Ziv-Zakai Error Bounds for Quantum Parameter Estimation
arXiv:1111.3568 · doi:10.1103/PhysRevLett.108.230401
Abstract
I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cramér-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a "Heisenberg" error limit that scales with the average energy and a limit similar to the quantum Cramér-Rao bound that scales with the energy variance. These results are further illustrated by applying the bound to a few examples of optical phase estimation, which show that a quantum Ziv-Zakai bound can be much higher and thus tighter than a quantum Cramér-Rao bound for states with highly non-Gaussian photon-number statistics in certain regimes and also stay close to the latter where the latter is expected to be tight.
v1: preliminary result, 3 pages; v2: major update, 4 pages + supplementary calculations, v3: another major update, added proof of "Heisenberg" limit, v4: accepted by PRL
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