Determination of the stationary basis from protective measurement on a single system

TL;DR

This paper extends protective measurement to joint measurements of multiple observables, enabling the determination of eigenstates of an unknown Hamiltonian from a single measurement on a qubit.

Contribution

It introduces a generalized method for joint protective measurement to identify Hamiltonian eigenstates, advancing quantum measurement techniques.

Findings

Successfully determined two eigenstates of an unknown Hamiltonian

Performed a single joint protective measurement of three Pauli matrices

Demonstrated precise eigenstate identification from minimal measurement data

Abstract

We generalize protective measurement for protective joint measurement of several observables. The merit of joint protective measurement is the determination of the eigenstates of an unknown Hamiltonian rather than the determination of features of an unknown quantum state. As an example, we precisely determine the two eigenstates of an unknown Hamiltonian by a single joint protective measurement of the three Pauli matrices on a qubit state.