Indistinguishability of pure orthogonal product states by LOCC
We construct two sets of incomplete and extendible quantum pure orthogonal product states
(POPS) in general bipartite high-dimensional quantum systems, which are all
indistinguishable by local operations and classical communication. The first set of POPS is
composed of two parts which are C^ m ⊗ C^ n_1 C m⊗ C n 1 with 5 ≤ m ≤ n_1 5≤ m≤ n 1
and C^ m ⊗ C^ n_2 C m⊗ C n 2 with 5 ≤ m ≤ n_2 5≤ m≤ n 2, where n_1 n 1 is odd and
n_2 n 2 is even. The second one is in C^ m ⊗ C^ n C m⊗ C n (m, n ≥ 4)(m, n≥ 4). Some …
(POPS) in general bipartite high-dimensional quantum systems, which are all
indistinguishable by local operations and classical communication. The first set of POPS is
composed of two parts which are C^ m ⊗ C^ n_1 C m⊗ C n 1 with 5 ≤ m ≤ n_1 5≤ m≤ n 1
and C^ m ⊗ C^ n_2 C m⊗ C n 2 with 5 ≤ m ≤ n_2 5≤ m≤ n 2, where n_1 n 1 is odd and
n_2 n 2 is even. The second one is in C^ m ⊗ C^ n C m⊗ C n (m, n ≥ 4)(m, n≥ 4). Some …
Abstract
We construct two sets of incomplete and extendible quantum pure orthogonal product states (POPS) in general bipartite high-dimensional quantum systems, which are all indistinguishable by local operations and classical communication. The first set of POPS is composed of two parts which are with and with , where is odd and is even. The second one is in . Some subsets of these two sets can be extended into complete sets that local indistinguishability can be decided by noncommutativity which quantifies the quantumness of a quantum ensemble. Our study shows quantum nonlocality without entanglement.
Springer
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