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Extreme quantum entanglement in a superposition of macroscopically distinct states
Abstract
A Bell inequality is derived for a state of n spin-1/2 particles which superposes two macroscopically distinct states. Quantum mechanics violates this inequality by an amount that grows exponentially with n.
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“While Bell’s inequality violation is established between pairs of quantum states through their density matrices (of size 2² × 2²)—which, in our case, are qubits—Mermin’s inequality applies to multi-particle interactions beyond isolated state pairs.”
From Mathematical proof of the Fisher-Escolà Q statistical distribution in quantum consciousness modeling (2025) · cites this paper as [46]
Citations
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- Bell, 1965, Physics (N.Y.), 1, 195
- Bohm, 1951, Quantum Theory
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Bell’s Theorem without Inequalities and Beyond
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“If each of the six variables can be assigned to predefined values −1 or +1, then we can get the following Merminlike inequality [39, 40]”
BackgroundBernstein's paradox of entangled quantum states
Belinskii, A. V., & Chirkin, A. S. (2013) · Uspekhi Fizicheskih Nauk · doi:10.3367/ufnr.0183.201311e.1231 · Cited by 4
Rizvi, S. M. A., Asif, N., Ulum, M. S., Duong, T. Q., & Shin, H. (2022) · Sensors · doi:10.3390/s22186767 · Cited by 5
“Similar to the CHSH inequality, which uses two measurement settings for each party in bipartite systems, there is the Mermin inequality for multipartite systems [52].”
MethodQuantum nonlocality in the presence of strong measurement dependence
Šupić, I., Bancal, J.-D., & Brunner, N. (2023) · Physical Review A · doi:10.1103/physreva.108.042207 · Cited by 4
“Our starting point are quantum nonlocal correlation arising from the Peres-Mermin (PM) magic-square game [25, 26], which have been proposed in Ref.”
BackgroundMethodDetecting the genuine multipartite two-way steerability with linear steering inequalities
Jiang, G., Wu, X., & Zhou, T. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03729-w · Cited by 4
“2 TheMermin operator With the usually used denotation X = σx , Y = σy , and Z = σz , the Mermin operator can be introduced [88],”
MethodGebhart, V., & Smerzi, A. (2022) · Physical Review A · doi:10.1103/physreva.106.062202 · Cited by 4
“6 inequality [53] and Svetlichny inequality [37] for N = 3.”
BackgroundMethodCosmic primordial density fluctuations and Bell inequalities
Dale, R., Lapiedra, R., & Morales-Lladosa, J. A. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.023506 · Cited by 4
“However, there exist extended inequalities for the multipartite case [27, 28].”
BackgroundThe Separability Problem in Two Qubits Revisited
Gnonfin, H., & Gouba, L. (2023) · Symmetry · doi:10.3390/sym15112089 · Cited by 4
Unbounded sequential multipartite nonlocality via violation of the Mermin inequality
Shen, B.-Z., & Li, M.-S. (2024) · Physical Review A · doi:10.1103/physreva.110.012217 · Cited by 4
“Secondly, referring to [24, 25], the multipartite Mermin polynomials M n can be calculated as follows .”
MethodNonlocality and Multipartite Entanglement in Asymptotically Flat Space-Times
Moradi, S., & Amiri, F. (2016) · Communications in Theoretical Physics · doi:10.1088/0253-6102/65/1/17 · Cited by 4
Violation of Mermin–Ardehali–Belinksii–Klyshko inequality in the three-Jaynes–Cummings model
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Feng, T., Ren, C., Feng, Q., Luo, M., Qiang, X., Chen, J., & Zhou, X. (2021) · Photonics Research · doi:10.1364/prj.411033 · Cited by 4
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Probabilistic and robust preparation of a GHZ-type state via atomic ensembles and linear optics
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Quantum Physics with Neutrons: From Spinor Symmetry to Kochen-Specker Phenomena
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Entanglement of Bell diagonal mixed states
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Explicit Lower and Upper Bounds on the Entangled Value of Multiplayer XOR Games
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Regularized tripartite continuous variable EPR-type states with Wigner functions and CHSH violations
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“Generalized N-mode Bell inequalities—CHSH inequalities, in terms of the Bell operator expectation values BN—exist (see for example [16]).”
BackgroundENTANGLEMENT DISTRIBUTION AND STATE DISCRIMINATION IN TRIPARTITE QUBIT SYSTEMS
Batle, J. A. I., & Casas, M. (2008) · International Journal of Quantum Information · doi:10.1142/s0219749908003487 · Cited by 4
Assadi, L., & Jafarpour, M. (2016) · International Journal of Theoretical Physics · doi:10.1007/s10773-016-3104-x · Cited by 4
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Anshu, A., Høyer, P., Mhalla, M., & Perdrix, S. (2017) · Lecture notes in computer science · doi:10.1007/978-3-662-55751-8_5 · Cited by 4
All-versus-nothing proofs with n qubits distributed between m parties
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Morimae, T. (2009) · Physical Review A · doi:10.1103/physreva.80.012105 · Cited by 4
Multipartite Entanglement for Continuous Variables
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Qiu, L., Wu, Y. X., & Wang, A. M. (2010) · Optics Communications · doi:10.1016/j.optcom.2010.03.050 · Cited by 4
On the use of double entanglement in four-photon experiments
Pittman, T. B. (1995) · Physics Letters A · doi:10.1016/0375-9601(95)00468-i · Cited by 4
Tripartite States Bell-Nonlocality Sudden Death under Stochastic Dephasing
Zhang, D.-Y., Li-Jun, X., Tang, S.-Q., Xiao-Gui, Z., & Feng, G. (2009) · Chinese Physics Letters · doi:10.1088/0256-307x/26/8/080301 · Cited by 4
T Cells as primary players in rheumatoid arthritis
Falta, M. T., & Kotzin, B. L. (1998) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-8823-3_11 · Cited by 4
Silicon Quantum Photonics ‐ Platform and Applications
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Sarubi, T. S., Zamora, S., Alves, M., Alves, V. F., Viswanathan, G. M., & Chaves, R. (2026) · Brazilian Journal of Physics · doi:10.1007/s13538-026-02008-8 · Cited by 4
“Inspired by this direct refutation of the EPR argument by means of considering 4-particle states, which seemed to show stronger correlations than those of 2-particle cases, in 1990 Mer-min considered n 1 / 2-spin particles and proposed a set of n -partite inequalities which now carry his name [71].”
Correlated multipartite quantum states
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“Moreover, we measure the quantum nonlocality of GHZ entanglement via both the all-versus-nothing (AVN) test [19,23] and the Mermin inequalities [50,51], showing the striking conflict of quantum physics to local realism in the multiphoton scenario.”
MethodXiao, Y., Wang, Z., Zhao, W., & Li, M. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202400101 · Cited by 3
“…a violation of this limit can be observed from the quantum correlations generated by performing local measurements on entangled particles, [2–4] which indicates that the predictions of quantum theory are incompatible with local realism theory and we thus refer to this striking phenomenon…”
BackgroundBell’s and Mermin’s Inequalities, Entangled Coherent States and Unitary Operators
sorella, S. P. (2024) · International Journal of Theoretical Physics · doi:10.1007/s10773-024-05764-y · Cited by 3
Many-body quantum resources of graph states
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Homogenization of Bell inequalities
Wu, Y.-C., & Żukowski, M. (2012) · Physical Review A · doi:10.1103/physreva.85.022119 · Cited by 3
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Ali, M. (2017) · International Journal of Quantum Information · doi:10.1142/s0219749917500228 · Cited by 3
Self-guided method to search maximal Bell violations for unknown quantum states
Yang, L.-K., Chen, G., Zhang, W.-H., Peng, X.-X., Yu, S., Ye, X.-J., Li, C., & Guo, G. (2017) · Physical Review A · doi:10.1103/physreva.96.052310 · Cited by 3
Typical Werner states satisfying all linear Bell inequalities with dichotomic measurements
Luo, M. (2018) · Physical Review A · doi:10.1103/physreva.97.042301 · Cited by 3
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Symmetrized persistency of Bell correlations for Dicke states and GHZ-based mixtures
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Shannon and von Neumann entropies of multi-qubit Schrödinger's cat states
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Quantifying Multipartite Nonlocality
Bancal, J.-D. (2013) · Springer theses · doi:10.1007/978-3-319-01183-7_5 · Cited by 3
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“For a mere classical system, that is, one which obeys a local hidden variable theory, it is well known that the correlation measure is bounded by the CHSH theorem [37].”
BackgroundExtending the fair sampling assumption using causal diagrams
Gebhart, V., & Smerzi, A. (2023) · Quantum · doi:10.22331/q-2023-01-13-897 · Cited by 3
“Using the LHV model, one can demonstrate inequalities that test multipartite nonlocality [46].”
BackgroundMethodProbing Mermin’s inequalities violations through pseudospin operators
Fabritiis, P. D., Roditi, I., & sorella, S. P. (2023) · Physics Open · doi:10.1016/j.physo.2023.100177 · Cited by 3
Macroscopic Wigner's friend paradoxes: Consistency with weak macroscopic realism
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Detecting and eliminating quantum noise of quantum measurements
Tang, S., Zheng, C., & Wang, K. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad7a2a · Cited by 5
“Our first application is to estimate the expectation values of Mermin polynomials [55], which are one of the most significant examples to test non-local quantum correlations in multipartite systems.”
BackgroundSemicoherent symmetric quantum processes: Theory and applications
Wang, Y., Chehade, S., & Dumitrescu, E. (2024) · AVS Quantum Science · doi:10.1116/5.0215919 · Cited by 3
“The factors appearing in 𝑀 𝑘 takes the form of the ladder operators 𝑎 𝑙 ± 𝑖𝑎 ′ 𝑙 = 𝜎 𝑥𝑙 ± 𝑖𝜎 = 𝜎 ± 𝑙 , which is exactly the same factor appeared in the polynomial defined by Mermin [36, Eq.”
BackgroundSharing tripartite nonlocality sequentially using only projective measurements
Xu, Y., Sun, H., Guo, F.-Z., Dong, H., & Wen, Q. (2025) · Quantum Information Processing · doi:10.1007/s11128-024-04638-w · Cited by 3
“This inequality takes the following form. where In 1987, Svetlichny [10] introduced genuine tripartite nonlocality, which means that when the correlations cannot be described by the following local hidden variable model, where 0 ≤ q ( ξ ) , q ( µ ) , q ( ν ) ≤ 1, and ξ q ( ξ )”
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“Forexample,in the qubit case, Mermin ’ s multi-player game 68 is implicitly integrated into R 2 over the variables preserved by the random restriction.”
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Dehingia, K., & Dutta, N. (2025) · Concurrency and Computation Practice and Experience · doi:10.1002/cpe.70221 · Cited by 3
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Weaving and neural complexity in symmetric quantum states
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“For k = 1,N = 3, the set P1 = { σ3 = σ[1] ⊗ σ[2] ⊗ σ[3] } consists of all the single-particle product states.”
The Kochen-Specker Theorem Based on the Kronecker Delta
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Faujdar, J., & Kumar, A. (2021) · Quantum Information Processing · doi:10.1007/s11128-021-02993-6 · Cited by 3
Hou, T., Ding, D., Wang, C., Zhang, X., & He, Y.-Q. (2021) · International Journal of Theoretical Physics · doi:10.1007/s10773-021-04815-y · Cited by 3
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Chain of Hardy-type local reality constraints for n qubits
Sibasish Ghosh, A., & Roy, S. M. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3512994 · Cited by 3
Exponential quantum enhancement for distributed addition with local nonlinearity
Marblestone, A. H., & Devoret, M. (2009) · Quantum Information Processing · doi:10.1007/s11128-009-0126-9 · Cited by 3
“Mermin’s Parity Game is itself a generalization of Mermin’s famous “arguments without inequalities” for quantum non-locality [12,13], which in turn built on the pioneering work of Greenberger, Horne and Zeilinger.”
ResultEntanglement between degrees of freedom of single neutrons
Hasegawa, Y., Badurek, G., Filipp, S., Klepp, J., Loidl, R., Sponar, S., & Rauch, H. (2009) · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment · doi:10.1016/j.nima.2009.07.060 · Cited by 3
New perspectives on quantum correlations
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Tripartite states Bell-nonlocality sudden death in a quantum-critical environment
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Tripartite entanglement generation using cavity-QED and its dynamics in dissipative environments
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Entanglement swapping of a GHZ state via a GHZ-like state
Tsai, C., & Hwang, T. (2011) · Physica Scripta · doi:10.1088/0031-8949/84/04/045006 · Cited by 4
Experimentally simulating the violation of Bell-type inequalities for generalized GHZ states
Ren, C., Lu, D., Shi, M., Peng, X., & Du, J. (2009) · Physics Letters A · doi:10.1016/j.physleta.2009.09.052 · Cited by 3
Unsharp observables and objectification problem in quantum theory
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Relation between nonlocality and contextuality for a biphoton
Soeda, A., Kurzyński, P., Ramanathan, R., Modi, K. K., & Kaszlikowski, D. (2013) · Physical Review A · doi:10.1103/physreva.87.022120 · Cited by 3
Entanglement and nonlocality for generalized Greenberger-Horne-Zeilinger state
Xiao-Qin, W., Huai-Xin, L., & Zhao, J.-Q. (2011) · Acta Physica Sinica · doi:10.7498/aps.60.110301 · Cited by 3
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Determining X -chains in graph states
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Relativistic three-partite non-locality
Moradpour, H., & Montakhab, A. (2016) · International Journal of Quantum Information · doi:10.1142/s0219749916500088 · Cited by 3
Local decoherence-resistant quantum states of large systems
Mishra, U., Sen, A., & Sen, U. (2014) · Physics Letters A · doi:10.1016/j.physleta.2014.11.037 · Cited by 3
Beating the Clauser-Horne-Shimony-Holt and the Svetlichny games with optimal states
Su, H.-Y., Ren, C., Chen, J., Zhang, F., Wu, C., Xu, Z., Gu, M., Vinjanampathy, S., & Kwek, L. C. (2016) · Physical Review A · doi:10.1103/physreva.93.022110 · Cited by 3
“So far, investigations on Bell-type inequalities for quantum systems of arbitrary parties and dimensions have been undertaken [6–10].”
BackgroundMajorization of quantum polarization distributions
Luis, A., & Donoso, G. (2016) · Physical Review A · doi:10.1103/physreva.94.063858 · Cited by 3
“Further states with interesting practical applications relying on their strong quantum properties are the N00N or Schrödinger’s cat states [22] which we shall refer to as N”
BackgroundNearly maximal violation of the Mermin-Klyshko inequality with multimode entangled coherent states
Sheng, J.-Q., Lin, L.-H., Zhong, Z.-R., & Zheng, S.-B. (2019) · Optics Express · doi:10.1364/oe.27.031864 · Cited by 3
Metadata
- Authors
- Mermin, N. D.
- Affiliations
- Cornell University (US)
- Corresponding author
- Mermin, N. David
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1990-10
- Volume
- 65
- Issue
- 15
- Pages
- 1838-1840
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2094119863
- Cited by
- 1,482
- References
- 3
- Citations by year
- 2026: 44 · 2025: 66 · 2024: 66 · 2023: 80 · 2022: 65 · 2021: 59 · 2020: 45 · 2019: 107 · 2018: 56 · 2017: 47 · 2016: 66 · 2015: 55 · 2014: 46 · 2013: 66 · 2012: 62
- FWCI
- 5.96
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- Bell inequalities, quantum entanglement, macroscopic superposition, spin-1/2 particles, quantum violation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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