2022/06/23 by Guillaume Aubrun, Aubrun, Guillaume, Alexander Müller‐Hermes +3 · 1 citation
Computer Science · Physics and Astronomy · #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Metric Geometry (math.MG) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2206.11805
openalex publication_date 2022/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A separable quantum state shared between parties A and B can be symmetrically extended to a quantum state shared between party A and parties B1,… ,Bk for every k\inN. Quantum states that are not separable, i.e., entangled, do not have this property. This phenomenon is known as "monogamy of entanglement". We show that monogamy is not only a feature of quantum theory, but that it characterizes the minimal tensor product of general pairs of convex cones CA and CB: The elements of the minimal tensor product CA⊗min CB are precisely the tensors that can be symmetrically extended to elements in the maximal tensor product CA⊗max C^⊗max kB for every k\inN. Equivalently, the minimal tensor product of two cones is the intersection of the nested sets of k-extendible tensors. It is a natural question when the minimal tensor product CA⊗min CB coincides with the set of k-extendible tensors for some finite k. We show that this is universally the case for every cone CA if and only if CB is a polyhedral cone with a base given by a product of simplices. Our proof makes use of a new characterization of products of simplices up to affine equivalence that we believe is of independent interest.