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arXiv:1905.06726 · New Journal of Physics

Sequential random access codes and self-testing of quantum measurement instruments

Karthik Mohan, Armin Tavakoli, Nicolas Brunner

Published Jul 31, 2019• 85 citations
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Abstract

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.

DOI
10.1088/1367-2630/ab3773

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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.
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.
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.
Abstract Unsharp measurements play an increasingly important role in quantum information theory. In this paper, we study a three-party prepare-transform-measure experiment with unsharp measurements based on 3 → 1 sequential random access codes (RACs). We derive optimal trade-off between the two correlation witnesses in 3 → 1 sequential quantum random access codes (QRACs), and use the result to complete the self-testing of quantum preparations, instruments and measurements for three sequential parties. We also give the upper and lower bounds of the sharpness parameter to complete the robustness analysis of the self-testing scheme. In addition, we find that classical correlation witness violation based on 3 → 1 sequential RACs cannot be obtained by both correlation witnesses simultaneously. This means that if the second party uses strong unsharp measurements to overcome the classical upper bound, the third party cannot do so even with sharp measurements. Finally, we give the analysis and comparison of the random number generation efficiency under different sharpness parameters based on the determinant value, 2 → 1 and 3 → 1 QRACs separately. This letter sheds new light on generating random numbers among multi-party in semi-device independent framework.
We present a hitherto unexplored semi-device-independent (SDI) self-testing protocol designed to certify unitary operations within a variant of prepare-measure framework. We consider a communication game which we refer to as a variant of 333-bit prepare-measure random access code (PMRAC) involving two parties, Alice and Bob, who share a prior two-qubit quantum state. Alice encodes her message by applying unitary operations on her subsystem and sends it to Bob. To decode the message, Bob performs a measurement on the whole system. We demonstrate that the optimal quantum advantage of the variant of 333-bit PMRAC over the classical bound enables the self-testing of Alice's unitary operations and Bob's measurements. The derivation of the optimal quantum success probability is fully analytical. The approach is so elegant that it can be generalized for any arbitrary nnn-bit PMRAC and may also be extended to other prepare-measure communication games.
Quantum random access code (QRAC) serves the communication task to encode a long message into a quantum system and allow the receiver to decode the initial information with a higher success probability than classical random access code (RAC). Here, we present an experimental demonstration of sequential 3 → 1 QRAC in the prepare-transform-measure scenario with one sender and three independent receivers. The experimental results show that, in the 3 → 1 QRAC scenario, three receivers can independently decode the initial information with an average success probability higher than the classical RAC.
Quantum random access codes (QRACs) are important communication tasks that are usually implemented in prepare-and-measure scenarios. The receiver tries to retrieve one arbitrarily chosen bit of the original bit-string from the code qubit sent by the sender. In this Letter, we analyze in detail the sequential version of the 3→1 QRAC with two receivers. The average successful probability for the strategy of unsharp measurement is derived. The prepare-and-measure strategy within projective measurement is also discussed. It is found that sequential 3→1 QRAC with weak measurement cannot be always superior to the one with projective measurement, as the 2→1 version can be.