Weak and strong measurement of a qubit using a switching-based detector

TL;DR

This paper investigates how a switching-based detector interacts with a qubit, revealing different measurement regimes and their effects on qubit state evolution, including weak and strong measurement scenarios.

Contribution

It introduces a theoretical model for a switching-based detector measuring a non-commuting observable of a qubit, analyzing various measurement regimes and their implications.

Findings

High-fidelity information can be obtained with a high-accuracy, incoherent detector.

Measurement basis depends on the detector's switching time accuracy.

Coherent detectors can measure in the energy eigenbasis with high fidelity.

Abstract

We analyze the operation of a switching-based detector that probes a qubit's observable that does not commute with the qubit's Hamiltonian, leading to a nontrivial interplay between the measurement and free-qubit dynamics. In order to obtain analytic results and develop intuitive understanding of the different possible regimes of operation, we use a theoretical model where the detector is a quantum two-level system that is constantly monitored by a macroscopic system. We analyze how to interpret the outcome of the measurement and how the state of the qubit evolves while it is being measured. We find that the answers to the above questions depend on the relation between the different parameters in the problem. In addition to the traditional strong-measurement regime, we identify a number of regimes associated with weak qubit-detector coupling. An incoherent detector whose switching time is measurable with high accuracy can provide high-fidelity information, but the measurement basis is determined only upon switching of the detector. An incoherent detector whose switching time can be known only with low accuracy provides a measurement in the qubit's energy eigenbasis with reduced measurement fidelity. A coherent detector measures the qubit in its energy eigenbasis and, under certain conditions, can provide high-fidelity information.