Joint Multi-Parameter Measurement

TL;DR

This paper explores joint measurement of multiple non-commuting observables using quantum entanglement and SU(1,1) interferometers, achieving simultaneous measurements surpassing standard quantum limits while respecting Heisenberg limits.

Contribution

It introduces a scheme utilizing quantum entanglement and SU(1,1) interferometers for joint measurement of non-commuting observables, demonstrating enhanced precision beyond standard quantum limits.

Findings

Simultaneous measurement exceeds standard quantum limit.

Heisenberg limit is maintained for each observable.

Resource conservation rule identified for joint measurement.

Abstract

Although quantum metrology allows us to make precision measurement beyond the standard quantum limit, it mostly works on the measurement of only one observable due to Heisenberg uncertainty relation on the measurement precision of non-commuting observables for one system. In this paper, we study the schemes of joint measurement of multiple observables which do not commute with each other by using the quantum entanglement between two systems. We focus on analyzing the performance of newly developed SU(1,1) interferometer on fulfilling the task of joint measurement. The results show that the information encoded in multiple non-commuting observables on an optical field can be simultaneously measured with a signal-to-noise ratio higher than the standard quantum limit, and the ultimate limit of each observable is still the Heisenberg limit. Moreover, we find a resource conservation rule for the joint measurement.