The information about the state of a charge qubit gained by a weakly coupled quantum point contact

TL;DR

This paper investigates how information about a charge qubit's initial state can be extracted through weak measurement by a quantum point contact, even when the qubit's Hamiltonian and measured operator do not commute, highlighting a method that complements existing approaches.

Contribution

It demonstrates that useful information about a qubit's initial state can be obtained from weak measurements despite non-commuting Hamiltonian and measurement operators, using a novel analysis approach.

Findings

Information can be extracted under suitable conditions.

Proper data analysis reveals initial qubit state.

Method complements existing quantum measurement models.

Abstract

We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. We consider the general case where the qubit Hamiltonian and the qubit's operator probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and the measurement data is mixed with a detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the initial state of the qubit can be extracted. Our approach complements the usual master-equation and quantum-trajectory approaches, which describe the evolution of the qubit's quantum state during the measurement process but do not keep track of the acquired measurement information.