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Measurement of qutrits

A. V. Burlakov, L. A. Krivitskiy, S. P. Kulik, Gleb Maslennikov, Maria V. Chekhova

Published Jan 1, 2002• 19 citations
OpenAlex

Abstract

We proposed the procedure of measuring the unknown state of the three-level system - the qutrit, which was realized as the arbitrary polarization state of the single-mode biphoton field. This procedure is accomplished for the set of the pure states of qutrits; this set is defined by the properties of SU(2) transformations, that are done by the polarization transformers.

Related papers

Measurement of qutrits

A. V. Burlakov, L. A. Krivitskii, S. P. Kulik +2 more

A method of optical realization of a protocol of restoration of the density matrix of an unknown state of a three-level system that represents an arbitrary polarization state of a single-mode biphoton field is proposed. The method is applied to a set of pure states of qutrits, with this set being determined by the properties of SU (2) transformations performed by polarization transformers (retardation plates).

arXiv:quant-ph/0207096•Optics and Spectroscopy•May 1, 2003•23 citations

Biphotons as three-level systems: Transformation and measurement

L. A. Krivitskiı̆, S. P. Kulik, Alexander N. Penin +1 more

Two algorithms for measuring the polarization state of the biphoton field prepared in the form of a three-level system (qutrit) are considered. On the basis of the general approach developed by Klyshko [21] for describing the polarization properties of single-mode electromagnetic fields in the fourth order in the field, a procedure for measuring the polarization density matrix of qutrits is proposed and implemented.

Journal of Experimental and Theoretical Physics•Oct 1, 2003•11 citations

A protocol of measurements providing direct, complete and single-valued recover of all a-priori unknown parameters of biphoton polarization qutrits

Mikhail Vladimirovich Fedorov, C. C. Mernova, K. V. Sliporod

We suggest and describe the protocol of measurements providing completely probabilistic representation of all parameters of biphoton polarization qutrits, i.e providing explicit expressions for all parameters of qutrits via the probabilities of getting those or other results in measurements.

arXiv:2401.15137•Jan 26, 2024•0 citations

A Protocol of Measurements Providing Direct, Complete and Single-Valued Recover of All a Priory Unknown Parameters of Polarization Biphoton Qutrits

Mikhail Vladimirovich Fedorov, S. S. Mernova, K. V. Sliporod

Abstract We suggest and describe the protocol of measurements providing completely probabilistic representation of all parameters of polarization biphoton qutrits, i.e. providing explicit expressions for all parameters of qutrits via the probabilities of getting those or other results in measurements.

Physics of Wave Phenomena•Jun 1, 2024•3 citations

Arbitrary unitary operations of the biphoton qutrits

Qing Lin

Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons in the same spatial-temporal mode, can be mapped to a single photon qutrit in spatial modes. It will make arbitrary unitary operation on such bi-photonic qutrit possible if we can also realize the inverse map to polarization space. Among the two schemes proposed in this paper, the one based only on linear optics realizes an arbitrary U(3) operation with a very small success probability. However, if added with weak nonlinearity, the success probability can be greatly improved. These schemes are feasible with the current experimental technology.

•May 20, 2009•0 citations

Manipulating Biphotonic Qutrits

B. P. Lanyon, Till J. Weinhold, Nathan K. Langford +4 more

Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement-induced nonlinearities can dramatically extend the range of possible transforms on biphotonic qutrits-three-level quantum systems formed by the polarization of two photons in the same spatiotemporal mode. We fully characterize the biphoton-photon entanglement that underpins our technique, thereby realizing the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.

arXiv:0707.2880•Physical Review Letters•Feb 14, 2008•182 citations
We proposed the procedure of measuring the unknown state of the three-level system - the qutrit, which was realized as the arbitrary polarization state of the single-mode biphoton field. This procedure is accomplished for the set of the pure states of qutrits; this set is defined by the properties of SU(2) transformations, that are done by the polarization transformers.
Qutrits, the triple level quantum systems in various forms, have been proposed for quantum information processing recently. By the methods presented in this paper a bi-photonic qutrit, which is encoded with the polarizations of two photons in the same spatial-temporal mode, can be mapped to a single photon qutrit in spatial modes. It will make arbitrary unitary operation on such bi-photonic qutrit possible if we can also realize the inverse map to polarization space. Among the two schemes proposed in this paper, the one based only on linear optics realizes an arbitrary U(3) operation with a very small success probability. However, if added with weak nonlinearity, the success probability can be greatly improved. These schemes are feasible with the current experimental technology.
Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement-induced nonlinearities can dramatically extend the range of possible transforms on biphotonic qutrits-three-level quantum systems formed by the polarization of two photons in the same spatiotemporal mode. We fully characterize the biphoton-photon entanglement that underpins our technique, thereby realizing the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.