Qubit models of weak continuous measurements

TL;DR

This paper presents a qubit-based framework for modeling weak continuous quantum measurements, connecting quantum optical master equations with quantum circuit representations, and offering a more fundamental understanding of the measurement process.

Contribution

It introduces a novel qubit model for continuous measurements, replacing the probe field with qubits, and reformulates the evolution using quantum circuits, bridging quantum optics and quantum information.

Findings

Reproduces standard quantum-optical master equations using qubits.

Provides a quantum circuit formulation of continuous measurement dynamics.

Highlights fundamental assumptions underlying the measurement process.

Abstract

In this paper we approach the theory of continuous measurements and the associated unconditional and conditional (stochastic) master equations from the perspective of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the theory, highlighting its fundamental underlying assumptions.