Two instances of random access code in the quantum regime

• URL: http://arxiv.org/abs/2208.14422v3
• Date: Wed, 14 Jun 2023 10:56:18 GMT
• Title: Two instances of random access code in the quantum regime
• Authors: Nitica Sakharwade, Micha{\l} Studzi\'nski, Micha{\l} Eckstein, and Pawe{\l} Horodecki
• Abstract summary: We consider two classes of quantum generalisations of Random Access Code (RAC) First class is based on a random access code with quantum inputs and output known as No-Signalling Quantum RAC (NS-QRAC) Second class is based on a random access code with a quantum channel and shared entanglement.
• Score: 0.09545101073027092
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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