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- W3011818888 abstract "Nonlocal sets of orthogonal product states (OPSs) are widely used in quantum protocols owing to their good property. Thus a lot of attention are paid to how to construct a nonlocal set of orthogonal product states though it is a difficult problem. In this paper, we propose a novel general method to construct a nonlocal set of orthogonal product states in $mathbb{C}^{d} otimes mathbb{C}^{d}$ for $dgeq3$. We give an ingenious proof for the local indistinguishability of those product states. The set of product states, which are constructed by our method, has a very good structure. Subsequently, we give a construction of nonlocal set of OPSs with smaller members in $mathbb{C}^{d} otimes mathbb{C}^{d}$ for $dgeq3$. On the other hand, we present two construction methods of nonlocal sets of OPSs in $mathbb{C}^{m} otimes mathbb{C}^{n}$, where $mgeq3$ and $ngeq3.$ Furthermore, we propose the concept of isomorphism for two nonlocal sets of OPSs. Our work is of great help to understand the structure and classification of locally indistinguishable OPSs." @default.
- W3011818888 created "2020-03-23" @default.
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- W3011818888 date "2020-03-16" @default.
- W3011818888 modified "2023-09-25" @default.
- W3011818888 title "Novel methods to construct nonlocal sets of orthogonal product states in arbitrary bipartite high-dimensional system" @default.
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- W3011818888 doi "https://doi.org/10.48550/arxiv.2003.08291" @default.
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