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OSA Trends in Optics and Photonics Series

Minimizing measurement resources for quantum tomography

Nathan K. Langford, Alexei Gilchrist, Andrew G. White, Daniel F. V. James

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

We show that it is possible to perform tomographic characterization of the state of a n-qubit quantum system by performing measurement on a single component only. Implications for quantum information technology will be discussed.

Related papers

Minimizing measurement resources for quantum tomography

Daniel F. V. James, Nathan K. Langford, Alexei Gilchrist +1 more

We show that it is possible to perform tomographic characterization of the state of a n-qubit quantum system by performing measurement on a single component only. Implications for quantum information technology will be discussed.

Conference on Lasers and Electro-Optics•Jan 1, 2004•0 citations

Adaptive quantum tomography

Evan R. Jeffrey, Joseph B. Altepeter, Nicholas A. Peters +4 more

Quantum states are characterized using quantum tomography, a benchmarking tool used to analyze quantum information systems. We report on advances in tomographic theory and practice which together increase the accuracy and effciency of this analysis.

Conference on Lasers and Electro-Optics•Jan 1, 2004•0 citations

Quantum Measurement on a Budget

Dylan H. Mahler

Quantum computation - the use of quantum systems as bits, or qubits, to perform computation - has been proven to be exponentially faster than what is thought possible with classical computation for several tasks. Quantum computers have the unique ability to store an amount of information that is exponential in the number of constituent particles used to encode that information. This property, which is arguably where quantum computers derive their power, makes it very difficult to characterize quantum systems. In order to fully characterize an unknown quantum state, a series of measurements must be performed on it and the state deduced from the results of those measurements. This process, called quantum tomography, is known to require exponential resources in the number of qubits. Both the number of measurements - the measurement complexity - and the number of times each measurement must be repeated - the sample complexity - present serious challenges when performing tomography. In addition, the measurement apparatus itself, which is usually a quantum system, must be characterized leading to even more experimental complexity. Here, I present three experiments which aim to reduce the experimental complexity of quantum tomography. The first aims to reduce the number of measurements needed to locate the decoherence-free subspaces of a noisy quantum channel. The process of locating these subspaces, which would normally require full process tomography, is performed with quadratically fewer measurement settings. The second experiment aims to characterize both an uncalibrated measurement apparatus and an unknown quantum state at the same time. With a specific model of measurement, it is found that an uncalibrated parameter of the measurement can be directly extracted using a single measurement. In the third experiment, I perform an experiment in which the optimal sample complexity for quantum state tomography is obtained using adaptivity: the ability to change measurement settings part way through an experiment. All three experiments were performed using the polarization degree of freedom of photons generated by spontaneous parametric downconversion. The source of photon pairs and the measurement techniques used are described in detail, along with the theory of quantum distinguishability and its relevance to tomography.

•Jun 1, 2015•0 citations

Tomographic characterization of three-qubit pure states with only two-qubit detectors

Daniel Cavalcanti, Leandro M. Cioletti, Marcelo Terra Cunha

A tomographic process for three-qubit pure states using only pairwise detections is presented.

arXiv:quant-ph/0408022•Physical Review A•Jan 3, 2005•6 citations

Quantum state tomography of a single qubit: comparison of methods

Roman Schmied

The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical density matrix of a single qubit: (scaled) direct inversion, maximum likelihood estimation (MLE), minimum Fisher information distance and Bayesian mean estimation (BME). We discuss the different prior densities in the space of density matrices, on which both MLE and BME depend, as well as ways of including experimental errors and of estimating tomography errors. As a measure of the accuracy of these methods, we average the trace distance between a given density matrix and the tomographic density matrices it can give rise to through experimental measurements. We find that the BME provides the most accurate estimate of the density matrix, and suggest using either the pure-state prior, if the system is known to be in a rather pure state, or the Bures prior if any state is possible. The MLE is found to be slightly less accurate. We comment on the extrapolation of these results to larger systems.

arXiv:1407.4759•Journal of Modern Optics•Feb 7, 2016•59 citations

Self-Calibrating Quantum State Tomography

Agata M. Brańczyk, Daniel F. V. James

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.

Frontiers in Optics•Jan 1, 2011•1 citation
Quantum computation - the use of quantum systems as bits, or qubits, to perform computation - has been proven to be exponentially faster than what is thought possible with classical computation for several tasks. Quantum computers have the unique ability to store an amount of information that is exponential in the number of constituent particles used to encode that information. This property, which is arguably where quantum computers derive their power, makes it very difficult to characterize quantum systems. In order to fully characterize an unknown quantum state, a series of measurements must be performed on it and the state deduced from the results of those measurements. This process, called quantum tomography, is known to require exponential resources in the number of qubits. Both the number of measurements - the measurement complexity - and the number of times each measurement must be repeated - the sample complexity - present serious challenges when performing tomography. In addition, the measurement apparatus itself, which is usually a quantum system, must be characterized leading to even more experimental complexity. Here, I present three experiments which aim to reduce the experimental complexity of quantum tomography. The first aims to reduce the number of measurements needed to locate the decoherence-free subspaces of a noisy quantum channel. The process of locating these subspaces, which would normally require full process tomography, is performed with quadratically fewer measurement settings. The second experiment aims to characterize both an uncalibrated measurement apparatus and an unknown quantum state at the same time. With a specific model of measurement, it is found that an uncalibrated parameter of the measurement can be directly extracted using a single measurement. In the third experiment, I perform an experiment in which the optimal sample complexity for quantum state tomography is obtained using adaptivity: the ability to change measurement settings part way through an experiment. All three experiments were performed using the polarization degree of freedom of photons generated by spontaneous parametric downconversion. The source of photon pairs and the measurement techniques used are described in detail, along with the theory of quantum distinguishability and its relevance to tomography.
The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical density matrix of a single qubit: (scaled) direct inversion, maximum likelihood estimation (MLE), minimum Fisher information distance and Bayesian mean estimation (BME). We discuss the different prior densities in the space of density matrices, on which both MLE and BME depend, as well as ways of including experimental errors and of estimating tomography errors. As a measure of the accuracy of these methods, we average the trace distance between a given density matrix and the tomographic density matrices it can give rise to through experimental measurements. We find that the BME provides the most accurate estimate of the density matrix, and suggest using either the pure-state prior, if the system is known to be in a rather pure state, or the Bures prior if any state is possible. The MLE is found to be slightly less accurate. We comment on the extrapolation of these results to larger systems.