On mutually unbiased bases: Passing from d to d**2
Maurice Robert Kibler (IPNL)
TL;DR
This paper presents a method to transform the problem of finding mutually unbiased bases in a d-dimensional space into finding specific vectors in a d^2-dimensional space, with solutions available when d is prime.
Contribution
It introduces a transformation that simplifies the search for mutually unbiased bases, particularly for prime dimensions, linking two related quantum state problems.
Findings
Transformation formulas exist for prime d
The problem reduces to finding vectors in a higher-dimensional space
Solutions are obtainable when d is prime
Abstract
We show how to transform the problem of finding d+1 mutually unbiased bases in the d-dimensional Hilbert space into the one of finding d(d+1) vectors in the N-dimensional Hilbert space with N=d**2. The transformation formulas admit a solution when d is a prime number.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Polynomial and algebraic computation · Matrix Theory and Algorithms