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Quantum entanglement in fermionic lattices
Open accessAbstract
The Fock space of a system of indistinguishable particles is isomorphic (in a nonunique way) to the state space of a composite, i.e., many modes, quantum system. One can then discuss quantum entanglement for fermionic as well as bosonic systems. We exemplify the use of this notion---central in quantum information---by studying some, e.g., Hubbard, lattice fermionic models relevant to condensed matter physics.
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“the amount of entanglement quantified with some measure may depend on the chosen decomposition.”
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“entanglement can only be defined for a particular decomposition of a complex system into subsystems”
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Cites
Quantum information and computation
Bennett, C. H., & DiVincenzo, D. P. (2000) · Nature · doi:10.1038/35005001 · Cited by 3,263
Quantum Theory: Concepts and Methods
Peres, A., & Ballentine, L. E. (1995) · American Journal of Physics · doi:10.1119/1.17946 · Cited by 2,561
Steane, A. (1998) · Reports on Progress in Physics · doi:10.1088/0034-4885/61/2/002 · Cited by 1,391
Natural Thermal and Magnetic Entanglement in the 1D Heisenberg Model
Arnesen, M. C., Bose, S., & Vedral, V. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.017901 · Cited by 787
Quantum Theory: Concepts and Methods
Peres, A., & Mayer, M. E. (1994) · Physics Today · doi:10.1063/1.2808757 · Cited by 703
Quantum correlations in two-fermion systems
Schliemann, J., Cirac, J. I., Kuś, M., Lewenstein, M., & Loss, D. (2001) · Physical Review A · doi:10.1103/physreva.64.022303 · Cited by 393
Zanardi, P. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.077901 · Cited by 328
Effects of anisotropy on thermal entanglement
Wang, X. (2001) · Physics Letters A · doi:10.1016/s0375-9601(01)00123-2 · Cited by 189
Entanglement in a two-identical-particle system
Li, Y. S., Zeng, B., Liu, X. S., & Long, G. (2001) · Physical Review A · doi:10.1103/physreva.64.054302 · Cited by 159
Quantum teleportation and Bell’s inequality using single-particle entanglement
Lee, H.-W., & Kim, J. (2000) · Physical Review A · doi:10.1103/physreva.63.012305 · Cited by 143
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Items 301–400 of 437
Crippa, L., Krivenko, I. S., Giuli, S., Bellomia, G., Kowalski, A., Petocchi, F., Scazzola, A., Wallerberger, M., Mazza, G., Medici, L. D., et al. (2025) · SciPost Physics Codebases · doi:10.21468/scipostphyscodeb.58 · Cited by 9
Entanglement dynamics between Ising spins and a central ancilla
Szabo, J. C., & Trivedi, N. (2022) · Physical Review A · doi:10.1103/physreva.105.052431 · Cited by 5
Quantum entanglement as an aspect of pure spinor geometry
Kiosses, V. I. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/40/405301 · Cited by 5
Existence of Bond-Order-Wave Phase in One-Dimensional Extended Hubbard Model
Liu, G., & Wang, C. (2011) · Communications in Theoretical Physics · doi:10.1088/0253-6102/55/4/35 · Cited by 5
How to observe duality in entanglement of two distinguishable particles
Karczewski, M., & Kurzyński, P. (2016) · Physical Review A · doi:10.1103/physreva.94.032124 · Cited by 5
Completely positive maps for reduced states of indistinguishable particles
Souza, L. D. S., Debarba, T., Ferreira, D. L. B., Iemini, F., & Vianna, R. O. (2018) · Physical Review A · doi:10.1103/physreva.98.052135 · Cited by 5
Entanglement and Non-Locality in Quantum Protocols with Identical Particles
Benatti, F., Roberto Floreanini, B., & Marzolino, U. (2021) · Entropy · doi:10.3390/e23040479 · Cited by 5
Multipartite entanglement in fermionic systems via a geometric measure
Lari, B., Durganandini, P., & Joag, P. S. (2010) · Physical Review A · doi:10.1103/physreva.82.062302 · Cited by 5
Correlation in fermion or boson systems as the minimum of entropy relative to all free statesPreprint
Gottlieb, A. D., & Mauser, N. J. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1403.7640 · Cited by 12
Rao, Q., & Xie, R. (2003) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(03)00256-5 · Cited by 5
Mode entanglement and isospin pairing in two-nucleon systems
Kovács, J., Kruppa, A. T., Legeza, Ö., & Salamon, P. (2024) · Journal of Physics G Nuclear and Particle Physics · doi:10.1088/1361-6471/ad9345 · Cited by 4
Entanglement of particles versus entanglement of fields: Independent quantum resources
Sperling, J., & Agudelo, E. (2023) · Physical Review A · doi:10.1103/physreva.107.042420 · Cited by 4
Phase entanglement negativity for bipartite fermionic systems
Xu, B., Qi, X., & Hou, J. (2024) · Physical Review A · doi:10.1103/physreva.110.032417 · Cited by 4
Entanglement Properties and Phase Diagram of the Two-Orbital Atomic Hubbard Model
Avella, A., Mancini, F. P., Scelza, G., & Chaturvedi, S. (2008) · Acta Physica Polonica A · doi:10.12693/aphyspola.113.417 · Cited by 4
Entanglement and double occupancy in many-electron states
Subrahmanyam, V. (2010) · Physics Letters A · doi:10.1016/j.physleta.2010.05.060 · Cited by 4
Correlation in quantum states of two identical particles
Zhou, D. (2009) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/88/10006 · Cited by 4
Maximal entanglement of two delocalized spin- 12 particles
Johansson, M. (2016) · Physical Review A · doi:10.1103/physreva.93.022328 · Cited by 4
Afzali, R., Ebrahimian, N., & Eghbalifar, B. (2016) · Physics Letters A · doi:10.1016/j.physleta.2016.08.003 · Cited by 4
Approximation of the entanglement in quantum dot chains using Hubbard models
Coe, J. P., França, V. V., & D’Amico, I. (2011) · Journal of Physics Conference Series · doi:10.1088/1742-6596/286/1/012048 · Cited by 4
Quantum entanglement in an interacting electron gas
Hamieh, S., & Zaraket, H. (2009) · The European Physical Journal D · doi:10.1140/epjd/e2009-00228-0 · Cited by 4
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Pan, F., & Draayer, J. P. (2006) · International Journal of Quantum Information · doi:10.1142/s0219749906002341 · Cited by 4
Constructing entanglement measures for fermions
Johansson, M., & Raissi, Z. (2016) · Physical Review A · doi:10.1103/physreva.94.042319 · Cited by 4
Bordone, P., Bertoni, A., & Jacoboni (2004) · doi:10.1109/iwce.2004.1407404 · Cited by 4
Numerical methods for strongly correlated many-body systems with bosonic degrees of freedom
Dorfner, F. (2017) · Elektronische Hochschulschriften der LMU München (Ludwig-Maximilians-Universität München) · doi:10.5282/edoc.20552 · Cited by 4
Bipartite representations and many-body entanglement of pure states of N indistinguishable particles
Cianciulli, J. A., Rossignoli, R., Tullio, M. D., Gigena, N., & Petrovich, F. (2024) · Physical Review A · doi:10.1103/physreva.110.032414 · Cited by 3
Reduced Density Matrix of Permutational Invariant Many-body Systems
Salerno, M., & Popkov, V. (2010) · Acta Applicandae Mathematicae · doi:10.1007/s10440-010-9585-3 · Cited by 3
Afzali, R., Fahimi, S., & Dehghan, M. (2017) · International Journal of Theoretical Physics · doi:10.1007/s10773-017-3296-8 · Cited by 3
Fermionic quantum detailed balance and entanglement
Duvenhage, R. (2018) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/aad1ff · Cited by 3
Fusion structure from exchange symmetry in (2+1)-dimensions
Valera, S. J. (2021) · Annals of Physics · doi:10.1016/j.aop.2021.168471 · Cited by 3
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Hamieh, S., & Zaraket, H. (2009) · The European Physical Journal D · doi:10.1140/epjd/e2009-00288-0 · Cited by 3
Schlingemann, D.-M., Cozzini, M., Keyl, M., & Venuti, L. C. (2008) · Physical Review A · doi:10.1103/physreva.78.032301 · Cited by 3
Fermionic-mode entanglement in non-Markovian environment
Cheng, J., Han, Y., An, Q.-Z., & Zhou, L. (2015) · Annals of Physics · doi:10.1016/j.aop.2015.01.023 · Cited by 3
POPKOV, V., & Salerno, M. (2012) · International Journal of Modern Physics B · doi:10.1142/s0217979212430096 · Cited by 3
Paul, G., Das, S., & Banerji, A. (2021) · Physical Review A · doi:10.1103/physreva.104.l010402 · Cited by 3
A lower bound on ground state entanglement between two regions for a free field
Reznik, B., Retzker, A., & Silman, J. (2004) · Journal of Modern Optics · doi:10.1080/09500340408233600 · Cited by 3
Optical generation and quantitative characterizations of electron-hole entanglement
Shi, Y. (2004) · Physical Review A · doi:10.1103/physreva.69.032318 · Cited by 3
Entanglement witnesses for fermionic lattices
Xu, B., Wang, Y., Qi, X., & Hou, J. (2025) · Physical Review A · doi:10.1103/j4pd-xrs1 · Cited by 2
Quantum entanglement of anyonic charges and emergent spacetime geometry
Le, H.-A., Lee, H. C., & Yang, S.-R. E. (2026) · New Journal of Physics · doi:10.1088/1367-2630/ae3a0b · Cited by 2
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Vesaghi, M. A., Babamoradi, M., & Saani, M. H. (2011) · Journal of Modern Physics · doi:10.4236/jmp.2011.27079 · Cited by 2
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Buks, E. (2024) · Advanced Quantum Technologies · doi:10.1002/qute.202400248 · Cited by 2
Entanglement of biphoton-based qutrits and ququarts
Kulik, S. P., & Straupe, S. S. (2014) · Laser Physics · doi:10.1088/1054-660x/24/9/094007 · Cited by 2
Pauletti, T., Sanino, M., Gimenes, L., Carvalho, I. M., & França, V. V. (2024) · Journal of Molecular Modeling · doi:10.1007/s00894-024-06059-z · Cited by 2
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Sanino, M., Carvalho, I. M., & França, V. V. (2025) · APL Quantum · doi:10.1063/5.0255322 · Cited by 2
Classifying fermionic states via many-body correlation measures
Semenyakin, M., Cheipesh, Y., & Herasymenko, Y. (2025) · Quantum · doi:10.22331/q-2025-04-15-1705 · Cited by 2
Qian, X., & Song, Z. (2006) · Physical Review A · doi:10.1103/physreva.74.022302 · Cited by 2
Phase diagram of the frustrated spin ladder with the next nearest intrachain couplings
Liu, G., Deng, X., & Wen, R. (2012) · Physica B Condensed Matter · doi:10.1016/j.physb.2012.02.006 · Cited by 2
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Ramšak, A., & Mravlje, J. (2008) · The European Physical Journal B · doi:10.1140/epjb/e2008-00089-9 · Cited by 2
Entanglement monogamy in indistinguishable particle systems
Das, S., Paul, G., & Sengupta, R. (2023) · Scientific Reports · doi:10.1038/s41598-023-46515-z · Cited by 2
Genuine multipartite entanglement from many-electron systems
Troiani, F., Angeli, C., Secchi, A., & Pittalis, S. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.l161110 · Cited by 2
Pairwise entanglement and geometric phase in high dimensional free-Fermion lattice systems
Cui, H. T., & Zhang, Y. F. (2009) · The European Physical Journal D · doi:10.1140/epjd/e2009-00025-9 · Cited by 2
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Bose, S., & Home, D. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0505217 · Cited by 2
von Neumann entropy and on-site localization for perpetually coupled qubits
Majumdar, K. (2009) · Physical Review B · doi:10.1103/physrevb.79.115134 · Cited by 2
Group representations in entanglement theory
Vrana, P. (2011) · Cited by 2
Reduced density matrix of nonlocal identical particlesPreprint
Chin, S., & Huh, J. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.00542 · Cited by 2
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Radhakrishnan, H., Thamm, M., Barghathi, H., Rosenow, B., & Maestro, A. D. (2023) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ace430 · Cited by 1
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Anonymous, Reilly, J., & Holland, M. (2026) · Physical Review Research · doi:10.1103/sq34-nf4v · Cited by 1
QUANTUM ENTANGLEMENT AND INFORMATION: THE EFFECT OF ENTROPY REVISITED
Brandão, C. A., & Borges, M. F. (2011) · UNESP Institutional Repository (São Paulo State University) · Cited by 1
Natural molecular shells as open subsystems of small molecules
Gottlieb, A. D., Head, J. D., & Perusse, D. (2011) · International Journal of Quantum Chemistry · doi:10.1002/qua.22980 · Cited by 1
Durganandini, P. (2012) · The European Physical Journal D · doi:10.1140/epjd/e2012-30302-3 · Cited by 1
Ma, R. (2025) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2025.117076 · Cited by 1
Majumder, A., & Sen, S. (2025) · Advanced Theory and Simulations · doi:10.1002/adts.202501224 · Cited by 1
Ma, Y., Wang, J.-X., Xu, X.-Y., Wei, Q., & Kais, S. (2014) · Chinese Physics Letters · doi:10.1088/0256-307x/31/6/060501 · Cited by 1
Entanglement creation for two-electron scattering in a 2D system
Buscemi, F., Bordone, P., & Bertoni, A. (2007) · Optics and Spectroscopy · doi:10.1134/s0030400x07070077 · Cited by 1
Coe, J. P., França, V. V., & D’Amico, I. (2011) · Journal of Physics Conference Series · doi:10.1088/1742-6596/303/1/012110 · Cited by 1
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Mondal, S. (2016) · Journal of High Energy Physics · doi:10.1007/jhep08(2016)121 · Cited by 1
Entropic and Information Inequalities for Indivisible Qudit Systems*
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Horvat, S., & Dakić, B. (2023) · New Journal of Physics · doi:10.1088/1367-2630/ad0751 · Cited by 1
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Pham, D. N., Bharadwaj, S., & Ram‐Mohan, L. R. (2024) · Journal of Applied Physics · doi:10.1063/5.0187988 · Cited by 1
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Tullio, M. R. D. (2021) · doi:10.35537/10915/130069 · Cited by 1
Manenti, R., & Motta, M. (2023) · Oxford University Press eBooks · doi:10.1093/oso/9780198787488.005.0003 · Cited by 1
Chen, C., & Gao, K. (2005) · Communications in Theoretical Physics · doi:10.1088/0253-6102/43/4/011
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Subrahmanyam, V. (2010) · Lecture notes in physics · doi:10.1007/978-3-642-11470-0_9
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Xu, F., An-Min, W., Ning-Bo, Z., Su, X.-Q., & Zhu, R.-G. (2006) · Communications in Theoretical Physics · doi:10.1088/0253-6102/46/4/004
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Heaney, L. (2011) · Lecture notes in computer science · doi:10.1007/978-3-642-18073-6_15
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Mondal, S. (2015) · arXiv (Cornell University)
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Johannesson, H., & Larsson, D. (2007) · Optics and Spectroscopy · doi:10.1134/s0030400x07070041
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Blasone, M., Dell’Anno, F., Siena, S. D., & Illuminati, F. (2009) · Journal of Physics Conference Series · doi:10.1088/1742-6596/174/1/012062
Classical & quantum dynamics of information and entanglement properties of fermion systems
Zander, C. (2012) · UpSpace Institutional Repository (University of Pretoria)
Local operation on identical particles systems
Rendón, O., & Medina, E. A. (2012) · Journal of Physics Conference Series · doi:10.1088/1742-6596/338/1/012015
Entanglement variations in model core-shell quantum dots
Marchisio, P. P., Coe, J. P., & D’Amico, I. (2010) · Journal of Physics Conference Series · doi:10.1088/1742-6596/245/1/012051
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Marzolino, U. (2010) · OpenstarTs (Univeristy of Trieste https://www.units.it/)
Thermodynamic properties of a spin half ladder system
Shik, H. Y., & Chen, R. (2010) · 物理学前沿：英文版 · doi:10.1007/s11467-010-0007-9
Fluctuations and entanglement in open quantum systems
Argentieri, G. (2014) · OpenstarTs (Univeristy of Trieste https://www.units.it/)
Fogueri, U. R. (2013) · University of North Texas Digital Library (University of North Texas) · doi:10.12794/metadc500195
Зацепление электронов во взаимодействующих молекулах
Maiolo, T. A. C., Sala, F. D., Martina, L., Солиани, Д., & Soliani, G. (2007) · Теоретическая и математическая физика · doi:10.4213/tmf6090
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Strakhov, A. A., & Man’ko, V. I. (2016) · Advances in Mathematical Physics · doi:10.1155/2016/7213197
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Gao, J.-M., Tang, R.-A., Zhang, Z.-M., & Xue, J.-K. (2016) · Communications in Theoretical Physics · doi:10.1088/0253-6102/66/5/555
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Lee, H. (2018) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.87.124702
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Aguiar, F. I. D. R. (2011) · Americanae (AECID Library)
Decoherence of charge density waves in beam splitters for interacting quantum wires
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Metadata
- Authors
- Zanardi, P.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2002-03-14
- Volume
- 65
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2039714816
- Cited by
- 447
- References
- 12
- Citations by year
- 2026: 8 · 2025: 12 · 2024: 11 · 2023: 32 · 2022: 11 · 2021: 18 · 2020: 16 · 2019: 15 · 2018: 9 · 2017: 15 · 2016: 17 · 2015: 9 · 2014: 19 · 2013: 17 · 2012: 16
- FWCI
- 15.60
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- 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 Mechanics and Applications
- Keywords
- quantum entanglement, Fock space, composite quantum systems, Hubbard model, condensed matter physics, quantum information
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