Projective measurements under qubit quantum channels

TL;DR

This paper explores how qubit channels affect projective measurements, revealing their relationship with measurement properties like bias and sharpness, and analyzing implications for measurement energy costs and non-Markovian effects.

Contribution

It establishes a framework connecting qubit channels with measurement properties, highlighting the shift from Schrödinger to Heisenberg picture and analyzing noise and non-Markovian effects.

Findings

Unital channels induce unbiased measurements.

Markovian channels cause sharpness to decrease monotonically over time.

Bias and sharpness influence measurement energy costs.

Abstract

The action of qubit channels on projective measurements on a qubit state is used to establish an equivalence between channels and properties of generalized measurements characterized by bias and sharpness parameters. This can be interpreted as shifting the description of measurement dynamics from the Schrodinger to the Heisenberg picture. In particular, unital quantum channels are shown to induce unbiased measurements. The Markovian channels are found to be equivalent to measurements for which sharpness is a monotonically decreasing function of time. These results are illustrated by considering various noise channels. Further, the effect of bias and sharpness parameters on the energy cost of a measurement and its interplay with non-Markovianity of dynamics is also discussed