Fidelity of Quantum Interferometers

Abstract

For a generic interferometer, the conditional probability density distribution, $p(\varphi |m)$, for the phase $\varphi$ given measurement outcome $m$, will generally have multiple peaks. Therefore, the phase sensitivity of an interferometer cannot be adequately characterized by the standard deviation, such as $\Delta \varphi \sim 1/\sqrt{N}$ (the standard limit), or $\Delta \varphi \sim 1/N$ (the Heisenberg limit). We propose an alternative measure of phase sensitivity--the fidelity of an interferometer--defined as the Shannon mutual information between the phase shift $\varphi$\ and the measurement outcomes $m$. As an example application of interferometer fidelity, we consider a generic optical Mach-Zehnder interferometer, used as a sensor of a classical field. We find the surprising result that an entangled {\it N00N} state input leads to a lower fidelity than a Fock state input, for the same photon number.

4 pages, 3 figures

References in corpus (9)

• Quantum metrology
• Super-resolving phase measurements with a multi-photon entangled state
• An Atom Michelson Interferometer on a Chip Using a Bose-Einstein Condensate
• Bose-Einstein condensation in a circular waveguide
• Phase Sensitivity of a Mach-Zehnder Interferometer
• Single-photon Sagnac interferometer
• Sagnac interferometry based on ultra-slow polaritons in cold atomic vapors
• Particle-number scaling of the phase sensitivity in realistic Bayesian twin-mode Heisenberg-limited interferometry
• Gyroscopic effects in interference of matter waves

Cited by in corpus (6)

• Quantum states for Heisenberg-limited interferometry
• Evaluation of Counterfactuality in Counterfactual Communication Protocols
• Phase Estimation with Non-Unitary Interferometers: Information as a Metric
• Dispersion and fidelity in quantum interferometry
• Optimal binary strategy for angular displacement estimation based upon fidelity appraisal
• Phase Sensitivity of a Mach-Zehnder Quantum Sensor