Self-calibrating tomography for multi-dimensional systems

TL;DR

This paper introduces a formalism for self-calibrating quantum tomography applicable to multi-dimensional systems, enabling the reconstruction of unknown states even with incomplete knowledge of measurement operations.

Contribution

It generalizes self-calibrating quantum tomography from qubits to qudits, demonstrating its applicability to complex multi-level atomic systems with unknown parameters.

Findings

Successful reconstruction of unknown states in d-level systems

Applicable to systems with unknown transition dipole moments

Retrieves state and process parameters except for a measure-zero set

Abstract

We present a formalism for self-calibrating tomography of arbitrary dimensional systems. Self-calibrating quantum state tomography was first introduced in the context of qubits, and allows the reconstruction of the density matrix of an unknown quantum state despite incomplete knowledge of the unitary operations used to change the measurement basis. We show how this can be generalized to qudits, i.e. d-level systems, and provide a specific example for a V-type three-level atomic system whose transition dipole moments are not known. We show that it is always possible to retrieve the unknown state and process parameters, except for a set of zero measure in the state-parameter space.