Quantum decoherence parameter estimation in an interferometer

David E. Pritchard

X. N. Feng, De He, L. F. Wei

Entanglement is an important quantum resource to achieve high-sensitivity quantum metrology. However, the rapid decoherence of quantum entangled states, due to the unavoidable environmental noise, results in practically the unwanted sharp drop of the measurement sensitivity. To overcome such a difficulty, here we propose a spin-oscillator hybrid quantum interferometer to achieve the desirable precise estimation of the parameter encoded in the vibrations of the oscillator. Differing from the conventional two-mode quantum interferometers input by the two-mode NOON state or entangled coherent states, whose achievable sensitivities are strongly limited by the decoherence of the entangled vibrational states, we demonstrate that the present interferometer, input by a spin-dependent two-mode entangled state, possesses a manifest advantage; i.e., the measurement sensitivity of the estimated parameter is not influenced by the decoherence from the spin-oscillator entanglement. This is because, by applying a spin-oscillator disentangled operation, the information of the estimated parameter encoded originally in the vibrational degrees can be effectively transferred into the spin degree and then can be sensitively estimated by the precise spin-state population measurements. As consequence, the proposed hybrid quantum interferometer possesses manifest robustness against the particle losses of the vibrational modes. Interestingly, the achieved phase measurement sensitivity can still surpass the standard quantum limit obviously, even if a relatively large number of particle loss occurs in one of the two modes. The potential application of the proposed spin-oscillator hybrid quantum interferometer is also discussed.

Corsin Pfister

Walker D. Larson, Bahaa E. A. Saleh

The supersensitivity attained in quantum phase estimation is known to be compromised in the presence of decoherence. This is particularly patent at blind spots---phase values at which sensitivity is totally lost. One remedy is to use a precisely known reference phase to shift the operation point to a less vulnerable phase value. Since this is not always feasible, we present here an alternative approach based on combining the probe with an ancillary degree of freedom containing adjustable parameters to create an entangled quantum state of higher dimension. We validate this concept by simulating a configuration of a Mach-Zehnder interferometer with a two-photon probe and a polarization ancilla of adjustable parameters, entangled at a polarizing beam splitter. At the interferometer output, the photons are measured after an adjustable unitary transformation in the polarization subspace. Through calculation of the Fisher information and simulation of an estimation procedure, we show that optimizing the adjustable polarization parameters using an adaptive measurement process provides globally supersensitive unbiased phase estimates for a range of decoherence levels, without prior information or a reference phase.

Piotr Szańkowski, Marek Trippenbach, Jan Chwedeńczuk

We demonstrate that memory in an $N$-qubit system subjected to decoherence, is a potential resource for the slowdown of the entanglement decay. We show that this effect can be used to retain the sub-shot-noise sensitivity of the parameter estimation in quantum interferometry. We calculate quantum Fisher information, which sets the ultimate bound for the precision of the estimation. We also derive the sensitivity of such a noisy interferometer, when the phase is either estimated from the measurements of the population imbalance or from the one-body density.

Akira Matsumura, Taishi Ikeda, Shingo Kukita