Path Integral for Quantum Operations

TL;DR

This paper develops a phase space path integral framework for general quantum operations, including non-unitary and Markovian processes, providing a new tool for analyzing quantum dynamics.

Contribution

It introduces a path integral formulation for quantum operations governed by Lindblad equations, extending the method beyond unitary evolution.

Findings

Path integral for Lindblad quantum operations derived

Applicable to non-unitary, time-dependent quantum processes

Provides a new analytical approach for quantum Markovian dynamics

Abstract

In this paper we consider a phase space path integral for general time-dependent quantum operations, not necessarily unitary. We obtain the path integral for a completely positive quantum operation satisfied Lindblad equation (quantum Markovian master equation). We consider the path integral for quantum operation with a simple infinitesimal generator.