Parameterizing qudit states

Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Arsen Khvedelidze, Dimitar Mladenov, Astghik Torosyan
Formato:	article
Lenguaje:	EN
Publicado:	Peoples’ Friendship University of Russia (RUDN University) 2021
Materias:	density matrix parameterization quantum system qubit qutrit quatrit qudit polynomial invariant theory convex geometry Electronic computers. Computer science QA75.5-76.95
Acceso en línea:	https://doaj.org/article/98cd6662dff447bfb8eb9a074a1e1b74
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:98cd6662dff447bfb8eb9a074a1e1b74
record_format	dspace
spelling	oai:doaj.org-article:98cd6662dff447bfb8eb9a074a1e1b742021-11-12T15:18:26ZParameterizing qudit states2658-46702658-714910.22363/2658-4670-2021-29-4-361-386https://doaj.org/article/98cd6662dff447bfb8eb9a074a1e1b742021-12-01T00:00:00Zhttp://journals.rudn.ru/miph/article/viewFile/29429/20004https://doaj.org/toc/2658-4670https://doaj.org/toc/2658-7149Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an NN-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N){SU(N)}-invariant counterpart of the NN-level state space BN{\mathcal{B}_N}, i.e., the unitary orbit space BN/SU(N){B_N/SU(N)}. It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of BN/SU(N){B_N/SU(N)}. To illustrate the general situation, a detailed description ofBN/SU(N){B_N/SU(N)} for low-level systems: qubit (N=2{N= 2}), qutrit (N=3{N=3}), quatrit (N=4{N= 4}) - will be given.Arsen KhvedelidzeDimitar MladenovAstghik TorosyanPeoples’ Friendship University of Russia (RUDN University)articledensity matrix parameterizationquantum systemqubitqutritquatritquditpolynomial invariant theoryconvex geometryElectronic computers. Computer scienceQA75.5-76.95ENDiscrete and Continuous Models and Applied Computational Science, Vol 29, Iss 4, Pp 361-386 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	density matrix parameterization quantum system qubit qutrit quatrit qudit polynomial invariant theory convex geometry Electronic computers. Computer science QA75.5-76.95
spellingShingle	density matrix parameterization quantum system qubit qutrit quatrit qudit polynomial invariant theory convex geometry Electronic computers. Computer science QA75.5-76.95 Arsen Khvedelidze Dimitar Mladenov Astghik Torosyan Parameterizing qudit states
description	Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an NN-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N){SU(N)}-invariant counterpart of the NN-level state space BN{\mathcal{B}_N}, i.e., the unitary orbit space BN/SU(N){B_N/SU(N)}. It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of BN/SU(N){B_N/SU(N)}. To illustrate the general situation, a detailed description ofBN/SU(N){B_N/SU(N)} for low-level systems: qubit (N=2{N= 2}), qutrit (N=3{N=3}), quatrit (N=4{N= 4}) - will be given.
format	article
author	Arsen Khvedelidze Dimitar Mladenov Astghik Torosyan
author_facet	Arsen Khvedelidze Dimitar Mladenov Astghik Torosyan
author_sort	Arsen Khvedelidze
title	Parameterizing qudit states
title_short	Parameterizing qudit states
title_full	Parameterizing qudit states
title_fullStr	Parameterizing qudit states
title_full_unstemmed	Parameterizing qudit states
title_sort	parameterizing qudit states
publisher	Peoples’ Friendship University of Russia (RUDN University)
publishDate	2021
url	https://doaj.org/article/98cd6662dff447bfb8eb9a074a1e1b74
work_keys_str_mv	AT arsenkhvedelidze parameterizingquditstates AT dimitarmladenov parameterizingquditstates AT astghiktorosyan parameterizingquditstates
_version_	1718430384870391808

Parameterizing qudit states

Ejemplares similares