Optimal phase measurements with pure Gaussian states

Details Optimal phase measurements with pure Gaussian states Optimal phase measurements with pure Gaussian states

2005-09-02

arxiv.org/abs/quant-ph/0509018v2

Phys. Rev. A 73, 033821 (2006)

Physics

Quantum Physics

9 pages. Revised version: two new sections added, revised conclusions. Corrected prose. Corrected references

Scientific paper

10.1103/PhysRevA.73.033821

We analyze the Heisenberg limit on phase estimation for Gaussian states. In the analysis, no reference to a phase operator is made. We prove that the squeezed vacuum state is the most sensitive for a given average photon number. We provide two adaptive local measurement schemes that attain the Heisenberg limit asymptotically. One of them is described by a positive operator-valued measure and its efficiency is exhaustively explored. We also study Gaussian measurement schemes based on phase quadrature measurements. We show that homodyne tomography of the appropriate quadrature attains the Heisenberg limit for large samples. This proves that this limit can be attained with local projective Von Neuman measurements.

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