Quantum process tomography: the role of initial correlations

TL;DR

This paper investigates quantum process tomography in scenarios with initial system-environment correlations, revealing that certain nonlinear or non-completely positive dynamics can be physically realized and verified.

Contribution

It demonstrates how arbitrary quantum maps can be implemented using specific preparators and unitary swaps, and discusses the properties of non-completely positive linear maps in process tomography.

Findings

Arbitrary quantum maps can be realized with preparators and SWAP operations.

Nonlinear and non-completely positive dynamics can describe system evolution.

Verification of preparator compatibility with the estimation process is addressed.

Abstract

We address the problem of quantum process tomography with the preparators producing states correlated with the environmental degrees of freedom that play role in the system-environment interactions. We discuss the physical situations, in which the dynamics is described by nonlinear, or noncompletely positive transformations. In particular, we show that arbitrary mapping $\varrho_{\rm in}\to\varrho_{\rm out}$ can be realized by using appropriate set of preparators and applying the unitary operation SWAP. The experimental ``realization'' of perfect NOT operation is presented. We address the problem of the verification of the compatibility of the preparator devices with the estimating process. The evolution map describing the dynamics in arbitrary time interval is known not to be completely positive, but still linear. The tomography and general properties of these maps are discussed.