Quantum Margulis expanders

Details Quantum Margulis expanders Quantum Margulis expanders

2007-10-03

arxiv.org/abs/0710.0651v2

Quant. Inf. Comp. 8, 722 (2008)

Physics

Quantum Physics

12 pages, 1 figure. Slightly expanded, material on phase space methods added, reference to arXiv:0709.1142 appended, replaced

Scientific paper

We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The quantum version shares all essential properties of the classical counterpart, e.g., it has the same degree and spectrum. Unlike previous constructions of quantum expanders, our method does not rely on non-Abelian harmonic analysis. Analogues for continuous variable systems are mentioned. Indeed, the construction seems one of the few instances where applications based on discrete and continuous phase space methods can be developed in complete analogy.

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