Scaling laws for precision in quantum interferometry and bifurcation landscape of optimal state

TL;DR

This paper investigates how phase measurement precision in large-photon quantum interferometry is affected by losses, revealing bifurcation phenomena and a loss-dependent scale for quantum advantage.

Contribution

It introduces a detailed analysis of optimal states under loss, identifying bifurcation behavior and a loss-dependent photon number scale for quantum metrology.

Findings

Optimal states undergo bifurcations with increasing loss or photon number.

A crossover photon number scale $N_c$ determines the loss of supra-classical precision.

Large losses lead to different optimal state structures from previous models.

Abstract

Phase precision in optimal 2-channel quantum interferometry is studied in the limit of large photon number $N\gg 1$, for losses occurring in either one or both channels. For losses in one channel an optimal state undergoes an intriguing sequence of local bifurcations as the losses or the number of photons increase. We further show that fixing the loss paramater determines a scale for quantum metrology -- a crossover value of the photon number $N_c$ beyond which the supra-classical precision is progressively lost. For large losses the optimal state also has a different structure from those considered previously.