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2009

Classifying all mutually unbiased bases in Rel

Evans, Julia, Duncan, Ross, Lang, Alex et al.

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Finding all the mutually unbiased bases in various dimensions is a problem of fundamental interest in quantum information theory and pure mathematics.

The general problem formulated in finite-dimensional Hilbert spaces is open.
In the categorical approach to quantum mechanics one can find examples of categories which behave ``like'' the category of finite-dimensional Hilbert spaces in various ways but are subtly different.
One such category is the category of sets and relations, $\mathbf{Rel}$.

Classifying all mutually unbiased bases in Rel · Around

Built on

The algebra of microscopic measurement
Julian Schwinger · 1959
Earlier work this paper cites.
The geometry of quantum states
Julian Schwinger · 1960
Earlier work this paper cites.
The special canonical group
Julian Schwinger · 1960
Earlier work this paper cites.
Unitary operator bases
Julian Schwinger · 1960
Earlier work this paper cites.
Quantum Theory: Concepts and Methods
A. Peres · 1995
Earlier work this paper cites.
Quantum mechanics: symbolism of atomic measurements
Julian Schwinger · 2003
Earlier work this paper cites.

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