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arXiv:2103.03075 · New Journal of Physics

Certification of three black boxes with unsharp measurements using 3 → 1 sequential quantum random access codes

Shihui Wei, Fenzhuo Guo, Fei Gao, Qiaoyan Wen

Published Apr 8, 2021• 8 citations
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Abstract

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.

DOI
10.1088/1367-2630/abf614

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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.
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 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.
Based on a sequential communication game, semi-device-independent certification of an unsharp instrument has recently been demonstrated [K. Mohan, A. Tavakoli, and N. Brunner, New J. Phys. 21, 083034 (2019)]. In this paper, we provide semi-device-independent self-testing protocols in the prepare-measure scenario to certify multiple unsharpness parameters along with the states and the measurement settings. This is achieved through the sequential quantum advantage shared by multiple independent observers in a suitable communication game known as the parity-oblivious random-access code. We demonstrate that in the three-bit parity-oblivious random-access code at most three independent observers can sequentially share quantum advantage. The optimal pair (triple) of quantum advantages enables us to uniquely certify the qubit states, the measurement settings, and the unsharpness parameter(s). The practical implementation of a given protocol involves inevitable losses. In a suboptimal scenario, we derive a certified interval within which a specific unsharpness parameter has to be confined. We extend our treatment to the four-bit case and show that at most two observers can share quantum advantage for the qubit system. Further, we provide an outline to argue that four sequential observers can share the quantum advantage for the two-qubit system, thereby enabling the certification of three unsharpness parameters.
The characterization of multi-time correlations in open quantum systems is of fundamental importance. In this work, we investigate multi-time processes using the process matrix formalism and show that the presence of a quantum-memory environment acts as a resource in enhancing the communication capacity in sequential prepare-transform-measure quantum random access codes (QRAC). The correlated environment enables a quantum advantage to multiple parties, even with projective measurements. In particular, we show that Markovian and classical-memory processes, i.e., non-Markovian quantum processes with classical feedback from the environment, do not yield a sequential quantum advantage. In contrast, it is possible to achieve an advantage in the presence of a quantum-memory environment. Therefore, this approach allows a semi-device-independent certification of quantum non-Markovianity. As opposed to entanglement-detection criteria which require knowledge of the complete process, this method allows to certify the presence of a quantum-memory environment from the observed measurement statistics. Moreover, quantum memory ameliorates the unambiguous certifiable region of unsharp instruments in a semi-device-independent manner.