Measurement of a qubit and measurement with a qubit

TL;DR

This paper explores how qubits can be used as detectors for other systems, providing exact solutions and weak measurement formulas, with implications for quantum information processing.

Contribution

It introduces a comprehensive analysis of qubit-based measurements, including postselection effects and generalized Wigner functions, advancing understanding of discrete-spectrum quantum measurements.

Findings

Exact solutions for qubit measurement scenarios

Formulas for weak measurement regimes with arbitrary states

Introduction of generalized Wigner functions in measurement analysis

Abstract

Generally, the measurement process consists in coupling a system to a detector that can give a continuous output. However, it may be interesting to use as a detector a system with a discrete spectrum, especially in view of applications to quantum information. Here, we study 1) a two-level system measuring another two-level system (qubit); 2) a generic system measuring a qubit; 3) a qubit measuring a generic system. The results include the case when a postselection on the measured system is made. We provide the exact solution, and also a controlled expansion in the coupling parameter, giving formulas valid in the weak measurement regime for arbitrary preparation and postselection. The concept of generalized Wigner functions is introduced.