Phase estimation with photon number constraint

Abstract

Many researches proposed the use of the noon state as the input state for phase estimation, which is one topic of quantum metrology. This is because the input noon state provides the maximum Fisher information at the specific point. However, the Fisher information does not necessarily give the attainable bound for estimation error. In this paper, we adopt the local asymptotic mini-max criterion as well as the mini-max criterion, and show that the maximum Fisher information does not give the attainable bound for estimation error under these criteria in the phase estimation. We also propose the optimal input state under the constraints for photon number of the input state instead of the noon state.

Several typos are fixed. New section "ANALYSIS ON NOON STATE" is added

References in corpus (11)

• Quantum-enhanced measurements: beating the standard quantum limit
• Quantum metrology
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• Quantum metrology for non-linear phase shifts with entangled coherent states
• Sub-Heisenberg estimation strategies are ineffective
• Optical interferometry in the presence of large phase diffusion
• Ultimate limits to quantum metrology and the meaning of the Heisenberg limit
• Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation
• Quantum measurement bounds beyond the uncertainty relations
• Phase sensitivity bounds for two-mode interferometers
• Quantum metrology: why entanglement?
• Quantum parameter estimation affected by unitary disturbance
• Achieving Heisenberg scaling with maximally entangled states: an analytic upper bound for the attainable root mean square error
• Experimental Quantum Enhanced Optical Interferometry
• Fourier Analytic Approach to Quantum Estimation of Group Action
• Enhancing phase sensitivity with number state filtered coherent states
• The Cramér-Rao approach and global quantum estimation of bosonic states