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Consider a two-party correlation that can be generated by performing localmeasurements on a bipartite quantum system. A question of fundamentalimportance is to understand how many resources, which we quantify by thedimension of the underlying quantum system, are needed to reproduce thiscorrelation. In this Letter, we identify an easy-to-compute lower bound on thesmallest Hilbert space dimension needed to generate a given two-party quantumcorrelation. We show that our bound is tight on many well-known correlationsand discuss how it can rule out correlations of having a finite-dimensionalquantum representation. We show that our bound is multiplicative under productcorrelations and also that it can witness the non-convexity of certainrestricted-dimensional quantum correlations.

Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation