Authors: C S Sudheer Kumar
Alice prepares two large qubit-ensembles E1 and E2 in the following states: She individually prepares each qubit of E1 in |0> or |1>, the eigenstates of Pauli-z operator Z, depending on the outcome of an unbiased coin toss. Similarly, she individually prepares each qubit of E2 in |+> or |-> the eigenstates of Pauli-x operator X. Bob, who is aware of the above states preparation procedures, but knows neither which of the two is E1 nor Alice's outcomes of coin tosses, needs to discriminate between the two maximally mixed ensembles. Here we argue that Bob can partially purify the mixed states (E1, E2), using the information supplied by central limit theorem. We will show that, subsequently Bob can discriminate between ensembles E1 and E2 by individually rotating each qubit state about the x-axis on Bloch sphere by a random angle, and then projectively measuring Z. By these operations, the variance of sample mean of Z measurement outcomes corresponding to the ensemble E1 gets reduced. On the other hand, qubit states in E2 are invariant under the x-rotations and therefore the variance remains unaltered. Thus Bob can discriminate between the two maximally mixed ensembles. We analyse the above problem both analytically as well as numerically, and show that the latter supports the former.
Comments: 21 Pages.
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