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Editors contains: "Kohayakawa, Y."

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  1. ; (, LATIN 2020: Theoretical Informatics)
    Kohayakawa, Y.; Miyazawa, F.K. (Ed.)
    In this work we are interested in the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given n copies of an unknown mixed quantum state ϱ on Cd⊗Cd , and one wants to test whether ϱ is separable or ϵ -far from all separable states in trace distance. We prove that n=Ω(d2/ϵ2) copies are necessary to test separability, assuming ϵ is not too small, viz. ϵ=Ω(1/d−−√) . We also study completely positive distributions on the grid [d]×[d] , as a classical analogue of separable states. We analogously prove that Ω(d/ϵ2) samples from an unknown distribution p are necessary to decide whether p is completely positive or ϵ -far from all completely positive distributions in total variation distance. 
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