Instantaneous indirect measurement principle in quantum mechanics

TL;DR

This paper introduces the instantaneous indirect measurement method in quantum mechanics, enabling the measurement of an operator's average value without collapsing the wave function, applicable to arbitrary states and involving instantaneous information transfer.

Contribution

The paper proposes a novel measurement technique that measures quantum operators indirectly and instantaneously, avoiding wave function collapse and applicable to any quantum state.

Findings

The method allows measurement of an operator's average value via instantaneous change detection.

It does not significantly disturb the quantum state or cause wave function collapse.

Applicable to coupled systems and quantum Fisher information measurement.

Abstract

In quantum systems, the measurement of operators and the measurement of the quantum states of the system are very challenging tasks. In this Letter, we propose a method to obtain the average value of one operator in a certain state by measuring the instantaneous change of the average value of another operator with the assistance of a known reference state. We refer to this measurement method as the instantaneous indirect measurement method. By studying the application of this method to some typical models, we find that this measurement can be applied to the measurement of an arbitrary state of a quantum system. Furthermore, for the system to be measured, we find that such measurement neither significantly affects the wave function of the system nor causes wave function collapse of the system. Also, our study shows that when two independent systems are coupled, the information mapping between them is done instantaneously. Finally, we discuss applying this measurement method to the measurement of quantum Fisher information, which quantizes the limited accuracy of estimating a parameter from a quantum state.