Stochastic Heisenberg limit: Optimal estimation of a fluctuating phase

Abstract

The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramer-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as 1/omega^p with p>1, the minimum mean-square error in any (single-time) phase estimate scales as N^{-2(p-1)/(p+1)}, where N is the photon flux. This gives the usual Heisenberg limit for a constant phase (as the limit p--> infinity) and provides a stochastic Heisenberg limit for fluctuating phases. For p=2 (Brownian motion), this limit can be attained by phase tracking.

5+4 pages, to appear in Physical Review Letters

References in corpus (6)

• Quantum-enhanced optical phase tracking
• Quantum metrology with open dynamical systems
• Time-Symmetric Quantum Theory of Smoothing
• Quantum theory of optical temporal phase and instantaneous frequency. II. Continuous time limit and state-variable approach to phase-locked loop design
• Collectively enhanced quantum measurements at the Heisenberg limit
• Adaptive phase measurements for narrowband squeezed beams

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