The effects of time delays in adaptive phase measurements

Abstract

It is not possible to make measurements of the phase of an optical mode using linear optics without introducing an extra phase uncertainty. This extra phase variance is quite large for heterodyne measurements, however it is possible to reduce it to the theoretical limit of log(n)/(4n^2) using adaptive measurements. These measurements are quite sensitive to experimental inaccuracies, especially time delays and inefficient detectors. Here it is shown that the minimum introduced phase variance when there is a time delay of tau is tau/(8n). This result is verified numerically, showing that the phase variance introduced approaches this limit for most of the adaptive schemes using the best final phase estimate. The main exception is the adaptive mark II scheme with simplified feedback, which is extremely sensitive to time delays. The extra phase variance due to time delays is considered for the mark I case with simplified feedback, verifying the tau/2 result obtained by Wiseman and Killip both by a more rigorous analytic technique and numerically.

10 pages, 4 figures, minor changes from published version

References in corpus (3)

• Adaptive single-shot phase measurements: The full quantum theory
• Continuous stochastic Schrodinger equations and localization
• Heterodyne and adaptive phase measurements on states of fixed mean photon number

Cited by in corpus (4)

• Adaptive phase estimation is more accurate than non-adaptive phase estimation for continuous beams of light
• Quantum feedback for rapid state preparation in the presence of control imperfections
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements
• Adaptive Phase Measurements