Two instances of random access code in the quantum regime

TL;DR

This paper explores quantum generalizations of Random Access Codes, establishing lower bounds for success probabilities in scenarios involving quantum inputs, entanglement, and constrained communication, advancing understanding of quantum information processing under resource limitations.

Contribution

It introduces new lower bounds for quantum RAC scenarios with various resource constraints and analyzes monogamy relations involving multiple senders and a single receiver.

Findings

Lower bounds established for success probabilities in quantum RACs with entanglement and communication constraints.

Monogamy relation for transmission fidelities involving multiple senders and one receiver.

Quantum lower bounds provided for dense coding with constrained quantum communication for d=2,3,4.

Abstract

We consider two classes of quantum generalisations of Random Access Code (RAC) and study lower 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 random access code with quantum inputs and output known as No-Signalling Quantum RAC (NS-QRAC) [A. Grudka et al. Phys. Rev. A 92, 052312 (2015)], 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. 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. We provide lower bounds for these scenarios. The second class is based on a random access code with a quantum channel and shared entanglement [A. Tavakoli et al. PRX Quantum 2 (4) 040357 (2021)]. 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 encoding employed utilises Gray codes.