Superadditivity of Krylov Complexity for Tensor Products

• URL: http://arxiv.org/abs/2601.08723v1
• Date: Tue, 13 Jan 2026 16:48:16 GMT
• Title: Superadditivity of Krylov Complexity for Tensor Products
• Authors: Jeff Murugan, Hendrik J. R. van Zyl,
• Abstract summary: We study Krylov complexity for quantum systems whose Hamiltonians factorise as tensor products.<n>We prove that complexity is superadditive under tensor products, $C_12ge C_1+C$, and identify a positive operator that quantifies the resulting excess complexity.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study Krylov complexity for quantum systems whose Hamiltonians factorise as tensor products. We prove that complexity is superadditive under tensor products, $C_{12}\ge C_1+C_2$, and identify a positive operator that quantifies the resulting excess complexity. The underlying mechanism is made transparent by introducing a Krylov graph representation in which tensor products generate a higher-dimensional lattice whose diagonal shells encode operator growth and binomial path multiplicities. In the continuum limit, Krylov dynamics reduces to diffusion on this graph, with superadditivity arising from geometric broadening across shells. Explicit examples illustrate how deviations from synchronous evolution generate bounded, oscillatory excess complexity.

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