New parametric entropy inequalities are derived from an accessible-information optimality criterion, reducing the quantum-pyramid conjecture to proving these inequalities.
On the Number of Elements Needed in a POVM Attaining the Accessible Information
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abstract
We investigate a symmetric set of three quantum states in three dimensions having 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 counterexample to a conjecture of Levitin.
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Quantum accessible information and classical entropy inequalities
New parametric entropy inequalities are derived from an accessible-information optimality criterion, reducing the quantum-pyramid conjecture to proving these inequalities.