STOC Conference 2025 Conference Paper
Asymptotic Tensor Rank Is Characterized by Polynomials
- Matthias Christandl
- Koen Hoeberechts
- Harold Nieuwboer
- Péter Vrana
- Jeroen Zuiddam
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Péter Vrana
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2STOC Conference 2018 Conference Paper
Universal points in the asymptotic spectrum of tensors
- Matthias Christandl
- Péter Vrana
- Jeroen Zuiddam
The asymptotic restriction problem for tensors s and t is to find the smallest β ≥ 0 such that the n th tensor power of t can be obtained from the (β n + o ( n ))th tensor power of s by applying linear maps to the tensor legs — this is called restriction — when n goes to infinity. Applications include computing the arithmetic complexity of matrix multiplication in algebraic complexity theory, deciding the feasibility of an asymptotic transformation between pure quantum states via stochastic local operations and classical communication in quantum information theory, bounding the query complexity of certain properties in algebraic property testing, and bounding the size of combinatorial structures like tri-colored sum-free sets in additive combinatorics.