A Rigidity Property of Complete Systems of Mutually Unbiased Bases-Reference-Cited by-同舟云学术

A Rigidity Property of Complete Systems of Mutually Unbiased Bases

Published:2021-09 Issue:03 Volume:28 Page:
ISSN:1230-1612
Container-title:Open Systems & Information Dynamics
language:en
Short-container-title:Open Syst. Inf. Dyn.

Author:

Matolcsi Máté¹²,Weiner Mihály¹³

Affiliation:

1. Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, Muegyetem rkp. 3., H–1111 Budapest, Hungary

2. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, H–1053, Realtanoda u 13-15, Budapest, Hungary

3. Hungary and MTA-BME Lendület Quantum Information Theory Research Group, Hungary

Abstract

Suppose that for some unit vectors [Formula: see text] in [Formula: see text] we have that for any [Formula: see text] [Formula: see text] is either orthogonal to [Formula: see text] or [Formula: see text] (i.e., [Formula: see text] and [Formula: see text] are unbiased). We prove that if [Formula: see text], then these vectors necessarily form a complete system of mutually unbiased bases, that is, they can be arranged into [Formula: see text] orthonormal bases, all being mutually unbiased with respect to each other.

Funder

NKFI

Publisher

World Scientific Pub Co Pte Ltd

Subject

Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1230161221500128

Reference14 articles.

1. A New Proof for the Existence of Mutually Unbiased Bases

2. A Criterion for Attaining the Welch Bounds with Applications for Mutually Unbiased Bases

3. Mutually unbiased bases and Hadamard matrices of order six

4. Maximal sets of mutually unbiased quantum states in dimension 6