Quantum non-demolition measurements of a qubit coupled to a harmonic oscillator

TL;DR

This paper presents a theoretical framework for weak quantum non-demolition measurements of a qubit coupled to a harmonic oscillator, analyzing factors that affect measurement fidelity and QND character.

Contribution

It introduces a POVM-based model for qubit measurement via an oscillator and identifies key mechanisms causing deviations from ideal QND measurements.

Findings

Quantum fluctuations of the oscillator impact measurement accuracy.

Quantum tunneling between qubit states affects QND fidelity.

The theory applies to superconducting qubits coupled to circuit oscillators.

Abstract

We theoretically describe the weak measurement of a two-level system (qubit) and quantify the degree to which such a qubit measurement has a quantum non-demolition (QND) character. The qubit is coupled to a harmonic oscillator which undergoes a projective measurement. Information on the qubit state is extracted from the oscillator measurement outcomes, and the QND character of the measurement is inferred by the result of subsequent measurements of the oscillator. We use the positive operator valued measure (POVM) formalism to describe the qubit measurement. Two mechanisms lead to deviations from a perfect QND measurement: (i) the quantum fluctuations of the oscillator, and (ii) quantum tunneling between the qubit states $|0>$ and $|1>$ during measurements. Our theory can be applied to QND measurements performed on superconducting qubits coupled to a circuit oscillator.