Rapid-purification protocols for optical homodyning

TL;DR

This paper introduces rapid-purification feedback protocols for optical homodyne detection that accelerate the increase of system purity, with deterministic evolution under strong feedback and improved speed to reach desired purity levels.

Contribution

It develops new rapid-purification protocols for optical homodyne detection, including deterministic and speed-up variants, and analyzes their performance considering detection efficiency.

Findings

Protocols speed up purity increase rate.

Deterministic purity evolution under strong feedback.

Performance depends on detection efficiency.

Abstract

We present a number of rapid-purification feedback protocols for optical homodyne detection of a single optical qubit. We derive first a protocol that speeds up the rate of increase of the average purity of the system, and find that like the equivalent protocol for a non-disspative measurement, this generates a deterministic evolution for the purity in the limit of strong feedback. We also consider two analogues of the Wiseman-Ralph rapid-purification protocol in this setting, and show that like that protocol they speed up the average time taken to reach a fixed level of purity. We also examine how the performance of these algorithms changes with detection efficiency, being an important practical consideration.