English
Related papers

Related papers: Formalizing CHSH Rigidity in Lean 4

200 papers

Reliable verification of entanglement is a central requirement for quantum networks. This paper presents a practical verification approach based on violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality. We derive tight mathematical…

Quantum Physics · Physics 2025-09-09 Xuan Du Trinh , Zhengyu Wu , Junlin Bai , Huan-Hsin Tseng , Nengkun Yu , Aruna Balasubramanian

The famous Clauser-Horne-Shimony-Holt (CHSH) inequality certifies a quantum violation, by a factor $\sqrt{2}$, of correlations predicted by the classical view of the world in the simplest possible nontrivial measurement setup (two systems…

Quantum Physics · Physics 2017-12-25 Ben Li

The Clauser-Horne-Shimony-Holt (CHSH) inequality is a constraint that local theories must obey. Quantum Mechanics predicts a violation of this inequality in certain experimental settings. Treatments of this subject frequently make…

Quantum Physics · Physics 2015-05-21 Peter Bierhorst

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of…

Quantum Physics · Physics 2007-05-23 Li-Bin Fu

Recently, Fan \textit{et al.} [Mod. Phys. Lett. A 36, 2150223 (2021)], presented a generalized Clauser-Horne-Shimony-Holt (CHSH) inequality, to identify $N$-qubit Greenberger-Horne-Zeilinger (GHZ) states. They showed an interesting…

Quantum Physics · Physics 2022-06-09 Gang-Gang He , Xing-Yan Fan , Fu-Lin Zhang

We evaluate the maximal Clauser-Horne-Shimony-Holt (CHSH) violation for a generic (typically mixed) qubit-qudit state, obtaining easily computable expressions in arbitrary qudit dimension. This represents the optimal (2-2-2) Bell…

Quantum Physics · Physics 2025-10-22 Alexander Bernal , J. Alberto Casas , Jesus M. Moreno

We establish a necessary and sufficient condition for the existence of a quantum state that reproduces given correlation values in the Clauser--Horne--Shimony--Holt (CHSH) setup for any fixed normalized observables. This result addresses a…

Quantum Physics · Physics 2025-06-17 Ryosuke Nogami , Jaeha Lee

Free will (or randomness) has been studied to achieve loophole-free Bell's inequality test and to provide device-independent quantum key distribution security proofs. The required randomness such that a local hidden variable model (LHVM)…

Quantum Physics · Physics 2017-03-29 Yifeng Teng , Shenghao Yang , Siwei Wang , Mingfei Zhao

Cirel'son inequality states that the absolute value of the combination of quantum correlations appearing in the Clauser-Horne-Shimony-Holt (CHSH) inequality is bound by $2 \sqrt 2$. It is shown that the correlations of two qubits belonging…

Quantum Physics · Physics 2009-07-28 Adan Cabello

Self-testing refers to the phenomenon that certain extremal quantum correlations (almost) uniquely identify the quantum system under consideration. For instance observing the maximal violation of the CHSH inequality certifies that the two…

Quantum Physics · Physics 2016-08-12 Jędrzej Kaniewski

We present a formalization of several fundamental notions and results from Quantum Information theory, including density matrices and projective measurements, along with the proof that the local hidden-variable hypothesis advocated by…

Quantum Physics · Physics 2023-06-23 Mnacho Echenim , Mehdi Mhalla

It is pointed out that the local hidden variables model of Bell and Clauser-Horne-Shimony-Holt (CHSH) gives $|<B>|\leq 2\sqrt{2}$ or $|<B>|\leq 2$ for the quantum CHSH operator $B={\bf a}\cdot {\bf \sigma}\otimes ({\bf b}+{\bf…

Quantum Physics · Physics 2012-07-03 Kazuo Fujikawa

There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser-Horne-Shimony-Holt (CHSH) inequality is very robust.…

Quantum Physics · Physics 2013-09-17 Sascha Vongehr

Two parties sharing entangled quantum systems can generate correlations that cannot be produced using only shared classical resources. These nonlocal correlations are a fundamental feature of quantum theory but also have practical…

Quantum Physics · Physics 2022-10-06 Lewis Wooltorton , Peter Brown , Roger Colbeck

The CHSH mod 3 Bell inequality is a natural testbed for higher-dimensional quantum nonlocality, yet its maximal quantum violation and self-testing properties have remained unresolved. We determine its exact maximal quantum value and show…

Optimization and Control · Mathematics 2026-04-07 Igor Klep , Nando Leijenhorst , Victor Magron

The Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, which is proven in the context of the local hidden variable theory, has been used as a test to reveal failure of the hidden variable theory and to prove validity of the quantum theory.…

Quantum Physics · Physics 2010-10-27 Tomohiro Isobe , Shogo Tanimura

In this work we aim to analyze the Clauser-Horne-Shimony-Holt CHSH inequality strictly in the context of probability theory. In the course of assembling inequality we have to take care not to produce assumptions a priori, that is,…

Quantum Physics · Physics 2018-05-31 Felipe Andrade Velozo , José A. C. Nogales , Gustavo Figueiredo Araújo

Relativistic causality forbids superluminal signaling between distant observers. By exploiting the non-signaling principle, we derive the exact relationship between the chained Clauser-Horne-Shimony-Holt sum of correlations CHSH_K and the…

Quantum Physics · Physics 2015-08-27 José L. Cereceda

It is well-known that no local model - in theory - can simulate the outcome statistics of a Bell-type experiment as long as the detection efficiency is higher than a threshold value. For the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality…

Quantum Physics · Physics 2023-02-14 Shihan Sajeed , Nigar Sultana , Charles Ci Wen Lim , Vadim Makarov

Scalable quantum computing relies on high-quality, long-range entanglement, a challenge on noisy, near-term devices. The need for practical insights for near-term algorithm design calls for trade-offs exploration in implementing dynamic…

Quantum Physics · Physics 2025-07-16 Jean-Baptiste Waring , Christophe Pere , Sébastien Le Beux
‹ Prev 1 2 3 10 Next ›