arXiv subjects

Hui-Juan Zuo

Publications and source records attributed to Hui-Juan Zuo.

11 recordsLinked to original sources

arXiv2026

Activate genuine nonlocality from distinguishable sets in tripartite systems

A set of orthogonal quantum states in multipartite systems is of genuine nonlocality if it is locally indistinguishable in every bipartition. If it is locally reducible when the parties are separated, we say that it has genuine nonlocality of type~\uppercase\expandafter{\romannumeral 1}; otherwise, it has genuine nonlocality of type~\uppercase\expandafter{\romannumeral 2}. For a locally distinguishable set without local redundancy, if there exist some orthogonality preserving local measurements such that each outcome leads to a locally indistinguishable set, then we say that it exhibits the activation of nonlocality. We activate type-\uppercase\expandafter{\romannumeral 1} and type-\uppercase\expandafter{\romannumeral 2} genuine nonlocality of orthogonal product state sets in tripartite systems. In particular, we tackle the local irredundancy problem with partial trace operation and $p$-ary numeral systems to significantly simplify the proofs. Our results also address the open question raised by S. Bandyopadhyay \textit{et al.}[\href{https://link.aps.org/doi/10.1103/PhysRevA.104.L050201}{Phys. Rev. A \textbf{104}, L050201 (2021)}]. Furthermore, we observe the activation of hidden genuine nonlocality in multipartite systems, which highlights the applications of nonlocality based on state discrimination in different practical scenarios.

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arXiv2024

Unextendible and strongly uncompletable product bases

In 2003, DiVincenzo {\it et al}. put forward the question that whether there exists an unextendible product basis (UPB) which is an uncompletable product basis (UCPB) in every bipartition [\href{https://link.springer.com/article/10.1007/s00220-003-0877-6}{DiVincenzo {\it et al}. Commun. Math. Phys. \textbf{238}, 379-410(2003)}]. Recently, Shi {\it et al}. presented a UPB in tripartite systems that is also a strongly uncompletable product basis (SUCPB) in every bipartition [\href{https://iopscience.iop.org/article/10.1088/1367-2630/ac9e14}{Shi {\it et al}. New J. Phys. \textbf{24}, 113-025 (2022)}]. However, whether there exist UPBs that are SUCPBs in only one or two bipartitions remains unknown. We provide a sufficient condition for the existence of SUCPBs based on a quasi U-tile structure. We analyze all possible cases about the relationship between UPBs and SUCPBs in tripartite systems. In particular, we construct a UPB with smaller size $d^3-3d^2+1$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}$, which is an SUCPB in every bipartition and has a smaller cardinality than the existing one.

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arXiv2024

Genuinely nonlocal sets without entanglement in multipartite systems

A set of multipartite orthogonal states is genuinely nonlocal if it is locally indistinguishable in every bipartition of the subsystems. If the set is locally reducible, we say it has genuine nonlocality of type \uppercase\expandafter{\romannumeral 1}. Otherwise, we say it has genuine nonlocality of type \uppercase\expandafter{\romannumeral 2}. Due to the complexity of the problem, the construction of genuinely nonlocal sets in general multipartite systems has not been completely solved so far. In this paper, we first provide a nonlocal set of product states in bipartite systems. We obtain a genuinely nonlocal set of type~\uppercase\expandafter{\romannumeral 1} without entanglement in general $n$-partite systems $\otimes^{n}_{i=1}\mathbb{C}^{d_{i}}$ $[3\leq (d_{1}-1)\leq d_{2}\leq \cdots\leq d_{n},n\geq3]$. Then we present two constructions with genuine nonlocality of type~\uppercase\expandafter{\romannumeral 2} in $\mathbb{C}^{d_{1}}\otimes\mathbb{C}^{d_{2}}\otimes\mathbb{C}^{d_{3}}$ $(3\leq d_{1}\leq d_{2}\leq d_{3})$ and $\otimes^{n}_{i=1}\mathbb{C}^{d_{i}}$ $(3\leq d_{1}\leq d_{2}\leq \cdots\leq d_{n},n\geq4)$. Our results further positively answer the open problem that there does exist a genuinely nonlocal set of type~\uppercase\expandafter{\romannumeral2} in multipartite systems [M. S. Li, Y. L. Wang, F. Shi, and M. H. Yung, J. Phys. A: Math. Theor. 54, 445301 (2021)] and highlight its related applications in quantum information processing.

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arXiv2024

Strongest nonlocal sets with minimum cardinality in multipartite systems

Quantum nonlocality based on state discrimination describes the global property of the set of orthogonal states and has a wide range of applications in quantum cryptographic protocols. Strongest nonlocality is the strongest form of quantum nonlocality recently presented in multipartite quantum systems: a set of orthogonal multipartite quantum states is strongest nonlocal if the only orthogonality-preserving local measurements on the subsystems in every bipartition are trivial. In this work, we found a construction of strongest nonlocal sets in $\mathbb{C}^{d_{1}}\otimes \mathbb{C}^{d_{2}}\otimes \mathbb{C}^{d_{3}}$ $(2\leq d_{1}\leq d_{2}\leq d_{3})$ of size $d_2d_3+1$ without stopper states. Then we obtain the strongest nonlocal sets in four-partite systems with $d^3+1$ orthogonal states in $\mathbb{C}^d\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}$ $(d\geq2)$ and $d_{2}d_{3}d_{4}+1$ orthogonal states in $\mathbb{C}^{d_{1}}\otimes \mathbb{C}^{d_{2}}\otimes \mathbb{C}^{d_{3}}\otimes \mathbb{C}^{d_{4}}$ $(2\leq d_{1}\leq d_{2}\leq d_{3}\leq d_{4})$. Surprisingly, the number of the elements in all above constructions perfectly reaches the recent conjectured lower bound and reduces the size of the strongest nonlocal set in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}$ of [\href{https://doi.org/10.1103/PhysRevA.108.062407}{Phys. Rev. A \textbf{108}, 062407 (2023)}] by $d-2$. In particular, the general optimal construction of the strongest nonlocal set in four-partite system is completely solved for the first time, which further highlights the theory of quantum nonlocality from the perspective of state discrimination.

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arXiv2024

Strongest nonlocal sets with minimum cardinality in tripartite systems

Strong nonlocality, proposed by Halder {\it et al}. [\href{https://doi.org/10.1103/PhysRevLett.122.040403}{Phys. Rev. Lett. \textbf{122}, 040403 (2019)}], is a stronger manifestation than quantum nonlocality. Subsequently, Shi {\it et al}. presented the concept of the strongest nonlocality [\href{https://doi.org/10.22331/q-2022-01-05-619}{Quantum \textbf{6}, 619 (2022)}]. Recently, Li and Wang [\href{https://doi.org/10.22331/q-2023-09-07-1101}{Quantum \textbf{7}, 1101 (2023)}] posed the conjecture about a lower bound to the cardinality of the strongest nonlocal set $\mathcal{S}$ in $\otimes _{i=1}^{n}\mathbb{C}^{d_i}$, i.e., $|\mathcal{S}|\leq \max_{i}\{\prod_{j=1}^{n}d_j/d_i+1\}$. In this work, we construct the strongest nonlocal set of size $d^2+1$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}\otimes \mathbb{C}^{d}$. Furthermore, we obtain the strongest nonlocal set of size $d_{2}d_{3}+1$ in $\mathbb{C}^{d_1}\otimes \mathbb{C}^{d_2}\otimes \mathbb{C}^{d_3}$. Our construction reaches the lower bound, which provides an affirmative solution to Li and Wang's conjecture. In particular, the strongest nonlocal sets we present here contain the least number of orthogonal states among the available results.

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arXiv2023

Locally stable sets with minimum cardinality

The nonlocal set has received wide attention over recent years. Shortly before, Li and Wang arXiv:2202.09034 proposed the concept of a locally stable set: the only possible orthogonality preserving measurement on each subsystem is trivial. Locally stable sets present stronger nonlocality than those sets that are just locally indistinguishable. In this work, we focus on the constructions of locally stable sets in multipartite quantum systems. First, two lemmas are put forward to prove that an orthogonality-preserving local measurement must be trivial. Then we present the constructions of locally stable sets with minimum cardinality in bipartite quantum systems $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$ $(d\geq 3)$ and $\mathbb{C}^{d_{1}}\otimes \mathbb{C}^{d_{2}}$ $(3\leq d_{1}\leq d_{2})$. Moreover, for the multipartite quantum systems $(\mathbb{C}^{d})^{\otimes n}$ $(d\geq 2)$ and $\otimes^{n}_{i=1}\mathbb{C}^{d_{i}}$ $(3\leq d_{1}\leq d_{2}\leq\cdots\leq d_{n})$, we also obtain $d+1$ and $d_{n}+1$ locally stable orthogonal states respectively. Fortunately, our constructions reach the lower bound of the cardinality on the locally stable sets, which provides a positive and complete answer to an open problem raised in arXiv:2202.09034 .

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arXiv2023

Quantum $k$-uniform states from quantum orthogonal arrays

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called $k$-uniform states whose every reductions to $k$ parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength 2 with levels of prime power, as well as some constructions of strength 3. As a consequence, we give infinite classes of 2-uniform states of $N$ systems with dimension of prime power $d\geq 2$ for arbitrary $N\geq 5$; 3-uniform states of $N$-qubit systems for arbitrary $N\geq 6$ and $N\neq 7,8,9,11$; 3-uniform states of $N$ systems with dimension of prime power $d\geq 7$ for arbitrary $N\geq 7$.

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arXiv2022

Nonlocality without entanglement in general multipartite quantum systems

The construction of nonlocal sets of quantum states has attracted much attention in recent years. We first introduce two Lemmas related to the triviality of orthogonality-preserving local measurements. Then we propose a general construction of nonlocal set of $n(d-1)+1$ orthogonal product states in $(\mathbb{C}^{d})^{\otimes n}$. The sets of nonlocal orthogonal product states are also put forward for the multipartite quantum systems with arbitrary dimensions. Our novel construction gives rise to nonlocal sets of orthogonal product states with much less members and thus reveals the phenomenon of nonlocality without entanglement more efficiently.

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arXiv2022

Mutually unbiased maximally entangled bases from difference matrices

Based on maximally entangled states, we explore the constructions of mutually unbiased bases in bipartite quantum systems. We present a new way to construct mutually unbiased bases by difference matrices in the theory of combinatorial designs. In particular, we establish $q$ mutually unbiased bases with $q-1$ maximally entangled bases and one product basis in $\mathbb{C}^q\otimes \mathbb{C}^q$ for arbitrary prime power $q$. In addition, we construct maximally entangled bases for dimension of composite numbers of non-prime power, such as five maximally entangled bases in $\mathbb{C}^{12}\otimes \mathbb{C}^{12}$ and $\mathbb{C}^{21}\otimes\mathbb{C}^{21}$, which improve the known lower bounds for $d=3m$, with $(3,m)=1$ in $\mathbb{C}^{d}\otimes \mathbb{C}^{d}$. Furthermore, we construct $p+1$ mutually unbiased bases with $p$ maximally entangled bases and one product basis in $\mathbb{C}^p\otimes \mathbb{C}^{p^2}$ for arbitrary prime number $p$.

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arXiv2022

Novel Constructions of Mutually Unbiased Tripartite Absolutely Maximally Entangled Bases

We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in $\mathbb{C}^{d} \otimes \mathbb{C}^{d} \otimes \mathbb{C}^{d}$ based on mutually orthogonal Latin squares. Then we generalize the approach to the case of $\mathbb{C}^{d_{1}} \otimes \mathbb{C}^{d_{2}} \otimes \mathbb{C}^{d_{1}d_{2}}$ by mutually weak orthogonal Latin squares. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably presented with generality. Detailed examples in $\mathbb{C}^{3} \otimes \mathbb{C}^{3} \otimes \mathbb{C}^{3},$ $\mathbb{C}^{2} \otimes \mathbb{C}^{2} \otimes \mathbb{C}^{4}$ and $\mathbb{C}^{2} \otimes \mathbb{C}^{5} \otimes \mathbb{C}^{10}$ are provided to illustrate the advantages of our approach.

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arXiv2021

Nonlocal sets of orthogonal multipartite product states with less members

We study the constructions of nonlocal orthogonal product states in multipartite systems that cannot be distinguished by local operations and classical communication. We first present two constructions of nonlocal orthogonal product states in tripartite systems $\mathcal{C}^{d}\otimes\mathcal{C}^{d}\otimes\mathcal{C}^{d}~(d\geq3)$ and $\mathcal{C}^d\otimes \mathcal{C}^{d+1}\otimes \mathcal{C}^{d+2}~(d\geq 3)$. Then for general tripartite quantum system $\mathcal{C}^{n_{1}}\otimes\mathcal{C}^{n_{2}}\otimes\mathcal{C}^{n_{3}}$ $(3\leq n_{1}\leq n_{2}\leq n_{3})$, we obtain $2(n_{2}+n_{3}-1)-n_{1}$ nonlocal orthogonal product states. Finally, we put forward a new construction approach in $\mathcal{C}^{d_{1}}\otimes \mathcal{C}^{d_{2}}\otimes\cdots\otimes \mathcal{C}^{d_{n}}$ $(d_1,d_2,\cdots d_n\geq3,\, n>6)$ multipartite systems. Remarkably, our indistinguishable sets contain less nonlocal product states than the existing ones, which improves the recent results and highlights their related applications in quantum information processing.

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