Measurement of modular values and connection to the annihilation operator

¹ State Key Laboratory of Low- Dimensional Quantum Physics and Department of Physics, Tsinghua University Beijing 100084, China
² Collaborative Innovation Center of Quantum Matter - Beijing 100084, China
³ Frontier Science Center for Quantum Information - Beijing 100084, China
⁴ Beijing National Research Center for Information Science and Technology - Beijing 100084, China
⁵ Beijing Academy of Quantum Information Sciences - Beijing 100193, China

Received: 7 July 2020
Accepted: 24 August 2020

Abstract

Modular value of an observable of a pre- and postselected quantum system is a concept similar to weak value, but in contrast to describing only weak coupling, it can describe the coupling of any strength but only for qubit meters, so it may be used more widely in some scenarios. Besides, modular value has been proved to have advantages on measuring weak values of nonlocal joint observables and nonlocal entanglement states. In this paper, we extend the work of J. S. Lundeen and K. J. Reschb on connection between the measured values of multiparticle observables of a pre- and postselected quantum system and annihilation operator by modular value and give their relation. Based on the above, we propose a new method different from tomography to measure modular values, and we find that our annihilation operator measurement (AOM) method can significantly reduce the number of measurements from O(4ⁿ) to O(2ⁿ) compared with the original tomography method.