Photonic Non‐Markovianity Identification by Quantum Process Capabilities of Non‐CP Processes

Abstract

AbstractA 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, a method is proposed 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. Additionally, an approach for witnessing non‐Markovianity by analyzing at least four system states without process tomography is provided. It is faithfully demonstrated that this 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. The results also can be used to explore non‐Markovianity in other dynamical systems where process or state tomography is implementable.