Abstract

We consider two classes of quantum generalisations of random access code (RAC) and study the bounds for probabilities of success for such tasks. It provides a useful framework for the study of certain information processing tasks with constrained resources. The first class is based on a RAC with quantum inputs and output known as the no-signalling quantum RAC (NS-QRAC) box (Grudka et al 2015 Phys. Rev. A 92 052312), where unbounded entanglement and constrained classical communication are allowed. We show that it can be seen as quantum teleportation with constrained classical communication and provide a lower quantum bound for the success probability. We consider two modifications to the NS-QRAC scenario: the first, where unbounded entanglement and constrained quantum communication is allowed and the second, where bounded entanglement and unconstrained classical communication is allowed. We find a monogamy relation for the transmission fidelities, which—in contrast to the usual communication schemes—involves multiple senders and a single receiver. We provide an upper bounds for the latter and a lower one for the former. The second class is based on a RAC with a quantum channel and shared entanglement (Tavakoli et al 2021 PRX Quantum 2 040357). 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. We show that such tasks can be seen as quantum dense-coding with constrained quantum communication and explicit protocols, which give lower quantum bounds for the tasks’ efficiency, in dimensions . The employed encoding utilises Gray codes.

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