Balancing efficiencies by squeezing in realistic eight-port homodyne detection

TL;DR

This paper explores methods to measure covariant phase observables with realistic eight-port homodyne detectors, addressing efficiency imbalances and proposing strategies to optimize measurement accuracy using beam splitters and squeezed vacuum states.

Contribution

It introduces techniques to balance detector efficiencies and enhance measurement fidelity of covariant phase observables with practical, implementable solutions.

Findings

Balancing efficiencies with a beam splitter is effective but reduces overall efficiency.

Using a squeezed vacuum improves efficiency compared to passive methods.

The proposed methods are feasible with current technology.

Abstract

We address measurements of covariant phase observables (CPOs) by means of realistic eight-port homodyne detectors. We do not assume equal quantum efficiencies for the four photodetectors and investigate the conditions under which the measurement of a CPO may be achieved. We show that balancing the efficiencies using an additional beam splitter allows us to achieve a CPO at the price of reducing the overall effective efficiency, and prove that it is never a smearing of the ideal CPO achievable with unit quantum efficiency. An alternative strategy based on employing a squeezed vacuum as a parameter field is also suggested, which allows one to increase the overall efficiency in comparison to the passive case using only a moderate amount of squeezing. Both methods are suitable for implementantion with current technology.