The encoding employed utilises Gray codes.Ĭorrelations in Einstein-Podolsky-Rosen (EPR) scenarios, captured by \textit of unnormalised quantum states, have recently caught the attention of the community, both from a foundational and an information-theoretic perspective. We study the set of tasks where two inputs made of two digits of $d$-base are encoded over a qudit and a maximally entangled state, which can be seen as quantum dense coding with constrained quantum communication, for which we provide quantum lower bounds for $d=2,3,4$. The second class is based on a random access code with a quantum channel and shared entanglement. We provide lower bounds for these scenarios. We consider two modifications to the NS-QRAC scenario, first where unbounded entanglement and constrained quantum communication is allowed and, second where bounded entanglement and unconstrained classical communication are allowed, where we find a monogamy relation for the transmission fidelities, which - in contrast to the usual communication schemes - involves multiple senders and a single receiver. The first class is based on a random access code with quantum inputs and output known as No-Signalling Quantum RAC (NS-QRAC), where unbounded entanglement and constrained classical communication are allowed, which can be seen as quantum teleportation with constrained classical communication, for which we provide a quantum lower bound.
It provides a useful framework for the study of certain information processing tasks with constrained resources. We consider two classes of quantum generalisations of Random Access Code (RAC) and study lower bounds for probabilities of success for such tasks.
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