Measuring the quantum state of a single system with minimum state disturbance

TL;DR

This paper presents a systematic method to minimize state disturbance during protective quantum measurements, enabling more accurate single-system quantum state determination by optimizing measurement interaction timing.

Contribution

It introduces a technique to design measurement interactions that significantly reduce state disturbance, surpassing previous strategies and achieving minimal disturbance decay rates.

Findings

Polynomial decay of disturbance to arbitrary order in 1/T

Subexponential decay of disturbance achieved

Minimal possible disturbance in protective measurement identified

Abstract

Conventionally, unknown quantum states are characterized using quantum-state tomography based on strong or weak measurements carried out on an ensemble of identically prepared systems. By contrast, the use of protective measurements offers the possibility of determining quantum states from a series of weak, long measurements performed on a single system. Because the fidelity of a protectively measured quantum state is determined by the amount of state disturbance incurred during each protective measurement, it is crucial that the initial quantum state of the system is disturbed as little as possible. Here we show how to systematically minimize the state disturbance in the course of a protective measurement, thus enabling the maximization of the fidelity of the quantum-state measurement. Our approach is based on a careful tuning of the time dependence of the measurement interaction and is shown to be dramatically more effective in reducing the state disturbance than the previously considered strategy of weakening the measurement strength and increasing the measurement time. We describe a method for designing the measurement interaction such that the state disturbance exhibits polynomial decay to arbitrary order in the inverse measurement time $1/T$. We also show how one can achieve even faster, subexponential decay, and we find that it represents the smallest possible state disturbance in a protective measurement. In this way, our results show how to optimally measure the state of a single quantum system using protective measurements.