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2 results

Freeness and The Partial Transposes of Wishart Random Matrices
Part of
James A. Mingo, Mihai Popa
Journal:

Canadian Journal of Mathematics / Volume 71 / Issue 3 / June 2019

Published online by Cambridge University Press:

09 January 2019, pp. 659-681

Print publication:

June 2019
- Article
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We show that the partial transposes of complex Wishart random matrices are asymptotically free. We also investigate regimes where the number of blocks is fixed but the size of the blocks increases. This gives an example where the partial transpose produces freeness at the operator level. Finally, we investigate the case of real Wishart matrices.

MORE CONSTRUCTIONS OF APPROXIMATELY MUTUALLY UNBIASED BASES
Part of
- Finite fields and commutative rings (number-theoretic aspects)
XIWANG CAO, WUN-SENG CHOU
Journal:

Bulletin of the Australian Mathematical Society / Volume 93 / Issue 2 / April 2016

Published online by Cambridge University Press:

17 August 2015, pp. 211-222

Print publication:

April 2016
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Let $m$ be a positive integer and $p$ a prime number. We prove the orthogonality of some character sums over the finite field $\mathbb{F}_{p^{m}}$ or over a subset of a finite field and use this to construct some new approximately mutually unbiased bases of dimension $p^{m}$ over the complex number field $\mathbb{C}$, especially with $p=2$.