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Frontiers in Optics

Experimental demonstration of loop state-preparation-and-measurement tomography

M. Beck, A. F. McCormick, S. J. van Enk

Published Jan 1, 2017• 1 citation
Publisher

Abstract

We have demonstrated, using qubits encoded in the polarization of heralded individual photons, that loop state-preparation-and-measurement tomography is capable of detecting correlated errors between the preparation and the measurement of a quantum system.
DOI
10.1364/fio.2017.fm2d.2

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We have performed an experiment demonstrating that loop state-preparation-and-measurement tomography [Jackson and van Enk, Phys. Rev. A 92, 042312 (2015)] is capable of detecting correlated errors between the preparation and the measurement of a quantum system. Specifically, we have prepared pure and mixed states of single qubits encoded in the polarization of heralded individual photons. By performing measurements using multiple state preparations and multiple measurement device settings we are able to detect if there are any correlated errors between them, and we are also able to determine which state preparations are correlated with which measurements. This is accomplished by going around a ``loop'' in parameter space, which allows us to check for self-consistency. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-valued measures (POVMs) describing the detector are known. In cases where no correlations are found we are able to perform quantum state tomography of the polarization qubits by using knowledge of the detector POVMs, or quantum detector tomography by using knowledge of the state preparations. Note, however, that the detection of correlated errors does not require estimating any state or measurement parameters.
We experimentally demonstrate that loop state-preparation-and-measurement (SPAM) tomography is capable of detecting correlated errors in a two-qubit system. We prepare photon pairs in a state that approximates a Werner state, which may or may not be entangled. By performing measurements with multiple different detector settings, we are able to detect correlated errors between two single-qubit measurements performed in different locations. No assumptions are made concerning either the state preparations or the measurements, other than that the dimensions of the states and the positive-operator-valued measures describing the detectors are known. The only other needed information is experimentally measured expectation values, which are analyzed for self-consistency. This demonstrates that loop SPAM tomography is a useful technique for detecting errors that would degrade the performance of multiple-qubit quantum information processors.
Traditional methods of quantum state characterization are impractical for systems of more than a few qubits due to exponentially expensive postprocessing and data storage and lack robustness against errors and noise. Here, we experimentally demonstrate self-guided quantum tomography performed on polarization photonic qubits. The quantum state is iteratively learned by optimizing a projection measurement without any data storage or postprocessing. We experimentally demonstrate robustness against statistical noise and measurement errors on single-qubit and entangled two-qubit states.