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8 May 2012 Probing correlation in quantum arrays
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Abstract
We consider the problem of identifying the degree of correlation θ in the depolarization rates of an array of qubits, such as might be found in a holding register in a quantum information processing architecture. We treat this as a problem in quantum channel identification and use the quantum Fisher information about θ in the channel output to compare different candidate probe states. We consider channel probes in general pure N-qubit cat states and find that partial entanglement is always suboptimal; the best cat probe state is either separable or maximally entangled, and we lay out for any given depolarizing rate p and correlation θ, the (p, θ)-regions for which separable and maximally entangled probes each yield the most information. In the case of very large qubit arrays, we find that the quantum Fisher information obtained about θ using any pure cat probe state is asymptotically independent of the state and identically equal to the information available about a classical coin's bias from a single coin toss. Finally, we turn our attention to arrays of N qudits (with common dimension D) that are depolarizing with some correlation θ. We consider both separable and maximally entangled cat probe states and find and compare their quantum Fisher informations in both the large N and large D regimes.
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Theodore J. Yoder and Michael R. Frey "Probing correlation in quantum arrays", Proc. SPIE 8400, Quantum Information and Computation X, 840002 (8 May 2012); https://doi.org/10.1117/12.919135
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