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Measuring polynomial functions of states

Todd A. Brun
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Abstract

In this paper I show that any $m$th-degree polynomial function of the elements of the density matrix $ρ$ can be determined by finding the expectation value of an observable on $m$ copies of $ρ$, without performing state tomography. Since a circuit exists which can approximate the measurement of any observable, in principle one can find a circuit which will estimate any such polynomial function by averaging over many runs. I construct some simple examples and compare these results to existing procedures.

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Todd A. Brun. 2004-08-30. Measuring polynomial functions of states. https://arxiv.org/abs/quant-ph/0401067

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