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A Hierarchy for Replica Quantum Advantage

by   Sitan Chen, et al.
Harvard University
berkeley college
California Institute of Technology

We prove that given the ability to make entangled measurements on at most k replicas of an n-qubit state ρ simultaneously, there is a property of ρ which requires at least order 2^n measurements to learn. However, the same property only requires one measurement to learn if we can make an entangled measurement over a number of replicas polynomial in k, n. Because the above holds for each positive integer k, we obtain a hierarchy of tasks necessitating progressively more replicas to be performed efficiently. We introduce a powerful proof technique to establish our results, and also use this to provide new bounds for testing the mixedness of a quantum state.


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