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Mutually unbiased unitary bases

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

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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.

Item Type: Article (Journal)
Additional Information: 3844/53093
Uncontrolled Keywords: Mutually unbiased; Unitary bases
Subjects: Q Science > QC Physics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science > Department of Physics
Depositing User: Dr. Jesni Shamsul Shaari
Date Deposited: 21 Jan 2017 04:00
Last Modified: 21 Oct 2017 15:02
URI: http://irep.iium.edu.my/id/eprint/53093

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