ON the Number of Elements Needed in a POVM Attaining the Accessible Information
We investigate an symmetric set of three quantum states in three dimensions with interesting properties, which we call the lifted trine states. We show that for the ensemble consisting of the three lifted trine states taken with equal probabilities, the POVM measurement realizing the accessible information must contain six projectors, giving a counter-example to a conjecture of Levitin.
KeywordsQuantum measurement accessible information POVM’s
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