2025/05/26 by Yasamin Panahi, Maria Ciudad Alañón, Panahi, Yasamin +11 · 1 citation
Mathematics · #Advanced Topics in Algebra #FOS: Physical sciences #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2505.20519
openalex publication_date 2025/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce novel upper bounds on the Hilbert space dimensions required to realize quantum correlations in Bell scenarios. We start by considering bipartite cases wherein one of the two parties has two settings and two outcomes. Regardless of the number of measurements and outcomes of the other party, the Hilbert space dimension of the first party can be limited to two while still achieving all convexly extremal quantum correlations. We then leverage Schmidt decomposition to show that the remaining party can losslessly also be restricted to a qubit Hilbert space. We then extend this idea to multipartite scenarios. We also adapt our results to provide upper bounds of local Hilbert space dimensions to achieve any quantum correlation, including convexly non-extremal correlations, by utilizing Caratheodory's theorem. Finally, we generalize our results to nonstandard Bell scenarios with communication. Taken together, our results fill in several previously unresolved aspects of the problem of determining sufficient Hilbert space dimensionality, expanding the collection of scenarios for which finite-dimensional quantum systems are known to be sufficient to reproduce any quantum correlation.