Qubit state monitoring by measurement of three complementary observables

TL;DR

This paper investigates how a qubit's state evolves under simultaneous continuous measurement of three non-commuting observables, revealing isotropic diffusion and state purification, and evaluates classical estimation methods based on measurement records.

Contribution

It introduces a detailed analysis of qubit state evolution under simultaneous measurement of three complementary observables and assesses classical estimation fidelity.

Findings

Qubit state approaches a pure state with a random Bloch vector direction

State undergoes isotropic diffusion in perpendicular directions

Classical estimates based on measurement records have quantifiable fidelity

Abstract

We consider the evolution of a spin 1/2 (qubit) under the simultaneous continuous measurement of three non-commuting qubit operators sigma_x, sigma_y, sigma_z. For identical ideal detectors the qubit state evolves by approaching a pure state with a random direction in the Bloch vector space and by undergoing locally isotropic diffusion in the perpendicular directions. The quantum state conditioned on the complete detector record is used to assess the fidelity of classically inspired estimates based on running time averages and discrete time bin detector outputs.