Abstract
Quantum random access codes (QRACs) are key tools for a variety of protocols in quantum information theory. These are commonly studied in prepare-and-measure scenarios in which a sender prepares states and a receiver measures them. Here, we consider a three-party prepare-transform-measure scenario in which the simplest QRAC is implemented twice in sequence based on the same physical system. We derive optimal trade-off relations between the two QRACs. We apply our results to construct semi-device independent self-tests of quantum instruments, i.e. measurement channels with both a classical and quantum output. Finally, we show how sequential QRACs enable inference of upper and lower bounds on the sharpness parameter of a quantum instrument.
Highlights
Random Access Codes (RACs) are an important class of communication tasks with a broad scope of applications
We consider a three-party prepare-transform-measure scenario in which the simplest Quantum Random Access Codes (QRACs) is implemented twice in sequence based on the same physical system
QRACs are common in foundational aspects of quantum theory; examples include the comparison of different quantum resources [7, 8], dimension witnessing [9], selftesting [10–12] and attempts at characterising quantum correlations from information-theoretic principles [13]
Summary
Random Access Codes (RACs) are an important class of communication tasks with a broad scope of applications. In a RAC, a party Alice holds a set of randomly sampled data and another party Bob attempts to recover some randomly chosen subset of Alice’s data This is made possible by Alice communicating with Bob. This is made possible by Alice communicating with Bob This corresponds to a prepareand-measure scenario in which Alice encodes her data into a message that she sends to Bob who aims to decode the relevant information. The probability of Bob to access the desired information can be increased if Alice substitutes her classical message with a quantum message of the same alphabet Such Quantum Random Access Codes (QRACs) have been introduced and developed for qubit systems [1, 2] as well as higher-dimensional quantum systems [3].
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