title: Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation.
abstract: Consider a two-party correlation that can be generated by performing local measurements on a bipartite quantum system. A question of fundamental importance is to understand how many resources, which we quantify by the dimension of the underlying quantum system, are needed to reproduce this correlation. In this Letter, we identify an easy-to-compute lower bound on the smallest Hilbert space dimension needed to generate a given two-party quantum correlation. We show that our bound is tight on many well-known correlations and discuss how it can rule out correlations of having a finite-dimensional quantum representation. We show that our bound is multiplicative under product correlations and also that it can witness the nonconvexity of certain restricted-dimensional quantum correlations.
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, Singapore 117543.|MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654.
authors.forename: Jamie
authors.initials: J
authors.lastname: Sikora
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, Singapore 117543.|MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654.|School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371.
authors.forename: Antonios
authors.initials: A
authors.lastname: Varvitsiotis
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, Singapore 117543.|MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore UMI 3654.|School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371.
authors.forename: Zhaohui
authors.initials: Z
authors.lastname: Wei