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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]
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- Bell, 1965, Physics (N.Y.), 1, 195
- Bohm, 1951, Quantum Theory
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On some neglected thermodynamic peculiarities of quantum non-locality
Elitzur, A. C. (1990) · Foundations of Physics Letters · doi:10.1007/bf00666022 · Cited by 10
Test of the violation of local realism in quantum mechanics without Bell inequalities
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“De forma geral, o aumento do número de sub-sistemas emaranhados permite criar contradições com a f́ısica clássica cada vez mais fortes [Mermin 1990b].”
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Playing Nonlocal Games across a Topological Phase Transition on a Quantum Computer
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“If the resource state is deformed from | GHZ ⟩ to | 𝜓 ⟩ then the probability of victory becomes where 𝑃 is a Mermin polynomial [8], which contains mono-mials of order composed of and operators.”
Multipartite nonlocality in one-dimensional quantum chains: A transfer-matrix theory
Sun, Z., Wen, H.-X., Li, M., & Guo, B. (2022) · Physical Review A · doi:10.1103/physreva.105.012213 · Cited by 9
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“The first Bell inequality for N = 3 qubits was provided by Mermin [39].”
MethodRevealing hidden genuine tripartite nonlocality
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Activation of the violation of the Svetlichny inequality
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Conversion of thermal equilibrium states into superpositions of macroscopically distinct states
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“The Bell inequalities are violated by quantum entanglement and provide a criterion for discriminating the quantum entanglement from any local classical hidden variable theories [12,13].”
BackgroundReid, M. D. (2019) · Physical Review A · doi:10.1103/physreva.100.052118 · Cited by 9
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“We further measure the fidelity of this GHZ state and demonstrate its applications in the violation of MABK inequalities [2] and a quantum cryptography protocol of quantum secret sharing [7].”
BackgroundMethodInfluentialEvents in quantum mechanics are maximally non-absolute
Moreno, G., Nery, R., Duarte, C., & Chaves, R. (2022) · Quantum · doi:10.22331/q-2022-08-24-785 · Cited by 9
“As described in the Appendix, the following symmetry of Mermin’s inequality [39] is also a valid LF inequality:”
BackgroundVersatile source of polarization-entangled photons
Maser, A., Wiegner, R., Schilling, U., Thiel, C., & von Zanthier, J. (2010) · Physical Review A · doi:10.1103/physreva.81.053842 · Cited by 11
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Logic of Local Inference for Contextuality in Quantum Physics and BeyondPreprint
Kishida, K. (2016) · arXiv (Cornell University) · doi:10.4230/lipics.icalp.2016.113 · Cited by 12
“A family of arguments of this sort, using XOR (or parity) equations, has been given to show the strong contextuality of a range of quantum examples; the first instance in literature was in [18] for the GHZ state [8].”
MethodSymmetric hypergraph states: entanglement quantification and robust Bell nonlocality
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“Its other variants include the Mermin form of Bell inequalities [185–187], the N -body inequalities [173, 175, 184, 188] or the Ardehali inequalities [189].”
BackgroundIntroduction to Bell’s Inequality in Quantum Mechanics
Guimarães, M. S., Roditi, I., & sorella, S. P. (2024) · Universe · doi:10.3390/universe10100396 · Cited by 8
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“Multiqubit states can contradict local realistic models in a new and stronger way than two-qubit states [34, 35], reflected by a stronger violation of Bell inequalities [36, 37].”
BackgroundQuantum-enhanced sensing with variable-range interactions
Monika, Lakkaraju, L. G. C., Ghosh, S., & Sen, A. (2025) · Physical Review A · doi:10.1103/physreva.111.042628 · Cited by 8
“Since it is known that possesses all the characteristics of being a resource for quantum metrology [7, 71], we maximize the fidelity between the output state obtained after evolution and the ( N − 1) party GHZ state, over the parameters involved in measurements, θ and ϕ .”
Multi-photon quantum interferometry
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Creating and observingN-partite entanglement with atoms
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MAXIMIZING GENUINE MULTIPARTITE ENTANGLEMENT OF N MIXED QUBITS
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Fast macroscopic-superposition-state generation by coherent driving
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Nonlocality of a type of multi-star-shaped quantum networks
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“In particular, the Greenberger–Horne–Zeilinger (GHZ) state [7, 8] achieves the ultimate precision called the Heisenberg limit in the absence of noise [9, 10].”
BackgroundExperimental Test of High-Dimensional Quantum Contextuality Based on Contextuality Concentration
Liu, Z., Meng, H.-X., Xu, Z., Zhou, J., Chen, J., Xu, J., Li, C., Guo, G., & Cabello, A. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.240202 · Cited by 9
Exclusion principle for nonlocal advantage of quantum coherence
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Entanglement swapping with atoms separated by long distance
Yuan, C.-H., 欧永成, & Zhi-Ming, Z. (2006) · Chinese Physics · doi:10.1088/1009-1963/15/8/027 · Cited by 8
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Quantum nonlocality of generic family of four-qubit entangled pure states
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“In the multipartite scenario, in turn, Criterion 1 covers important multipartite [34] and genuinely multipartite [35–37] Bell inequalities, as well as (N − 1)-sided DI genuine N -partite entanglement witnesses [38, 39].”
BackgroundTight upper bound for the maximal expectation value of the Mermin operators
Siddiqui, M. A., & Sazim, S. (2019) · Quantum Information Processing · doi:10.1007/s11128-019-2246-1 · Cited by 9
“The operator M is known as Mermin operator and the MI for three qubits reads 〈M〉ρ ≤ 2 [9,16].”
BackgroundMethodDETECTING EINSTEIN–PODOLSKY–ROSEN STEERING FOR CONTINUOUS VARIABLE WAVEFUNCTIONS
Su, H.-Y., Chen, J., Wu, C., Deng, D.-L., & Oh, C. H. (2013) · International Journal of Quantum Information · doi:10.1142/s0219749913500196 · Cited by 8
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“Mermin inequalities [19] are one of the classes of facet inequalities of the fully local (or, 3-local) polytope [35,36].”
BackgroundInequalities for experimental tests of the Kochen-Specker theorem
Nagata, K. (2005) · Journal of Mathematical Physics · doi:10.1063/1.2081115 · Cited by 9
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Unmasking the polygamous nature of quantum nonlocality
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“Note that this state lies in the same subspace as | ψ max ⟩ in (9).”
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“Quantum theory predicts that for the GHZ and LC state the ratio D n can be made arbitrarily large by increasing the number of qubits [5, 30, 34].”
InfluentialScalable and noise-robust communication advantage of multipartite quantum entanglement
Chakraborty, A., Patra, R. K., Agarwal, K., Sen, S., Ghosal, P., Naik, S. G., & Banik, M. (2025) · Physical Review A · doi:10.1103/physreva.111.032617 · Cited by 8
“Recall that, this particular condition is the requirement of ( n + 1 ) -player Pseudo-Telepathy game introduced by Mermin [ 54 ], where the maximum achievable success probability with classical correlation is bounded above by P (see also [ 55 ]), thereby establishing that P n R ≥ P for all n ≥ 2.”
Probabilistic Results for Six Detectors in a Three-Particle GHZ Experiment
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Probabilistic simulation of mesoscopic “Schrödinger cat” states
Opanchuk, B., Rosales-Zárate, L., Reid, M. D., & Drummond, P. D. (2014) · Physics Letters A · doi:10.1016/j.physleta.2014.01.045 · Cited by 6
“(5) For odd N we follow Mermin [7] and take φ = π/2, measuring F = = 〈 Â 〉 , while for even N we follow Ardehali [22] and take φ = π, measuring F = − 〈 Â 〉 .”
BackgroundMethodInfluentialSmall violations of full-correlation Bell inequalities for multipartite pure random states
Drumond, R. C., & Oliveira, R. I. (2012) · Physical Review A · doi:10.1103/physreva.86.012117 · Cited by 7
Realistic limits on the nonlocality of an N -partite single-photon superposition
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Higher-dimensional Bell inequalities with noisy qudits
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Engineering multipartite steady entanglement of distant atoms via dissipation
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Semi-device-independent multiparty quantum key distribution in the asymptotic limit
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BackgroundSome measures for fermionic entanglement in the cosmological de Sitter spacetime
Bhattacharya, S., Gaur, H., & Joshi, N. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.045017 · Cited by 10
“In this work we wish to investigate two measures – namely the violation of the Bell-Mermin-Klyshko inequality [2, 3, 10, 11, 12] and the quantum discord [16, 17] for Dirac fermions in the cosmological de Sitter background.”
BackgroundMethodConnector tensor networks: a renormalization-type approach to quantum certification
Navascues, M., Singh, S., & Acin, A. (2020) · MPG.PuRe (Max Planck Society) · Cited by 7
Quantum nonlocality and topological quantum phase transitions in the extended Ising chain
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Angular-momentum nonclassicality by breaking classical bounds on statistics
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The Bell inequality cannot be validly applied to the Einstein-Podolsky-Rosen-Bohm (EPRB) experiments
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Multipartite nonlocal quantum correlations resistant to imperfections
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Generation of cluster-type entangled squeezed vacuum states
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“Here M,M ′ are Mermin–Klyshko parameters [31,32].”
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Study of nonclassicality in tripartite correlations beyond standard Bell nonlocality paradigm
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“In this tripartite scenario, there are two-way local correlations that violate a Mermin inequality (MI) [18].”
BackgroundMethodAlmost Equivalent Paradigms of Contextuality
Wester, L. (2018) · Electronic Proceedings in Theoretical Computer Science · doi:10.4204/eptcs.266.1 · Cited by 7
Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
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“with N , thus extending the observation of Mermin [11] to higher spin.”
BackgroundMethodInfluentialOn four-photon entanglement from parametric down-conversion process
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Complementarity and Entanglement in Quantum Information TheoryPreprint
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“Secondly, there exist Bell-type inequalities forN -qubit GHZ states which are violated by an amount that grows exponentially with N [134].”
BackgroundMultiparticle and higher-spin tests of quantum mechanics using parametric down-conversion
Munro, W. J., & Reid, M. D. (1994) · Physical Review A · doi:10.1103/physreva.50.3661 · Cited by 7
All Incompatible Measurements on Qubits Lead to Multiparticle Bell Nonlocality
Plávala, M., Gühne, O., & Quintino, M. T. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.200201 · Cited by 6
“We can however obtain an upper bound on η Bell3 ( T ) , for that it is enough to find a tripartite quantum state ρ such that Tr[ ρ ( T η a | x ⊗ T η b | y ⊗ T η c | z )] , and verifying if a behaviour is Bell local can be done by linear programming [5].”
Device-Independent Full Network Nonlocality for Arbitrary-Party and Unbounded-Input Scenario
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“The multipartite Bell scenario [15–17], although hugely complex, is a natural extension of the bipartite scenario and features only one source that distributes a physical system to each of the parties.”
Three-body non-locality in particle decays
Horodecki, P., Sakurai, K., Shaleena, A. S., & Spannowsky, M. (2025) · Journal of High Energy Physics · doi:10.1007/jhep10(2025)160 · Cited by 8
“Our numerical optimization of measurement axes, particularly for the tight 4 × 4 × 2 inequality, has yielded insights into the detection capabilities of different Bell-type inequalities for various initial spin and decay configurations.”
InfluentialQuantifying contextuality via linear programming
Barbosa, R. S. (2016) · Cited by 6
Sun, Z., Huang, H., Wen, H.-X., Li, M., Zhao, X., Cheng, H.-G., Zhang, D., & Guo, B. (2022) · Physical Review A · doi:10.1103/physreva.106.022208 · Cited by 6
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“Multi-photon entanglement-based QCKA protocols require the generation of Greenberger-Horne-Zeilinger (GHZ) states [37, 42, 45, 50, 51] or “twisted” versions of them [52–54] corresponding to the number of participants.”
Probing Many-Body Bell Correlation Depth with Superconducting Qubits
Wang, K., Li, W., Xu, S., Hu, M., Chen, J., Wu, Y., Zhang, C., Jin, F., Zhu, X., Gao, Y. Q., et al. (2025) · Physical Review X · doi:10.1103/physrevx.15.021024 · Cited by 14
“The Mermin and Svetlichny Bell inequalities are used to detect the Bell correlation depth for the multipartite scenario in this work [37, 38, 40, 41, 63].”
MethodGeneration of cavity field cluster and GHZ states using Bragg-regime atom interferometry
Abbas, T., Rameez‐ul‐Islam, Khosa, A. H., & Saif, F. (2009) · Journal of Russian Laser Research · doi:10.1007/s10946-009-9072-3 · Cited by 6
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
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