Continuous decomposition of quantum measurements via qubit probe feedback

TL;DR

This paper characterizes the limitations of decomposing two-outcome quantum measurements into continuous processes using qubit probes and feedback, showing that only measurements with two distinct singular values are achievable.

Contribution

It demonstrates that with a qubit probe and constant interaction Hamiltonian, only certain generalized measurements can be realized through continuous feedback.

Findings

Only measurements with two distinct singular values are achievable.

A generalized qubit measurement can be decomposed using a qubit probe and simple interaction.

Arbitrary unitary pulses do not extend the class of achievable measurements.

Abstract

It is known that any two-outcome quantum measurement can be decomposed into a continuous stochastic process using a feedback loop. In this article, we characterize which of these decompositions are possible when each iteration of the feedback loop consists of a weak measurement caused by an interaction with a probe system. We restrict ourselves to the case when the probe is a qubit and the interaction Hamiltonian between the probe and system is constant. We find that even given the ability to perform arbitrary unitary pulses throughout the continuous decomposition, only generalized measurements with two distinct singular values are achievable. However, this is sufficient to decompose a generalized qubit measurement using a qubit probe and a simple interaction Hamiltonian.