occasional meanderings in physics' brave new world

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Location: New Zealand

Marni D. Sheppeard

## Wednesday, July 09, 2008

### Mermin Magic

This week's PIRSA lectures include an enjoyable talk by M. Skotiniotis on his 2007 paper about epistemic models for hidden variable versions of Spekkens' toy quantum mechanics. In particular, the Mermin-Peres magic square is introduced. This is a $3 \times 3$ square of tensor products of Pauli operators of the form

$X^1$, $X^2$, $X^1 X^2$
$Y^2$, $Y^1$, $Y^1 Y^2$
$X^1 Y^2$, $X^2 Y^1$, $Z^1 Z^2$

corresponding to two qubits in three directions, which is related to the 2-direction three qubit Mermin pentagram of the form The number theoretic nature of these objects is discussed in the arxiv link. M theorists will notice the likeness of the magic square to certain mixing matrices in HEP phenomenology.