Direct measurement of nonlocal quantum states without approximation

Abstract

Efficient acquiring information from a quantum state is important for research in fundamental quantum physics and quantum information applications. Instead of using standard quantum state tomography method with reconstruction algorithm, weak values were proposed to directly measure density matrix elements of quantum state. Recently, similar to the concept of weak value, modular values were introduced to extend the direct measurement scheme to nonlocal quantum wavefunction. However, this method still involves approximations, which leads to inherent low precision. Here, we propose a new scheme which enables direct measurement for ideal value of the nonlocal density matrix element without taking approximations. Our scheme allows more accurate characterization of nonlocal quantum states, and therefore has greater advantages in practical measurement scenarios.