### 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.

$X^1$, $X^2$, $X^1 X^2$

$Y^2$, $Y^1$, $Y^1 Y^2$

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

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.

## 1 Comments:

Great stuff! Truly magical! This points the way for a future in M-theory that really can be taught to children. Einstein and many others were originally inspired by geometry. I am sure that your posts will someday form an entertaining book.

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