We use the frustrated XY model approximation of BEC in a rotating optical lattice and formulate the problem of the ground state in terms of eigenvectors and eigenvalues of frustrated adjacency matrix (coupling matrix). By using this formulation, we show that there is a lower bound for ground state energy in terms of maximum eigenvalue of this matrix.

arXiv:1211.4121Nov 17, 20120 citations

Quantum Information Processing

Local discrimination of lattice states via adjacent matrix

Ying‐Hui Yang, Qi-Yue Zhao, Pei-Ying Chen, Shi-Jiao Geng, Jiangtao Yuan

Published May 31, 2024• 2 citations

Publisher

DOI: 10.1007/s11128-024-04436-4

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p

being a prime and

r

being an integer. Based on the partitions of qudit lattice unitaries into commuting sets, we present a sufficient condition for local discrimination of qudit lattice states, in which the commutativity plays an efficient role. It turns out that any set of

l

qudit lattice states with $2\ensuremath{\le}l\ensuremath{\le}{p}^{r}$, including $k\ensuremath{\le}l$ mutually commuting qudit lattice unitaries and satisfying $l(l\ensuremath{-}1)\ensuremath{-}(k+1)(k\ensuremath{-}2)\ensuremath{\le}2{p}^{r}$, can be locally distinguished, not only extending Fan's result [H. Fan, Phys. Rev. Lett. 92, 177905 (2004)] to the prime power quantum system but also involving the local discrimination of a larger number of maximally entangled states.

\mathcal{S}

of generalized Bell states. In fact, we get an efficient criterion. That is, if the difference set $\mathrm{\ensuremath{\Delta}}\mathcal{S}$ of

\mathcal{S}

is disjoint with or completely contained in some MCS, then the set

\mathcal{S}

is locally distinguishable. Furthermore, we give a useful characterization of MCS for arbitrary dimensions, which provides great convenience for detecting the local discrimination of generalized Bell states. Our method can be generalized to more general settings which contain the lattice qudit basis. The results of Fan [Phys. Rev. Lett. 92, 177905 (2004)], Tian et al. [Phys. Rev. A 92, 042320 (2015)], and a recent work Yuan et al. [arXiv:2109.07390] can be deduced as special cases of our result.