Measuring polynomial functions of states

Details Measuring polynomial functions of states Measuring polynomial functions of states

2004-01-12

arxiv.org/abs/quant-ph/0401067v2

Quantum Information and Computation 4, 401 (2004).

Physics

Quantum Physics

Minor revisions in response to referee comments

Scientific paper

In this paper I show that any $m$th-degree polynomial function of the elements of the density matrix $\rho$ can be determined by finding the expectation value of an observable on $m$ copies of $\rho$, 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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