Mutually unbiased unitary bases

We consider the notion of unitary transformations forming bases for subspaces of M(d,C) such that the square of the Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case, we construct the maximal number of such bases for the four- and two-dimens...

Full description

Bibliographic Details
Main Authors:	Shamsul Shaari, Jesni, N. M. Nasir, Rinie, Mancini, Stefano
Format:	Article
Language:	English English
Published:	American Physical Society 2016
Subjects:	QC Physics
Online Access:	http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/1/PhysRevA.94.052328.pdf http://irep.iium.edu.my/53093/7/53093_Mutually%20unbiased_scopus.pdf

id	iium-53093
recordtype	eprints
spelling	iium-530932017-10-21T07:02:36Z http://irep.iium.edu.my/53093/ Mutually unbiased unitary bases Shamsul Shaari, Jesni N. M. Nasir, Rinie Mancini, Stefano QC Physics We consider the notion of unitary transformations forming bases for subspaces of M(d,C) such that the square of the Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case, we construct the maximal number of such bases for the four- and two-dimensional subspaces while proving the nonexistence of such a construction for the three-dimensional case. Extending this to higher dimensions, we commit to such a construct for the case of qutrits and provide evidence for the existence of such unitaries for prime dimensional quantum systems. Focusing on the qubit case, we show that the average fidelity for estimating any such transformation is equal to the case for estimating a completely unknown unitary from SU(2). This is then followed by a quick application for such unitaries in a quantum cryptographic setup. American Physical Society 2016-11-21 Article PeerReviewed application/pdf en http://irep.iium.edu.my/53093/1/PhysRevA.94.052328.pdf application/pdf en http://irep.iium.edu.my/53093/7/53093_Mutually%20unbiased_scopus.pdf Shamsul Shaari, Jesni and N. M. Nasir, Rinie and Mancini, Stefano (2016) Mutually unbiased unitary bases. Physical Review A, 94 (5). 052328-1. ISSN 2469-9926 E-ISSN 2469-9934 http://journals.aps.org/pra/ 10.1103/PhysRevA.94.052328
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	QC Physics
spellingShingle	QC Physics Shamsul Shaari, Jesni N. M. Nasir, Rinie Mancini, Stefano Mutually unbiased unitary bases
description	We consider the notion of unitary transformations forming bases for subspaces of M(d,C) such that the square of the Hilbert-Schmidt inner product of matrices from the differing bases is a constant. Moving from the qubit case, we construct the maximal number of such bases for the four- and two-dimensional subspaces while proving the nonexistence of such a construction for the three-dimensional case. Extending this to higher dimensions, we commit to such a construct for the case of qutrits and provide evidence for the existence of such unitaries for prime dimensional quantum systems. Focusing on the qubit case, we show that the average fidelity for estimating any such transformation is equal to the case for estimating a completely unknown unitary from SU(2). This is then followed by a quick application for such unitaries in a quantum cryptographic setup.
format	Article
author	Shamsul Shaari, Jesni N. M. Nasir, Rinie Mancini, Stefano
author_facet	Shamsul Shaari, Jesni N. M. Nasir, Rinie Mancini, Stefano
author_sort	Shamsul Shaari, Jesni
title	Mutually unbiased unitary bases
title_short	Mutually unbiased unitary bases
title_full	Mutually unbiased unitary bases
title_fullStr	Mutually unbiased unitary bases
title_full_unstemmed	Mutually unbiased unitary bases
title_sort	mutually unbiased unitary bases
publisher	American Physical Society
publishDate	2016
url	http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/ http://irep.iium.edu.my/53093/1/PhysRevA.94.052328.pdf http://irep.iium.edu.my/53093/7/53093_Mutually%20unbiased_scopus.pdf
first_indexed	2023-09-18T21:15:10Z
last_indexed	2023-09-18T21:15:10Z
_version_	1777411513871499264

Mutually unbiased unitary bases

Similar Items