A note on quantum expanders

• URL: http://arxiv.org/abs/2302.07772v3
• Date: Mon, 16 Sep 2024 08:58:39 GMT
• Title: A note on quantum expanders
• Authors: Cécilia Lancien, Pierre Youssef,
• Abstract summary: We prove that a wide class of random quantum channels with few Kraus operators exhibit a large spectral gap. Our result provides a recipe to construct random quantum expanders from their classical (random or deterministic) counterparts.
• Score: 0.6906005491572401
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We prove that a wide class of random quantum channels with few Kraus operators, sampled as random matrices with some sparsity and moment assumptions, typically exhibit a large spectral gap, and are therefore optimal quantum expanders. In particular, our result provides a recipe to construct random quantum expanders from their classical (random or deterministic) counterparts. This considerably enlarges the list of known constructions of optimal quantum expanders, which was previously limited to few examples. Our proofs rely on recent progress in the study of the operator norm of random matrices with dependence and non-homogeneity, which we expect to have further applications in several areas of quantum information.

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