A tomographic approach to non-Markovian master equations

TL;DR

This paper introduces a symplectic tomography-based method to reconstruct unknown parameters in non-Markovian Gaussian quantum evolutions, demonstrated on a harmonic oscillator model with explicit tomogram requirements.

Contribution

It presents a novel tomographic reconstruction technique for non-Markovian master equations, including integral and differential approaches, with explicit parameter retrieval in a benchmark model.

Findings

Reconstruction of unknown parameters using finite tomograms.

Explicit computation of tomogram requirements for a harmonic oscillator model.

Demonstration of two reconstruction approaches: integral and differential.

Abstract

We propose a procedure based on symplectic tomography for reconstructing the unknown parameters of a convolutionless non-Markovian Gaussian noisy evolution. Whenever the time-dependent master equation coefficients are given as a function of some unknown time-independent parameters, we show that these parameters can be reconstructed by means of a finite number of tomograms. Two different approaches towards reconstruction, integral and differential, are presented and applied to a benchmark model made of a harmonic oscillator coupled to a bosonic bath. For this model the number of tomograms needed to retrieve the unknown parameters is explicitly computed.