期刊
PHYSICAL REVIEW A
卷 80, 期 5, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.80.052306
关键词
boson systems; error analysis; geometry; measurement theory; noise; perturbation theory; quantum entanglement; symmetry
In this paper, we present progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state admitting an N Bose-symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from N Bose-symmetric extensions with positive partial transpose (PPT) decreases at least as fast as O(1/N-2). From these results, we derive upper bounds on the time and space complexity of the weak membership problem of separability when attacked via algorithms that search for PPT-symmetric extensions. Finally, we show how to estimate the error we incur when we approximate the set of separable states by the set of (PPT) N-extendable quantum states in order to compute the maximum average fidelity in pure state estimation problems, the maximal output purity of quantum channels, and the geometric measure of entanglement.
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