Phase variance of squeezed vacuum states

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 $N\le 4$ 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.

Minor changes, version to appear in PRA, 8 pages, 2 figures

References in corpus (5)

• Generalized Limits for Single-Parameter Quantum Estimation
• Coherent control of vacuum squeezing in the Gravitational-Wave Detection Band
• Optimal phase measurements with pure Gaussian states
• Quantum-limited metrology with product states
• Quantum limits in the measurement of very small displacements in optical images

Cited by in corpus (2)

• Phase estimation for thermal Gaussian states
• Phase-Covariant Quantum Benchmarks