A general bound for the dimension of quantum behaviours in the prepare-and-measure scenario

Abstract

The prepare-and-measure scenario offers the possibility to infer the dimension of an unknown physical system in a device-independent way, i.e. using only raw measurement data with apparatuses regarded as black boxes. We provide here a general lower bound on the dimension necessary to observe arbitrary quantum behaviours in this scenario based on simple matrix analysis. This bound holds even if the preparer and measurer share randomness. This is relevant in scenarios were the parties are free to access this resource or it is not safe to assume that the devices are not correlated. We further use this result to bound the success probability of random access codes in general as a function of the dimension of the quantum systems sent from one party to another and we provide constructions of dimension witnesses.

9 pages. v2: Reference added

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Cited by in corpus (6)

• Device-independent certification of Hilbert space dimension using a family of Bell expressions
• Communication tasks in operational theories
• Quantum stochastic communication via high-dimensional entanglement
• Simple and general bounds on quantum random access codes
• The geometry of Bloch space in the context of quantum random access codes
• Orthogonal Projections on Hyperplanes Intertwined With Unitaries