Photonic non-Markovianity identification by quantum process capabilities of non-CP processes

TL;DR

This paper introduces a practical method to identify and measure non-Markovian quantum processes by analyzing non-CP processes as quantum capabilities, avoiding extensive state optimization and entanglement, and is experimentally feasible with optical setups.

Contribution

It proposes a novel approach to quantify and witness non-Markovianity using minimal experimental efforts without full process tomography or entanglement resources.

Findings

Method successfully identifies non-Markovianity in optical systems.

Can be implemented with all-optical setups and minimal states.

Applicable to single-photon and two-photon dynamics.

Abstract

A Markovian quantum process can be arbitrarily divided into two or more legitimate completely-positive (CP) subprocesses. When at least one non-CP process exists among the divided processes, the dynamics is considered non-Markovian. However, how to utilize minimum experimental efforts, without examining all process input states and using entanglement resources, to identify or measure non-Markovianity is still being determined. Herein, we propose a method to quantify non-CP processes for identifying and measuring non-Markovianity without the burden of state optimization and entanglement. This relies on the non-CP processes as new quantum process capabilities and can be systematically implemented by quantum process tomography. We additionally provide an approach for witnessing non-Markovianity by analyzing at least four system states without process tomography. We faithfully demonstrate that our method can be explicitly implemented using all-optical setups and applied to identify the non-Markovianity of single-photon and two-photon dynamics in birefringent crystals. Our results can also be used to explore non-Markovianity in other dynamical systems where process or state tomography is implementable.