quantum bell-ziv-zakai bounds and heisenberg limits for waveform estimation
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2015
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Abstract
We propose quantum versions of the Bell-Ziv-Zakai lower bounds for the error in multiparameter estimation. As an application, we consider measurement of a time-varying optical phase signal with stationary Gaussian prior statistics and a power-law spectrum ∼1/|ω|^{p}, with p>1. With no other assumptions, we show that the mean-square error has a lower bound scaling as 1/N^{2(p-1)/(p+1)}, where N is the time-averaged mean photon flux. Moreover, we show that this scaling is achievable by sampling and interpolation, for any p>1. This bound is thus a rigorous generalization of the Heisenberg limit, for measurement of a single unknown optical phase, to a stochastically varying optical phase.
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berry2015physicalquantum
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| Authors | ;Dominic W. Berry;Mankei Tsang;Michael J. W. Hall;Howard M. Wiseman |
| Journal | american journal of transplantation |
| Year | 2015 |
| DOI |
10.1103/PhysRevX.5.031018
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