The effect on (2, N , 2) Bell tests with distributed measurement dependence
- PDF / 1,411,496 Bytes
- 29 Pages / 439.37 x 666.142 pts Page_size
- 10 Downloads / 210 Views
The effect on (2, N, 2) Bell tests with distributed measurement dependence Dan-Dan Li1,2 Yan Ma1
· Lin-Yan Chen3 · Ya Cao4 · Xiao-Hong Huang1 · Fei Gao4,5 ·
Received: 14 December 2019 / Accepted: 12 August 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Bell tests, as primitive tools to detect nonlocality in bipartite systems, rely on an assumption, i.e., measurement independence. In practice, it is difficult to ensure measurement independence. It is necessary to investigate how Bell tests are affected by relaxing measurement independence. In the simplest (2, 2, 2) CHSH Bell test which consists of two parties, two measurements per party and two possible outcomes per measurement, the results between the maximal value of CHSH correlation function and distributed measurement dependence (DMD) are given, where DMD is a general measure of relaxing measurement independence. However, in a general Bell scenario of an arbitrary number of measurements per party, i.e., (2, N , 2), pertinent results are still missing. To solve it, we establish the relations between the maximal value of (2, N , 2) Pearle–Braunstein–Caves (PBC) chain correlation function that maintains the locality and the degree of DMD, denoted as DMD-induced PBC chain inequalities. Furthermore, we show the tightness of these derived inequalities via constructing local hidden variable models that fake the upper bounds. Compared with the simplest CHSH Bell test, our derived inequalities need less amount of measurement dependence to fake the quantum prediction with N increasing, which is beneficial to analyze the security of device-independent quantum information processing tasks such as randomness expansion.
B
Xiao-Hong Huang [email protected]
1
School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and Telecommunications, Beijing 100876, China
2
State Key Laboratory of Cryptology, P. O. Box 5159, Beijing 100878, China
3
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
4
State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China
5
Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518055, China 0123456789().: V,-vol
123
339
Page 2 of 29
D.-D. Li et al.
Keywords Measurement dependence · PBC chain test · Randomness expansion
1 Introduction Measurements on separated subsystems in an entangled state may display correlations that cannot be mimicked by local hidden variable (LHV) models [1]. Such correlations are termed as nonlocality [2–4]. In recent years, quantum nonlocality, as a resource, has drawn more and more interest on quantum information processing tasks like quantum key distribution [5–7], randomness expansion [8–13], robust certification [14] and self-testing [15–17]. Bell tests [15,18,19], as primitive tools to detect nonlocality, are widely applied to device-independent (DI) quantum information processing tasks, where the
Data Loading...
