[1] Schrödinger E. Discussion of probability relations between separated systems[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 31, 555-563(1935).
[2] Einstein A, Podolsky B, Rosen N. Can quantum-mechanical description of physical reality be considered complete?[J]. Physical Review, 47, 777-780(1935).
[3] Born M. Quantenmechanik der stoßvorgänge[J]. Zeitschrift Für Physik, 38, 803-827(1926).
[4] Wiseman H M, Jones S J, Doherty A C. Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox[J]. Physical Review Letters, 98, 140402(2007).
[5] Uola R, Costa A C, Nguyen H C et al. Quantum steering[J]. Reviews of Modern Physics, 92, 015001(2020).
[6] Xiang Y, Sun F X, He Q Y et al. Advances in multipartite and high-dimensional Einstein-Podolsky-Rosen steering[J]. Fundamental Research, 1, 99-101(2021).
[7] Branciard C, Cavalcanti E G, Walborn S P et al. One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering[J]. Physical Review A, 85, 010301(2012).
[8] Walk N, Hosseini S, Geng J et al. Experimental demonstration of Gaussian protocols for one-sided device-independent quantum key distribution[J]. Optica, 3, 634-642(2016).
[9] Passaro E, Cavalcanti D, Skrzypczyk P et al. Optimal randomness certification in the quantum steering and prepare-and-measure scenarios[J]. New Journal of Physics, 17, 113010(2015).
[10] Skrzypczyk P, Cavalcanti D. Maximal randomness generation from steering inequality violations using qudits[J]. Physical Review Letters, 120, 260401(2018).
[11] Brask J B, Martin A, Esposito W et al. Megahertz-rate semi-device-independent quantum random number generators based on unambiguous state discrimination[J]. Physical Review Applied, 7, 054018(2017).
[12] Jones B D, Šupić I, Uola R et al. Network quantum steering[J]. Physical Review Letters, 127, 170405(2021).
[13] Silva R, Gisin N, Guryanova Y et al. Multiple observers can share the nonlocality of half of an entangled pair by using optimal weak measurements[J]. Physical Review Letters, 114, 250401(2015).
[14] Xiang Y, Cheng S M, Gong Q H et al. Quantum steering: practical challenges and future directions[J]. PRX Quantum, 3, 030102(2022).
[15] Żukowski M, Dutta A, Yin Z. Geometric bell-like inequalities for steering[J]. Physical Review A, 91, 032107(2015).
[16] Li J, Wang C Y, Liu T J et al. Experimental verification of steerability via geometric Bell-like inequalities[J]. Physical Review A, 97, 032107(2018).
[17] Cavalcanti D, Skrzypczyk P, Aguilar G H et al. Detection of entanglement in asymmetric quantum networks and multipartite quantum steering[J]. Nature Communications, 6, 7941(2015).
[18] Piani M, Watrous J. Necessary and sufficient quantum information characterization of Einstein-Podolsky-Rosen steering[J]. Physical Review Letters, 114, 060404(2015).
[19] Schneeloch J, Broadbent C J, Walborn S P et al. Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations[J]. Physical Review A, 87, 062103(2013).
[20] Cavalcanti D, Skrzypczyk P. Quantum steering: a review with focus on semidefinite programming[J]. Reports on Progress in Physics, 80, 024001(2017).
[21] Ji W T, Chai Z H, Wang M Q et al. Spin quantum heat engine quantified by quantum steering[J]. Physical Review Letters, 128, 090602(2022).
[22] Cavalcanti P J, Selby J H, Sikora J et al. Post-quantum steering is a stronger-than-quantum resource for information processing[J]. NPJ Quantum Information, 8, 76(2022).
[23] Heisenberg W. Über den anschaulichen inhalt der quantentheoretischen kinematik und mechanik[J]. Zeitschrift Für Physik, 43, 172-198(1927).
[24] Wolf M M, Perez-Garcia D, Fernandez C. Measurements incompatible in quantum theory cannot be measured jointly in any other no-signaling theory[J]. Physical Review Letters, 103, 230402(2009).
[25] Cavalcanti D, Skrzypczyk P. Quantitative relations between measurement incompatibility, quantum steering, and nonlocality[J]. Physical Review A, 93, 052112(2016).
[26] Ku H Y, Hsieh C Y, Chen S L et al. Complete classification of steerability under local filters and its relation with measurement incompatibility[J]. Nature Communications, 13, 4973(2022).
[27] Zhang X L, Qu R, Chang Z H et al. Witnessing quantum incompatibility structures in high-dimensional multimeasurement systems[J]. Physical Review Letters, 133, 190202(2024).
[28] Renner M J. Compatibility of generalized noisy qubit measurements[J]. Physical Review Letters, 132, 250202(2024).
[29] Reid M D, Drummond P D, Bowen W P et al. Colloquium: the Einstein-Podolsky-Rosen paradox: from concepts to applications[J]. Reviews of Modern Physics, 81, 1727-1751(2009).
[30] Weedbrook C, Pirandola S, García-Patrón R et al. Gaussian quantum information[J]. Reviews of Modern Physics, 84, 621-669(2012).
[31] Li X L, Zhai S Q, Liu K. Quantum steering via four‐wave mixing processes and linear beam splitters[J]. Acta Optica Sinica, 45, 0127001(2025).
[32] Wang N, Wang M H, Su X L et al. Quantum steering of gaussian biased entangled states[J]. Journal of Quantum Optics, 30, 020302(2024).
[33] Liu Y, Zheng K M, Kang H J et al. Distillation of Gaussian Einstein-Podolsky-Rosen steering with noiseless linear amplification[J]. NPJ Quantum Information, 8, 38(2022).
[34] Liu S H, Han D M, Wang N et al. Experimental demonstration of remotely creating Wigner negativity via quantum steering[J]. Physical Review Letters, 128, 200401(2022).
[35] Xiang Y, Liu S H, Guo J J et al. Distribution and quantification of remotely generated Wigner negativity[J]. NPJ Quantum Information, 8, 21(2022).
[36] Wang N, Wang M H, Tian C X et al. Experimental demonstration of quantum steering swapping with Gaussian entangled states[J]. Laser & Photonics Reviews, 18, 2300653(2024).
[37] Brasil T B, Novikov V, Kerdoncuff H et al. Two-colour high-purity Einstein-Podolsky-Rosen photonic state[J]. Nature Communications, 13, 4815(2022).
[38] Zeng L, Ma R, Wen H et al. Deterministic distribution of orbital angular momentum multiplexed continuous-variable entanglement and quantum steering[J]. Photonics Research, 10, 777-785(2022).
[39] He Q Y, Reid M D. Genuine multipartite Einstein-Podolsky-Rosen steering[J]. Physical Review Letters, 111, 250403(2013).
[40] Cai Y, Roslund J, Thiel V et al. Quantum enhanced measurement of an optical frequency comb[J]. NPJ Quantum Information, 7, 82(2021).
[41] Wang J W, Paesani S, Ding Y H et al. Multidimensional quantum entanglement with large-scale integrated optics[J]. Science, 360, 285-291(2018).
[42] Armstrong S, Wang M, Teh R Y et al. Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks[J]. Nature Physics, 11, 167-172(2015).
[43] Guo Y, Cheng S M, Hu X M et al. Experimental measurement-device-independent quantum steering and randomness generation beyond qubits[J]. Physical Review Letters, 123, 170402(2019).
[44] Hao Z Y, Sun K, Wang Y et al. Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering[J]. Physical Review Letters, 128, 120402(2022).
[45] de Gois C, Plávala M, Schwonnek R et al. Complete hierarchy for high-dimensional steering certification[J]. Physical Review Letters, 131, 010201(2023).
[46] Zhang Q X, Fang X X, Lu H. Experimental distillation of tripartite quantum steering with an optimal local filtering operation[J]. Photonics Research, 12, 552-562(2024).
[47] Srivastav V, Designolle S, Uola R et al. Quick quantum steering: overcoming loss and noise with qudits[J]. Physical Review X, 12, 041023(2022).
[48] Qu R, Wang Y L, An M et al. Retrieving high-dimensional quantum steering from a noisy environment with N measurement settings[J]. Physical Review Letters, 128, 240402(2022).
[49] Qu R, Wang Y L, Zhang X L et al. Robust method for certifying genuine high-dimensional quantum steering with multimeasurement settings[J]. Optica, 9, 473-478(2022).
[50] Designolle S, Srivastav V, Uola R et al. Genuine high-dimensional quantum steering[J]. Physical Review Letters, 126, 200404(2021).
[51] Händchen V, Eberle T, Steinlechner S et al. Observation of one-way Einstein-Podolsky-Rosen steering[J]. Nature Photonics, 6, 596-599(2012).
[52] Sun K, Ye X J, Xu J S et al. Experimental quantification of asymmetric Einstein-Podolsky-Rosen steering[J]. Physical Review Letters, 116, 160404(2016).
[53] Zeng Q, Wang B, Li P Y et al. Experimental high-dimensional Einstein-Podolsky-Rosen steering[J]. Physical Review Letters, 120, 030401(2018).
[54] Wang T, Han X, Liu S T et al. Manipulation and enhancement of asymmetric steering via down-converted nondegenerate photons[J]. AAPPS Bulletin, 32, 33(2022).
[55] Qu R, Zhang C, Chang Z H et al. Observation of diverse asymmetric structures in high-dimensional Einstein-Podolsky-Rosen steering[J]. Physical Review Letters, 132, 210202(2024).
[56] Sekatski P, Giraud F, Uola R et al. Unlimited one-way steering[J]. Physical Review Letters, 131, 110201(2023).
[57] Guan S Y, Wang H F, Yi X X. Cooperative-effect-induced one-way steering in open cavity magnonics[J]. NPJ Quantum Information, 8, 102(2022).
[58] Breuer H P, Laine E M, Piilo J et al. Colloquium: Non-Markovian dynamics in open quantum systems[J]. Reviews of Modern Physics, 88, 021002(2016).
[59] Wang Y, Hao Z Y, Li J K et al. Observation of non-Markovian evolution of Einstein-Podolsky-Rosen steering[J]. Physical Review Letters, 130, 200202(2023).
[60] Tavakoli A. Quantum steering with imprecise measurements[J]. Physical Review Letters, 132, 070204(2024).
[61] Bowles J, Šupić I, Cavalcanti D et al. Device-independent entanglement certification of all entangled states[J]. Physical Review Letters, 121, 180503(2018).
[62] Wittmann B, Ramelow S, Steinlechner F et al. Loophole-free Einstein-Podolsky-Rosen experiment via quantum steering[J]. New Journal of Physics, 14, 053030(2012).
[63] Jiao Y F, Wang J, Zhang Q et al. Nonreciprocal quantum optics: new effects and applications in quantum sensing[J/OL]. Fundamental Research, 1-4. https://www.sciencedirect.com/science/article/pii/S2667325825000020?via%3Dihub
[64] Lu T X, Wang Y, Xia K Y et al. Quantum squeezing induced nonreciprocal phonon laser[J]. Science China Physics, 67, 260312(2024).
[65] Slussarenko S, Joch D J, Tischler N et al. Quantum steering with vector vortex photon states with the detection loophole closed[J]. NPJ Quantum Information, 8, 20(2022).
[66] Zhao Y Y, Zhang C, Cheng S M et al. Device-independent verification of Einstein-Podolsky-Rosen steering[J]. Optica, 10, 66-71(2023).
[67] Hu M J, Zhou Z Y, Hu X M et al. Observation of non-locality sharing among three observers with one entangled pair via optimal weak measurement[J]. NPJ Quantum Information, 4, 63(2018).
[68] Sasmal S, Das D, Mal S et al. Steering a single system sequentially by multiple observers[J]. Physical Review A, 98, 012305(2018).
[69] Cai Z N, Ren C L, Feng T F et al. A review of quantum correlation sharing: The recycling of quantum correlations triggered by quantum measurements[J]. Physics Reports, 1098, 1-53(2025).
[70] Yao D, Ren C L. Steering sharing for a two-qubit system via weak measurements[J]. Physical Review A, 103, 052207(2021).
[71] Gupta S, Maity A G, Das D et al. Genuine Einstein-Podolsky-Rosen steering of three-qubit states by multiple sequential observers[J]. Physical Review A, 103, 022421(2021).
[72] Liu T J, Liu K, Fang W et al. Witnessing multi-observer steering on both sides simultaneously via weak measurements[J]. Optics Express, 30, 41196-41203(2022).
[73] Pironio S, Acín A, Massar S et al. Random numbers certified by Bell’s theorem[J]. Nature, 464, 1021-1024(2010).
[74] Liu Y, Yuan X, Li M H et al. High-speed device-independent quantum random number generation without a detection loophole[J]. Physical Review Letters, 120, 010503(2018).
[75] Zhang J F, Li Y, Zhao M Y et al. One-sided device-independent random number generation through fiber channels[J]. Light: Science & Applications, 14, 25(2025).
[76] Li Y, Xiang Y, Yu X D et al. Randomness certification from multipartite quantum steering for arbitrary dimensional systems[J]. Physical Review Letters, 132, 080201(2024).
[77] Saggio V, Asenbeck B E, Hamann A et al. Experimental quantum speed-up in reinforcement learning agents[J]. Nature, 591, 229-233(2021).
[78] Ren C L, Chen C B. Steerability detection of an arbitrary two-qubit state via machine learning[J]. Physical Review A, 100, 022314(2019).
[79] Wang H M, Ku H Y, Lin J Y et al. Deep learning the hierarchy of steering measurement settings of qubit-pair states[J]. Communications Physics, 7, 72(2024).
