classical states based on discrete Fourier transform: Representation with directed graph

The Kirkwood-Dirac (KD) quasiprobability distribution is a fundamental representation for quantum states and has been widely applied in quantum metrology, quantum chaos, weak values in recent years. A quantum state is KD-classical if its KD-quasiprobability distribution forms a valid classical probability distribution with respect to two given bases, and KD-nonclassical otherwise, with the latter being closely associated with quantum advantages in various quantum processes. In this work, we investigate the structural characteristics of the KD-classical state set when the transition matrix between two orthonormal bases takes the form of a discrete Fourier transform (DFT) matrix. First, we adopt an alternative analytical approach to prove that the set of KD-classical states in a $p^r$-dimensional Hilbert space is the convex hull of KD-classical pure states--a conclusion that was recently established by De Bi{\`e}vre et al [Annales Henri Poincar{\'e}, 1-20, 2025]. Furthermore, we define a directed graph and use it to characterize KD-classical pure states in a Hilbert space of arbitrary dimension $d$. That is, the convex hull of KD-classical pure states along any path from the start vertex to the end vertex in this directed graph is exactly the intersection of the KD-classical state set and the linear space spanned by these path-associated KD-classical pure states. This general result not only yields the $p^r$-dimensional conclusion in a straightforward manner but also encompasses Theorem 2 in the existing work [J. Phys. A, 57, 435303, 2024], demonstrating its generality and inclusiveness.

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↗

arXiv2024

Geometry of Kirkwood-Dirac classical states: A case study based on discrete Fourier transform

The characterization of Kirkwood-Dirac (KD) classicality or non-classicality is very important in quantum information processing. In general, the set of KD classical states with respect to two bases is not a convex polytope[J. Math. Phys. \textbf{65} 072201 (2024)], which makes us interested in finding out in which circumnstances they do form a polytope. In this paper, we focus on the characterization of KD classicality of mixed states for the case where the transition matrix between two bases is a discrete Fourier transform (DFT) matrix in Hilbert space with dimensions $p^2$ and $pq$, respectively, where $p, q$ are prime. For the two particular cases we investigate, the sets of extremal points are finite, implying that the set of KD classical states we characterize forms a convex polytope. We show that for $p^2$ dimensional system, the set $\rm{KD}_{\mathcal{A},\mathcal{B}}^+$ is a convex hull of the set $\rm {pure}({\rm {KD}_{\mathcal{A},\mathcal{B}}^+})$ based on DFT, where $\rm{KD}_{\mathcal{A},\mathcal{B}}^+$ is the set of KD classical states with respect to two bases and $\rm {pure}({\rm {KD}_{\mathcal{A},\mathcal{B}}^+})$ is the set of all the rank-one projectors of KD classical pure states with respect to two bases. In $pq$ dimensional system, we believe that this result also holds. Unfortunately, we do not completely prove it, but some meaningful conclusions are obtained about the characterization of KD classicality.

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↗

arXiv2023

Characterizing Kirkwood-Dirac nonclassicality and uncertainty diagram based on discrete Fourier transform

In this paper, we investigate the Kirkwood-Dirac nonclassicality and uncertainty diagram based on discrete Fourier transform (DFT) in a $d$ dimensional system. The uncertainty diagram of complete incompatibility bases $\mathcal {A},\mathcal {B}$ are characterized by De Bièvre [arXiv: 2207.07451]. We show that for the uncertainty diagram of the DFT matrix which is a transition matrix from basis $\mathcal {A}$ to basis $\mathcal {B}$, there is no ``hole" in the region of the $(n_{\mathcal {A}}, n_{\mathcal {B}})$-plane above and on the line $n_{\mathcal {A}}+n_{\mathcal {B}}\geq d+1$, whether the bases $\mathcal {A},\mathcal {B}$ are not complete incompatible bases or not. Then we present that the KD nonclassicality of a state based on the DFT matrix can be completely characterized by using the support uncertainty relation $n_{\mathcal {A}}(ψ)n_{\mathcal {B}}(ψ)\geq d$, where $n_{\mathcal {A}}(ψ)$ and $n_{\mathcal {B}}(ψ)$ count the number of nonvanishing coefficients in the basis $\mathcal {A}$ and $\mathcal {B}$ representations, respectively. That is, a state $|ψ\rangle$ is KD nonclassical if and only if $n_{\mathcal {A}}(ψ)n_{\mathcal {B}}(ψ)> d$, whenever $d$ is prime or not. That gives a positive answer to the conjecture in [Phys. Rev. Lett. \textbf{127}, 190404 (2021)].

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↗

arXiv2015

Constructing locally indistinguishable orthogonal product bases in an $m \otimes n$ system

Recently, Zhang et al [Phys. Rev. A 92, 012332 (2015)] presented $4d-4$ orthogonal product states that are locally indistinguishable and completable in a $d\otimes d$ quantum system. Later, Zhang et al. [arXiv: 1509.01814v2 (2015)] constructed $2n-1$ orthogonal product states that are locally indistinguishable in $m\otimes n$ ($3\leq m \leq n$). In this paper, we construct a locally indistinguishable and completable orthogonal product basis with $4p-4$ members in a general $m\otimes n$ ($3\leq m \leq n$) quantum system, where $p$ is an arbitrary integer from $3$ to $m$, and give a very simple but quite effective proof for its local indistinguishability. Specially, we get a completable orthogonal product basis with $8$ members that cannot be locally distinguished in $m\otimes n$ ($3\leq m \leq n$) when $p=3$. It is so far the smallest completable orthogonal product basis that cannot be locally distinguished in a $m\otimes n$ quantum system. On the other hand, we construct a small locally indistinguishable orthogonal product basis with $2p-1$ members, which is maybe uncompletable, in $m\otimes n$ ($3\leq m \leq n$ and $p$ is an arbitrary integer from $3$ to $m$). We also prove its local indistinguishability. As a corollary, we give an uncompletable orthogonal product basis with $5$ members that are locally indistinguishable in $m\otimes n$ ($3\leq m \leq n$). All the results can lead us to a better understanding of the structure of a locally indistinguishable product basis in $m \otimes n$.

quant-ph↗

arXiv2014

Cryptanalysis and improvement of a quantum-communication-based online shopping mechanism

Recently, Chou et al. [Electron Commer Res, DOI 10.1007/s10660-014-9143-6] presented a novel controlled quantum secure direct communication protocol which can be used for online shopping. The authors claimed that their protocol was immune to the attacks from both external eavesdropper and internal betrayer. However, we find that this protocol is vulnerable to the attack from internal betrayer. In this paper, we analyze the security of this protocol to show that the controller in this protocol is able to eavesdrop the secret information of the sender (i.e., the customer's shopping information), which indicates that it cannot be used for secure online shopping as the authors expected. Moreover, an improvement to resist the controller's attack is proposed.

quant-ph↗