Quantum inflation and source-transfer hierarchies are complete for tree networks

arXiv:2609.19310 · quant-ph, math-ph, math.MP, math.OA · Submitted 2026-09-16 · Read on arXiv

quant-ph, math-ph, math.MP, math.OA

Submitted: 2026-09-16

Updated: 2026-09-20

Terminology

• NPA Hierarchy — 22× in this paper · explained in 2 episodes
• Hilbert Space — 17× in this paper · explained in 2 episodes
• Core — 14× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Noncommutative Polynomial Optimization — 2× in this paper · explained in 2 episodes
• Causal Inference — 1× in this paper · explained in 4 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Spectral Gap — 1× in this paper · explained in 5 episodes
• Steering — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Verifier — 1× in this paper · explained in 2 episodes

Sources

• Online Locality Meets Distributed Quantum Computing
• Distributed Quantum Advantage for Local Problems
• Quantitative quantum soundness for all multipartite compiled nonlocal games
• MIP*=RE
• Fermions are fundamentally more nonlocal than Bosons
• Quantitative Quantum Soundness for Bipartite Compiled Bell Games via the Sequential NPA Hierarchy
• MIPco=coRE
• Experimental randomness certification in a quantum network with independent sources
• The Inflation Technique Completely Solves the Causal Compatibility Problem
• Universal bound on the cardinality of local hidden variables in networks
• Bell nonlocality in networks
• Quantitative Tsirelson's Theorems via Approximate Schur's Lemma and Probabilistic Stampfli's Theorems
• The bulk spectral gap is certifiable from above but uncomputable from below
• Mutually-commuting von Neumann algebra models of quantum networks and violation of Bell-type inequalities

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity