It is well-known that the super-sensitivity of phase estimation in two-photon interferometery is diminished by the effect of decoherence. Specific to the paradigm of local phase estimation, any presence of decoherence removes all sensitivity to small shifts in the neighborhood of certain phases. For estimates of the phase difference between two arms of an interferometer using two-photon coincidence measurements, all sensitivity is lost for phase differences in the neighborhood of π/2. The benefit of employing an ancillary optical degree of freedom alongside the principal interfering degree of freedom was recently found to fortify super-sensing two-photon states against the debilitating effect of spectral distinguishability: an effect that reduces the visibility of two-photon interference.
In the present work, we investigate the use of an ancillary degree of freedom when measuring a phase shift by use of a two-photon Mach-Zehnder-interferometer contaminated by a depolarizing channel causing decoherence: an effect that reduces both two-photon and single-photon interference visibility. We model our input state as single photons entering both input ports of an interferometer. The principal interferometer-path modes are coupled to polarization, and decoherence is modeled by replacing the density matrix describing this input with a maximally mixed state with some probability p. We calculate the sensitivity through the quantum fisher information, finding that the process of fortifying input states retains sensing at or above the standard quantum limit in the neighborhood of phase differences around π/2, for all probabilities below 1/4 — an advantage impossible without employing the ancillary degree of freedom.
Walker D. Larson and Bahaa E. A. Saleh, "Ancilla-aided recovery of quantum super-sensitivity diminished by decoherence (Conference Presentation)," Proc. SPIE 10118, Advances in Photonics of Quantum Computing, Memory, and Communication X, 1011810 (Presented at SPIE OPTO: February 03, 2017; Published: 2 June 2017); https://doi.org/10.1117/12.2250977.5397361512001.
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