A rigidity property of complete systems of mutually unbiased bases
- URL: http://arxiv.org/abs/2112.00090v1
- Date: Tue, 30 Nov 2021 20:47:16 GMT
- Title: A rigidity property of complete systems of mutually unbiased bases
- Authors: M\'at\'e Matolcsi and Mih\'aly Weiner
- Abstract summary: We prove that for some unit vectors $b_1,ldots b_n$ in $mathbb Cd$, they can be arranged into $d+1$ orthonormal bases.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Suppose that for some unit vectors $b_1,\ldots b_n$ in $\mathbb C^d$ we have
that for any $j\neq k$ $b_j$ is either orthogonal to $b_k$ or $|\langle
b_j,b_k\rangle|^2 = 1/d$ (i.e. $b_j$ and $b_k$ are unbiased). We prove that if
$n=d(d+1)$, then these vectors necessarily form a complete system of mutually
unbiased bases, that is, they can be arranged into $d+1$ orthonormal bases, all
being mutually unbiased with respect to each other.
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