Optimality of feedback control for qubit purification under inefficient measurement

TL;DR

This paper demonstrates that optimal feedback control can significantly speed up qubit purification even at measurement efficiencies below 0.5, challenging previous assumptions and enabling more practical quantum system improvements.

Contribution

It introduces a global optimal feedback control strategy for qubit purification that works effectively at low measurement efficiencies, using the Bloch vector length as a key metric.

Findings

Speedup achievable at efficiencies below 0.5

Backward iteration algorithm finds global optimal strategy

Potential for experimental implementation

Abstract

A quantum system may be purified, i.e., projected into a pure state, faster if one applies feedback operations during the measurement process. However existing results suggest that such an enhancement is only possible when the measurement efficiency exceeds 0.5, which is difficult to achieve experimentally. We address the task of finding the global optimal feedback control for purifying a single qubit in the presence of measurement inefficiency. We use the Bloch vector length, a more physical and practical quantity than purity, to assess the quality of the state, and employ a backward iteration algorithm to find the globally optimal strategy. Our results show that a speedup is available for quantum efficiencies well below 0.5, which opens the possibility of experimental implementation in existing systems.