Quantum metrology with imperfect states and detectors

TL;DR

This paper analyzes how imperfections like losses and inefficiencies affect quantum optical metrology and proposes strategies to optimize input states and measurement methods to achieve near-Heisenberg limit precision despite these imperfections.

Contribution

It identifies the impact of different imperfections on quantum metrology and demonstrates feasible states and measurement strategies that maintain high precision under realistic conditions.

Findings

Sensor losses are less damaging than input state inefficiency.

Feasible photonic states can reach the Heisenberg limit without losses.

Bounds are provided for the trade-offs between imperfections.

Abstract

Quantum enhancements of precision in metrology can be compromised by system imperfections. These may be mitigated by appropriate optimization of the input state to render it robust, at the expense of making the state difficult to prepare. In this paper, we identify the major sources of imperfection an optical sensor: input state preparation inefficiency, sensor losses, and detector inefficiency. The second of these has received much attention; we show that it is the least damaging to surpassing the standard quantum limit in a optical interferometric sensor. Further, we show that photonic states that can be prepared in the laboratory using feasible resources allow a measurement strategy using photon-number-resolving detectors that not only attains the Heisenberg limit for phase estimation in the absence of losses, but also deliver close to the maximum possible precision in realistic scenarios including losses and inefficiencies. In particular, we give bounds for the trade off between the three sources of imperfection that will allow true quantum-enhanced optical metrology.