Quantum metrology with imperfect states and detectors

TLDR

Quantum enhancements of precision in metrology can be compromised by system imperfections, but optimizing the input state can render it robust, albeit at the cost of difficult preparation. The study aims to identify the major sources of imperfection in an optical sensor: input state preparation inefficiency, sensor losses, and detector inefficiency. The authors analyze these imperfections by modeling input state preparation inefficiency, sensor losses, and detector inefficiency in an optical interferometric sensor. They find that sensor losses are the least damaging to surpass the standard quantum limit, that feasible photonic states with photon‑number‑resolving detectors can reach the Heisenberg limit without losses and near‑optimal precision with realistic losses, and they provide bounds on the trade‑off among the three imperfection sources to enable true quantum‑enhanced optical metrology.

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.