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Frontiers in Optics

Self-Calibrating Quantum State Tomography

Agata M. Brańczyk, Daniel F. V. James

Published Jan 1, 2011• 1 citation
Publisher

Abstract

We report on scheme for performing quantum state tomography using only an unknown, repeatable, unitary operation and one measurement basis. We recover the quantum state as well as the quantum process implemented by the unitary.
DOI
10.1364/fio.2011.fthz6

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Quantum state tomography relies on the ability to perform well-characterized unitary operations, which are not always available. This places restrictions on which physical systems can be characterized using such techniques. We develop a formalism that circumvents the requirement for well-characterized unitary operations by treating unknown parameters in the state and unitary process on the same footing, thereby simultaneously performing state and partial process tomography. Our formalism is generalized to ddd-level systems, and we provide a specific example for a V\mathsf{V}V-type three-level atomic system whose transition dipole moments are not known. We show that it is always possible to retrieve not only the unknown state but also the process parameters, except for a set of zero measure in the state-parameter space.
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