Abstract
Quantum communication leads to strong correlations, that can outperform classical ones. Complementary to previous works in this area, we investigate correlations in prepare-and-measure scenarios assuming a bound on the information content of the quantum communication, rather than on its Hilbert-space dimension. Specifically, we explore the extent of classical and quantum correlations given an upper bound on the one-shot accessible information. We provide a characterisation of the set of classical correlations and show that quantum correlations are stronger than classical ones. We also show that limiting information rather than dimension leads to stronger quantum correlations. Moreover, we present device-independent tests for placing lower bounds on the information given observed correlations. Finally, we show that quantum communication carrying logd bits of information is at least as strong a resource as d-dimensional classical communication assisted by pre-shared entanglement.
Highlights
Separated parties, initially independent, can become correlated via communication
The strength of the correlations may vary depending on the nature of the communication; for example if the message is carried by a quantum system rather than a classical one
We show that ensembles of higher-dimensional quantum states carrying no more than one bit of information can generate stronger correlations than two-dimensional quantum systems
Summary
Initially independent, can become correlated via communication. Intuitively, more communication enables stronger correlations. The answer is very natural: we are interested in the information that the message contains about Alice’s input x We formalise this problem and investigate classical and quantum correlations for informationally restricted communication. We quantify the information content of an ensemble of prepared states (classical or quantum) via a one-shot version of accessible information based on min-entropies [13] This choice of information measure has a two-fold motivation. For the case of classical systems, we show that the relevant set of correlations forms a convex polytope, which can be fully characterised This allows one to find the minimal amount of information required to reproduce a given correlation using classical communication. We show that any correlations achievable with classical communication (of a d-dimensional message) assisted by pre-shared entanglement can be achieved using quantum communication carrying log d bits of information
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