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We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between the two states, with high probability. This result gives us the first sufficient condition and an information-theoretic solution for the following quantum state distinction problem: given an a priori known ensemble of quantum states, is there a single POVM that gives reasonably large total variation distance between every pair of states from the ensemble? Our random POVM method also gives us the first information-theoretic upper bound on the number of copies required to solve the quantum state identification problem for general ensembles, i.e., given some number of independent copies of a quantum state from an a priori known ensemble, identify the state. The standard quantum approach to solving the hidden subgroup problem (HSP) is a special case of the state identification problem where the ensemble consists of so-called coset states of candidate hidden subgroups. Combining Fourier sampling with our random POVM result gives us single register algor

Author

Sen, Pranab

Published

2005

Language

EN