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Communications in Theoretical Physics

Chain Inequality Violation with Quantum Weak Measurement Technology*

Zheng-Mao Xu, Hong-Wei Li

Published Apr 1, 2019• 0 citations
Publisher

Abstract

Abstract Bell inequality is an important resource in the quantum information theory, which can be applied to guarantee security of the device independent quantum information protocols. By utilizing the quantum weak measurement technology, we propose the Chain inequality violation with three parties, and the analysis result demonstrates that double Chain inequality violation can be observed in the case of Alice and Bob have two different measurement bases. Since the weak measurement model can be assumed to be an eavesdropping model, our analysis model may be applied to analyze security of the device independent quantum information protocols .

DOI
10.1088/0253-6102/71/4/393

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Abstract Bell inequality is an important resource in the quantum information theory, which can be applied to guarantee security of the device independent quantum information protocols. By utilizing the quantum weak measurement technology, we propose the Chain inequality violation with three parties, and the analysis result demonstrates that double Chain inequality violation can be observed in the case of Alice and Bob have two different measurement bases. Since the weak measurement model can be assumed to be an eavesdropping model, our analysis model may be applied to analyze security of the device independent quantum information protocols .
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.
We propose two quantum key distribution (QKD) protocols based on Bell's inequality, which can be considered as modified time-reversed E91 protocol. Similar to the measurement-device-independent quantum key distribution (MDI-QKD) protocol, the first scheme requires the assumption that Alice and Bob perfectly characterize the encoded quantum states. However, our second protocol does not require this assumption, which can defeat more known and unknown source-side attacks compared with the MDI-QKD. The two protocols are naturally immune to all hacking attacks with respect to detections. Therefore, the security of the two protocols can be proven based on the violation of Bell's inequality with measurement data under fair-sampling assumption. In our simulation, the results of both protocols show that long-distance quantum key distribution over 200 km remains secure with conventional lasers in the asymptotic-data case. We present a new technique to estimate the Bell's inequality violation, which can also be applied to other fields of quantum information processing.
The goal of two-party cryptography is to enable two parties, Alice and Bob, to solve common tasks without the need for mutual trust. Examples of such tasks are private access to a database, and secure identification. Quantum communication enables security for all of these problems in the noisy-storage model by sending more signals than the adversary can store in a certain time frame. Here, we initiate the study of device-independent (DI) protocols for two-party cryptography in the noisy-storage model. Specifically, we present a relatively easy to implement protocol for a cryptographic building block known as weak string erasure and prove its security even if the devices used in the protocol are prepared by the dishonest party. DI two-party cryptography is made challenging by the fact that Alice and Bob do not trust each other, which requires new techniques to establish security. We fully analyse the case of memoryless devices (for which sequential attacks are optimal) and the case of sequential attacks for arbitrary devices. The key ingredient of the proof, which might be of independent interest, is an explicit (and tight) relation between the violation of the Clauser–Horne–Shimony–Holt inequality observed by Alice and Bob and uncertainty generated by Alice against Bob who is forced to measure his system before finding out Alice's setting (guessing with postmeasurement information). In particular, we show that security is possible for arbitrarily small violation.
We aim to explore the scenario that a single Alice steers multiple Bobs by using weak measurements. The multiple violations of two different Einstein-Podolsky-Rosen steering inequalities were discussed. Based on unbiased inputs, a single Alice can steer two Bobs when the double violation of the Clauser-Horne-Shimony-Holt-like inequality is realized. Meanwhile, three Bobs can be steered by a single Alice when the triple violation of the three-settings linear steering inequality is observed. More importantly, we theoretically inferred the analytical formula of the maximal violation for the corresponding inequality, which applied an arbitrary two-qubit state.
In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two parties, Alice and Bob each make one of ddd possible measurements, each measurement has nnn outcomes, the Bell inequalities based on the choice of two orbits are derived. The classical bound is only dependent on the number of measurements, but the quantum bound is dependent both on nnn and ddd. Even so, when ddd is large enough, the quantum bound is only dependent on ddd. The subset of probabilities for four parties based on the choice of six orbits under group action is derived and its violation is described. Restricting the six orbits to three parties by forgetting the last party, and guaranteeing the classical bound invariant, the Bell inequality based on the choice of four orbits is derived. All the corresponding nonlocal games are analyzed.
Quantum nonlocality is a significant feature in quantum information theory, prompting recent investigations into the potential reuse of post-measurement states to uncover nonlocality among sequentially measuring observers. While prior studies primarily focused on bipartite or tripartite systems and observers with one chain, such as multiple Bobs with a single Alice or multiple Charlies with a single Alice and Bob, our work extends beyond this framework. We explore sequential nonlocality in systems comprising more parties and observer chains. Our findings reveal that in nnn-partite systems, regardless of whether it is a single-chain or double-chain scenario, there exist unbounded sequential observers capable of detecting nonlocality through violations of the Mermin inequality. In contrast to the conjecture that sequential Bell nonlocality cannot manifest with multiple Alices and Bobs in bipartite systems (i.e., the double-chain setting)[Phys. Rev. A 104, L060201 (2021)], our results suggest that increasing the number of subsystems may enable more observer chains to detect nonlocality alongside single observers. Our study advances research on sequential nonlocality, providing valuable insights into its detection across diverse scenarios.