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arXiv:1712.06810 · Communications Physics

Three-observer classical dimension witness violation with weak measurement

Hong-Wei Li, Yong-Sheng Zhang, Xue-Bi An, Zheng‐Fu Han, Guang‐Can Guo

Published Mar 5, 2018• 16 citations
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Abstract

Abstract Dimension is an important resource in quantum information theory. Based on weak measurement technology, we propose the three-observer dimension witness protocol in a prepare-and-measure setup. By applying the dimension witness inequality based on the quantum random access code and the nonlinear determinant value, we demonstrate that double classical dimension witness violation is achievable if we choose appropriate weak measurement parameters. Analysis of the results will shed new light on the interplay between the multi-observer quantum dimension witness and the weak measurement technology, which can also be applied in the generation of semi-device-independent quantum random numbers and quantum key distribution protocols.

DOI
10.1038/s42005-018-0011-x

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Abstract Dimension is an important resource in quantum information theory. Based on weak measurement technology, we propose the three-observer dimension witness protocol in a prepare-and-measure setup. By applying the dimension witness inequality based on the quantum random access code and the nonlinear determinant value, we demonstrate that double classical dimension witness violation is achievable if we choose appropriate weak measurement parameters. Analysis of the results will shed new light on the interplay between the multi-observer quantum dimension witness and the weak measurement technology, which can also be applied in the generation of semi-device-independent quantum random numbers and quantum key distribution protocols.
Random number generation is an important task in modern science. A variety of quantum random number generation protocols have been proposed and realized. These protocols, however, are all based on two parties. Based on the weak measurement technique, we propose and realize a quantum random number generator among three observers. The violation of a double classical dimension witness based on the determinant value is first observed in experiment. With the heralding single-photon source, our experimental setup attains the independent assumption and the dimension assumption, which means our setup is semi-device-independent (DI). This Letter sheds new light on generating DI-type random number among multi-user and it has potential application prospect on the quantum cryptography and quantum random number in network environment.
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Abstract A dimension witness is a criterion that sets a lower bound on the dimension needed to reproduce the observed data. Three types of dimension witnesses can be found in the literature: device-dependent ones, in which the bound is obtained assuming some knowledge on the state and the measurements; device-independent prepare-and-measure ones, that can be applied to any system including classical ones; and device-independent Bell-based ones, that certify the minimal dimension of some entangled systems. Here we consider the Collins–Gisin–Linden–Massar–Popescu Bell-type inequality for four outcomes. We show that a sufficiently high violation of this inequality witnesses d ≥ 4 and present a proof-of-principle experimental observation of such a violation. This presents a first experimental violation of the third type of dimension witness beyond qutrits.
Semi-device-independent quantum key distribution (SDI-QKD) has been proposed by applying the quantum dimension correlation, and the security relies on the violation of quantum dimension witness inequalities. We prove the security of the SDI-QKD protocol under the depolarization channel by considering the quantum dimension witness inequalities and minimum entropy and the specific process of the QKD protocol, combining with a four-quantum-state preparation and three measurement bases. We also provide the relationship between the dimension witness value, the error rate and the security key rate by the numerical simulation.
We report on an experimental test of classical and quantum dimension. We have used a dimension witness that can distinguish between quantum and classical systems of dimensions two, three, and four and performed the experiment for all five cases. The witness we have chosen is a base of semi-device-independent cryptographic and randomness expansion protocols. Therefore, the part of the experiment in which qubits were used is a realization of these protocols. In our work we also present an analytic method for finding the maximum quantum value of the witness along with corresponding measurements and preparations. This method is quite general and can be applied to any linear dimension witness.
We consider the problem of testing the dimension of uncharacterized classical and quantum systems in a prepare-and-measure setup. Here we assume the preparation and measurement devices to be independent, thereby making the problem nonconvex. We present a simple method for generating nonlinear dimension witnesses for systems of arbitrary dimension. The simplest of our witnesses is highly robust to technical imperfections, and can certify the use of qubits in the presence of arbitrary noise and arbitrarily low detection efficiency. Finally, we show that this witness can be used to certify the presence of randomness, suggesting applications in quantum information processing.