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The power of random measurements: measuring Tr(\rho^n) on single copies of \rho
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While it is known that Tr(\rho^n) can be measured directly (i.e., without first reconstructing the density matrix) by performing joint measurements on n copies of the same state rho, it is shown here that random measurements on single copies suffice, too. Averaging over the random measurements directly yields estimates of Tr(\rho^n), even when it is not known what measurements were actually performed (so that one cannot reconstruct \rho).
Forward citations
Cited by 2 Pith papers
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Scrambling Enabled Entropy Accumulation in Open Quantum Systems
A weak probe coupled to an open quantum system accumulates a finite Rényi entropy increase only when the system is in the scrambling phase, vanishing in the dissipative phase as the probe coupling goes to zero.
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Kinematic budget of quantum correlations
Global and marginal purities alone are claimed to place any state in a two-dimensional kinematic diagram whose boundary crossings certify NPT entanglement, steering, Bell nonlocality, and bounds on magic.
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