Achieving Holevo Bound in Quantum Measurement

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We show that information gain in a qubit measurement is optimal under a Von Neumann measurement. For an initially mixed apparatus kept in touch with a qubit, the conditions for achieving the equality sign of Holevo bound on the information accessible to apparatus are derived. These constraints can be identified as the conditions for the optimization of information gain in a qubit measurement. At the end, we will generalize the idea to qudit measurements using a phase-shift gate.