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Chinese Optics Letters

Sequential 3 → 1 quantum random access code utilizing unsharp measurements

Zhiguang Pang, Jiang Gao, Tianlei Hou, Min Wei, Jian Li, Qin Wang

Published Jan 1, 2021• 0 citations
Publisher

Abstract

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.

DOI
10.3788/col202119.112701

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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.
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 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.
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.
Unsharp measurements are increasingly important for foundational insights in quantum theory and quantum information applications. Here, we report an experimental implementation of unsharp qubit measurements in a sequential communication protocol, based on a quantum random access code. The protocol involves three parties; the first party prepares a qubit system, the second party performs operations that return both a classical and quantum outcome, and the latter is measured by the third party. We demonstrate a nearly optimal sequential quantum random access code that outperforms both the best possible classical protocol and any quantum protocol that utilizes only projective measurements. Furthermore, while only assuming that the involved devices operate on qubits and that detected events constitute a fair sample, we demonstrate the noise-robust characterization of unsharp measurements based on the sequential quantum random access code. We apply this characterization towards quantifying the degree of incompatibility of two sequential pairs of quantum measurements.