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arXiv · 0807.4108

Phase variance of squeezed vacuum states

Emilio Bagan·Alex Monras·Ramon Munoz-Tapia
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Abstract

We consider the problem of estimating the phase of squeezed vacuum states within a Bayesian framework. We derive bounds on the average Holevo variance for an arbitrary number $N$ of uncorrelated copies. We find that it scales with the mean photon number, $n$, as dictated by the Heisenberg limit, i.e., as $n^{-2}$, only for $N>4$. For $N\leq 4$ this fundamental scaling breaks down and it becomes $n^{-N/2}$. Thus, a single squeezed vacuum state performs worse than a single coherent state with the same energy. We find the optimal splitting of a fixed given energy among various copies. We also compute the variance for repeated individual measurements (without classical communication or adaptivity) and find that the standard Heisenberg-limited scaling $n^{-2}$ is recovered for large samples.

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Emilio Bagan, Alex Monras, Ramon Munoz-Tapia. 2008-07-25. Phase variance of squeezed vacuum states. https://doi.org/10.1103/physreva.78.043829

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