Por Eliahu Cohen (Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Israel).

Quantum correlations exhibit unique features on both conceptual and applied levels. After a brief introduction, I will describe a framework we developed for analyzing them, known as Relativistic Independence [1]. This framework enables to derive the strength of quantum correlations from outside the quantum formalism based on a single assumption regarding the locality of generalized uncertainty principles. Furthermore, it has provided us to with new bounds on quantum correlations, e.g. multiplicative [2] and multipartite [3] Bell inequalities, bounds on topological zero modes [4], bounds on temporal correlations [5], and also suggested us better ways to detect and quantify bipartite [6] and multipartite [7] entanglement. Recently, this framework has been successfully tested in quantum optical experiments [8,9]. I will address all the above and if time permits also mention some applications for quantum algorithms [10] and quantum voting.

References:

• [1] Carmi A., Cohen E., “Relativistic independence bounds nonlocality”, Sci. Adv. 5, eaav8370 (2019).
• [2] Te'eni A., Peled, B.Y., Cohen E., Carmi A., "Multiplicative Bell inequalities", Phys. Rev. A 99 040102(R) (2019).
• [3] Lenny R., Ben Porath D., Cohen E., "Refined Tsirelson bounds on multipartite Bell inequalities", Phys. Rev. A 110, 032435 (2024).
• [4] Carmi A., Herasymenko Y., Cohen E., Snizhko K., "Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes", New J. Phys. 21, 073032 (2019).
• [5] Ben Porath, D. Cohen, E., Leggett-Garg-like Inequalities from a Correlation Matrix Construction, Quantum Rep. 5, 398-406 (2023).
• [6] Peled B.Y., Te'eni A., Carmi A., Cohen E., "Correlation Minor Norm as a Detector and Quantifier of Entanglement", Sci. Rep. 11, 2849 (2021).
• [7] Lenny R., Te'eni A., Peled B., Carmi A., Cohen E., "Multipartite Entanglement Detection via Correlation Minor Norm", Quantum Inf. Process 22, 292 (2023).
• [8] Paneru D., Te'eni A., Peled B. Y., Hubble J., Zhang Y., Carmi A., Cohen E., Karimi E., "Experimental tests of multiplicative Bell inequalities and the fundamental role of local correlations", Phys. Rev. Research 3, L012025 (2021).
• [9] Atzori, F. et al., "Experimental Test of Nonlocality Limits from Relativistic Independence." PRX Quantum 5, 040351 (2024).
• [10] Te'eni A., Schwartzman-Nowik Z., Nowakowski M., Horodecki P., Cohen E. "Oracle problems as communication tasks and optimization of quantum algorithms", arXiv:2409.15549.