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Entanglement of Formation of an Arbitrary State of Two Qubits
Open accessAbstract
The entanglement of a pure state of a pair of quantum systems is defined as the entropy of either member of the pair. The entanglement of formation of a mixed state $\ensuremath{\rho}$ is the minimum average entanglement of an ensemble of pure states that represents \ensuremath{\rho}. An earlier paper conjectured an explicit formula for the entanglement of formation of a pair of binary quantum objects (qubits) as a function of their density matrix, and proved the formula for special states. The present paper extends the proof to arbitrary states of this system and shows how to construct entanglement-minimizing decompositions.
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“The concurrence, entanglement of formation and tangle are measures of the quantum-coherence properties of a mixed quantum state [29].”
From Measurement of qubits (2001) · cites this paper as [29]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“As for the concurrence, rigorously, its original Wootters' definition [20] is invalid for two-qudit states with d > 2.”
From Entanglement of biphoton states: qutrits and ququarts (2011) · cites this paper as [20]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“It is also known [19] that in the case of bipartite states with the dimensionality of the oneparticle Hilbert space d = 2, there is a simple algebraic relation between Wootters' concurrence C [20] and the Schmidt entanglement parameter K , owing to which”
From Entanglement of biphoton states: qutrits and ququarts (2011) · cites this paper as [20]
The cited source says what the claim attributes to it.
In the citing paper
“Note that expressions for the concurrence C (equation (5.3) and the last formula of equation (5.4)) can also be derived directly from the original Wootters' definition [20].”
From Entanglement of biphoton states: qutrits and ququarts (2011) · cites this paper as [20]
In the citing paper
“This entanglement, being that of a 2 × 2 system, can also be distilled [7] into pure singlets and used for teleportation.”
From Quantum Communication through an Unmodulated Spin Chain (2003) · cites this paper as [7]
In the citing paper
“Concurrence (CQ) measures the degree of entanglement in a system, where CQ > 0.5 indicates a partially entangled system [73].”
From Mathematical proof of the Fisher-Escolà Q statistical distribution in quantum consciousness modeling (2025) · cites this paper as [73]
In the citing paper
“Only for states of smallest possible dimensions, i.e., for bipartite two-level systems, do a few measures exist that can be evaluated algebraically [27,28,29]”
From Measures and dynamics of entangled states (2005) · cites this paper as [27]
In the citing paper
“For these low dimensional systems, the entanglement of a pure state can be expressed as a function of its concurrence, E (Ψ) = E ( c (Ψ)), with [27]”
From Measures and dynamics of entangled states (2005) · cites this paper as [27]
In the citing paper
“The infimum of this quantity is known [27] to be given by”
From Measures and dynamics of entangled states (2005) · cites this paper as [27]
In the citing paper
“However, concurrence can also be considered as an independent entanglement measure [27].”
From Measures and dynamics of entangled states (2005) · cites this paper as [27]
In the citing paper
“The relation between the present and the original approach to concurrence [27,57] becomes apparent with the observation that the matrix τ defined here coincides with that introduced in Eq. (38)”
From Measures and dynamics of entangled states (2005) · cites this paper as [27]
In the citing paper
“The amount of entanglement can also be quantified by concurrence[45], which is directly related to e ij with C ( e ij ) = max { 0 , -1 2 + 3 2 e ij } .”
From Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems (2011) · cites this paper as [45]
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Citations
Cites
Horn, R. A., & Johnson, C. R. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9780511810817 · Cited by 25,904
Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203
On the Einstein Podolsky Rosen paradox
Bell, J. S. (1964) · Physics Physique Fizika · doi:10.1103/physicsphysiquefizika.1.195 · Cited by 12,252
Mixed-state entanglement and quantum error correction
Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review A · doi:10.1103/physreva.54.3824 · Cited by 5,272
Self-citationSakurai, J. J., & Napolitano, J. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108587280 · Cited by 3,672
Concentrating partial entanglement by local operations
Bennett, C. H., Bernstein, H. J., Popescu, S., & Schumacher, B. W. (1996) · Physical Review A · doi:10.1103/physreva.53.2046 · Cited by 3,151
Discussion of Probability Relations between Separated Systems
Schrödinger, E. (1935) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100013554 · Cited by 3,124
Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
Bennett, C. H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.722 · Cited by 2,961
Self-citationEntanglement of a pair of quantum bits
Hill, S., & Wootters, W. K. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.5022 · Cited by 2,823
Self-citationVedral, V., Plenio, M. B., Rippin, M. A., & Knight, P. L. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.2275 · Cited by 1,967
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Sorted by citations
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Dark periods and revivals of entanglement in a two-qubit system
Ficek, Z., & Tanaś, R. (2006) · Physical Review A · doi:10.1103/physreva.74.024304 · Cited by 379
Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems
López, C. E., Romero, G., Lastra, F., et al. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.080503 · Cited by 370
Autonomously stabilized entanglement between two superconducting quantum bits
Shankar, S., Hatridge, M., Leghtas, Z., Sliwa, K., Narla, A., Vool, U., Girvin, S. M., Frunzio, L., Mirrahimi, M., & Devoret, M. (2013) · Nature · doi:10.1038/nature12802 · Cited by 374
Altepeter, J. B., Jeffrey, E. R., & Kwiat, P. G. (2005) · Advances in atomic, molecular, and optical physics · doi:10.1016/s1049-250x(05)52003-2 · Cited by 372
O'Connor, K. M., & Wootters, W. K. (2001) · Physical Review A · doi:10.1103/physreva.63.052302 · Cited by 369
Self-citationDiverging Entanglement Length in Gapped Quantum Spin Systems
Verstraete, F., Martin-Delgado, M. A., & Cirac, J. I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.087201 · Cited by 361
Divincenzo, D. P., Leung, D., & Terhal, B. M. (2002) · IEEE Transactions on Information Theory · doi:10.1109/18.985948 · Cited by 356
INTRODUCTION TO THE BASICS OF ENTANGLEMENT THEORY IN CONTINUOUS-VARIABLE SYSTEMS
Eisert, J., & Plenio, M. B. (2003) · International Journal of Quantum Information · doi:10.1142/s0219749903000371 · Cited by 356
Quantum metasurface for multiphoton interference and state reconstruction
Wang, K., Titchener, J., Kruk, S., Xu, L., Chung, H.-P., Parry, M., Kravchenko, I. I., Chen, Y.-H., Solntsev, A. S., Kivshar, Y. S., et al. (2018) · Science · doi:10.1126/science.aat8196 · Cited by 370
Rigetti, C. T., & Devoret, M. (2010) · Physical Review B · doi:10.1103/physrevb.81.134507 · Cited by 368
Heralded Entanglement between Atomic Ensembles: Preparation, Decoherence, and Scaling
Laurat, J., Choi, K. S., Deng, H., Chou, C. W., & Kimble, H. J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.180504 · Cited by 357
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Horodecki, M., Horodecki, P., & Horodecki, R. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.2014 · Cited by 347
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Ghosh, S., Rosenbaum, T. F., Aeppli, G., & Coppersmith, S. N. (2003) · Nature · doi:10.1038/nature01888 · Cited by 345
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Hayden, P. M., Horodecki, M., & Terhal, B. M. (2001) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/34/35/314 · Cited by 329
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Yu, T., & Eberly, J. H. (2006) · Optics Communications · doi:10.1016/j.optcom.2006.01.061 · Cited by 339
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Kamta, G. L., & Starace, A. F. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.107901 · Cited by 336
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Experimental determination of entanglement with a single measurement
Walborn, S. P., Ribeiro, P. H. S., Davidovich, L., Mintert, F., & Buchleitner, A. (2006) · Nature · doi:10.1038/nature04627 · Cited by 329
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Wei, T.-C., Nemoto, K., Goldbart, P. M., Kwiat, P. G., Munro, W. J., & Verstraete, F. (2003) · Physical Review A · doi:10.1103/physreva.67.022110 · Cited by 314
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Giedke, G., Wolf, M. M., Krüger, O., Werner, R. F., & Cirac, J. I. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.107901 · Cited by 327
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Yönaç, M., Yu, T., & Eberly, J. H. (2006) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/39/15/s09 · Cited by 319
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Kwiat, P. G., Barraza-Lopez, S., Stefanov, A., & Gisin, N. (2001) · Nature · doi:10.1038/35059017 · Cited by 352
Optimizing the density-matrix renormalization group method using quantum information entropy
Legeza, Ö., & Sólyom, J. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.68.195116 · Cited by 326
Quantum teleportation of an arbitrary two qubit state and its relation to multipartite entanglement
Rigolin, G. (2005) · Physical Review A · doi:10.1103/physreva.71.032303 · Cited by 315
Quantum feedback: Theory, experiments, and applications
Zhang, J., Liu, Y.-X., Wu, R.-B., Jacobs, K., & Nori, F. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.02.003 · Cited by 346
Concurrence of Arbitrary Dimensional Bipartite Quantum States
Chen, K., Albeverio, S. A., & Fei, S.-M. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.040504 · Cited by 310
A comparison of entanglement measures
Eisert, J., & Plenio, M. B. (1999) · Journal of Modern Optics · doi:10.1080/09500349908231260 · Cited by 361
Thermalizing Quantum Machines: Dissipation and Entanglement
Scarani, V., Ziman, M., Štelmachovič, P., Gisin, N., & Bužek, V. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.097905 · Cited by 312
Entanglement in a Quantum Annealing Processor
Lanting, T., Przybysz, A. J., Smirnov, A. Y., Spedalieri, F. M., Amin, M. H., Berkley, A. J., Harris, R., Altomare, F., Boixo, S., Bunyk, P., et al. (2014) · Physical Review X · doi:10.1103/physrevx.4.021041 · Cited by 317
Multiphoton quantum optics and quantum state engineering
Dell’Anno, F., Siena, S. D., & Illuminati, F. (2006) · Physics Reports · doi:10.1016/j.physrep.2006.01.004 · Cited by 310
Quantum Entanglement of Moving Bodies
Gingrich, R. M., & Adami, C. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.270402 · Cited by 306
Fundamentals of quantum information theory
Keyl, M. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00266-1 · Cited by 321
Minimally entangled typical thermal state algorithms
Stoudenmire, E. M., & White, S. R. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/5/055026 · Cited by 301
Measure of genuine multipartite entanglement with computable lower bounds
Ma, Z., Chen, Z., Chen, J., Spengler, C., Gabriel, A., & Huber, M. (2011) · Physical Review A · doi:10.1103/physreva.83.062325 · Cited by 315
Potential multiparticle entanglement measure
Wong, A. K. C., & Christensen, N. L. (2001) · Physical Review A · doi:10.1103/physreva.63.044301 · Cited by 297
Classification of multiqubit mixed states: Separability and distillability properties
Dür, W., & Cirac, J. I. (2000) · Physical Review A · doi:10.1103/physreva.61.042314 · Cited by 291
Bipartite entanglement and entropic boundary law in lattice spin systems
Hamma, A., Ionicioiu, R., & Zanardi, P. (2005) · Physical Review A · doi:10.1103/physreva.71.022315 · Cited by 309
Entanglement in a second-order quantum phase transition
Vidal, J., Palacios, G., & Mosseri, R. (2004) · Physical Review A · doi:10.1103/physreva.69.022107 · Cited by 298
Roch, N., Schwartz, M. E., Motzoi, F., Macklin, C., Vijay, R., Eddins, A., Korotkov, A. N., Whaley, K. B., Sarovar, M., & Siddiqi, I. A. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.170501 · Cited by 295
Non-Markovian effect on the quantum discord
Wang, B., Xu, Z., Chen, Z., & Feng, M. (2010) · Physical Review A · doi:10.1103/physreva.81.014101 · Cited by 290
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Reports on Progress in Physics · doi:10.1088/0034-4885/78/4/042001 · Cited by 328
Entanglement dynamics of two independent qubits in environments with and without memory
Bellomo, B., Franco, R. L., & Compagno, G. (2008) · Physical Review A · doi:10.1103/physreva.77.032342 · Cited by 288
Dynamics of entanglement in one-dimensional spin systems
Luigi Amico, A., Osterloh, A., Plastina, F., Fazio, R., & Palma, G. M. (2004) · Physical Review A · doi:10.1103/physreva.69.022304 · Cited by 286
Persistent Quantum Beats and Long-Distance Entanglement from Waveguide-Mediated Interactions
Zheng, H., & Baranger, H. U. (2013) · Physical Review Letters · doi:10.1103/physrevlett.110.113601 · Cited by 284
Telecom-heralded entanglement between multimode solid-state quantum memories
Lago-Rivera, D., Grandi, S., Rakonjac, J. V., Seri, A., & de Riedmatten, H. (2021) · Nature · doi:10.1038/s41586-021-03481-8 · Cited by 303
Fakultät für Physik und Astronomie
Physik, Schultz-Coulon, H.-C., Herrmann, N., Levin, I., & Ostrowski, A. (2007) · Cited by 288
Manipulation of molecules with electromagnetic fields
Lemeshko, M., Krems, R. V., Doyle, J. M., & Kais, S. (2013) · Molecular Physics · doi:10.1080/00268976.2013.813595 · Cited by 279
Normal forms and entanglement measures for multipartite quantum states
Verstraete, F., Dehaene, J., & Moor, B. D. (2003) · Physical Review A · doi:10.1103/physreva.68.012103 · Cited by 282
Monogamy inequality in terms of negativity for three-qubit states
Ou, Y.-C., & Fan, H. (2007) · Physical Review A · doi:10.1103/physreva.75.062308 · Cited by 285
Separability and Distillability of Multiparticle Quantum Systems
Dür, W., Cirac, J. I., & Tarrach, R. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.3562 · Cited by 279
Deterministic teleportation of a quantum gate between two logical qubits
Chou, K. S., Blumoff, J., Wang, C. S., Reinhold, P., Axline, C. J., Gao, Y. Y., Frunzio, L., Devoret, M., Jiang, L., & Schoelkopf, R. J. (2018) · Nature · doi:10.1038/s41586-018-0470-y · Cited by 296
Thermal concurrence mixing in a one-dimensional Ising model
Gunlycke, D., Kendon, V. M., Vedral, V., & Bose, S. (2001) · Physical Review A · doi:10.1103/physreva.64.042302 · Cited by 277
Byrd, M. S., & Khaneja, N. (2003) · Physical Review A · doi:10.1103/physreva.68.062322 · Cited by 268
Classification of multipartite entangled states by multidimensional determinants
Miyake, A. (2003) · Physical Review A · doi:10.1103/physreva.67.012108 · Cited by 273
Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
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Entanglement in the steady state of a collective-angular-momentum (Dicke) model
Schneider, S., & Milburn, G. J. (2002) · Physical Review A · doi:10.1103/physreva.65.042107 · Cited by 265
Quantum coherence and correlations in quantum system
Xi, Z., Li, Y., & Fan, H. (2015) · Scientific Reports · doi:10.1038/srep10922 · Cited by 264
Strongly correlated quantum walks with a 12-qubit superconducting processor
Yan, Z., Zhang, Y.-R., Gong, M., Wu, Y., Zheng, Y., Li, S., Wang, C., Liang, F., Lin, J., Xu, Y., et al. (2019) · Science · doi:10.1126/science.aaw1611 · Cited by 264
Eberly, J. H., & Yu, T. (2007) · Science · doi:10.1126/science.1142654 · Cited by 264
Volume of the set of separable states. II
Życzkowski, K. (1999) · Physical Review A · doi:10.1103/physreva.60.3496 · Cited by 259
Sudden death and sudden birth of entanglement in common structured reservoirs
Mazzola, L., Maniscalco, S., Piilo, J., Suominen, K., & Garraway, B. M. (2009) · Physical Review A · doi:10.1103/physreva.79.042302 · Cited by 256
Qubit disentanglement and decoherence via dephasing
Yu, T., & Eberly, J. H. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.68.165322 · Cited by 261
Experimental investigation of the entanglement-assisted entropic uncertainty principle
Li, C., Xu, J., Xu, X.-Y., Li, K., & Guo, G. (2011) · Nature Physics · doi:10.1038/nphys2047 · Cited by 257
Thermal and magnetic quantum discord in Heisenberg models
Werlang, T., & Rigolin, G. (2010) · Physical Review A · doi:10.1103/physreva.81.044101 · Cited by 257
Nonequilibrium physics in biology
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Open-system dynamics of entanglement:a key issues review
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Entanglement percolation in quantum networks
Acín, A., Cirac, J. I., & Lewenstein, M. (2007) · Nature Physics · doi:10.1038/nphys549 · Cited by 255
“In this limit, the so-called concur-rence [24], another measure of entanglement, decreases exponentially with the number of repeaters, unless the connecting states are maximally entangled (see Meth-ods).”
BackgroundMaximally entangled mixed states of two qubits
Verstraete, F., Audenaert, K. M. R., & Moor, B. D. (2001) · Physical Review A · doi:10.1103/physreva.64.012316 · Cited by 255
Concurrence of mixed bipartite quantum states in arbitrary dimensions
Mintert, F., Kuś, M., & Buchleitner, A. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.167902 · Cited by 246
Entanglement of formation for isotropic states
Terhal, B. M., & Vollbrecht, K. G. H. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.2625 · Cited by 254
Dusuel, S., & Vidal, J. (2005) · Physical Review B · doi:10.1103/physrevb.71.224420 · Cited by 255
Delayed sudden birth of entanglement
Ficek, Z., & Tanaś, R. (2008) · Physical Review A · doi:10.1103/physreva.77.054301 · Cited by 253
Ground state entanglement and geometric entropy in the Kitaev model
Hamma, A., Ionicioiu, R., & Zanardi, P. (2005) · Physics Letters A · doi:10.1016/j.physleta.2005.01.060 · Cited by 256
DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS
Franco, R. L., Bellomo, B., Maniscalco, S., & Compagno, G. (2012) · International Journal of Modern Physics B · doi:10.1142/s0217979213450537 · Cited by 255
Salles, A., de Melo, F., de Almeida, M. P., Hor-Meyll, M. O., Walborn, S. P., Ribeiro, P. H. S., & Davidovich, L. (2008) · Physical Review A · doi:10.1103/physreva.78.022322 · Cited by 256
Schmidt measure as a tool for quantifying multiparticle entanglement
Eisert, J., & Briegel, H. J. (2001) · Physical Review A · doi:10.1103/physreva.64.022306 · Cited by 249
Induced measures in the space of mixed quantum states
Zyczkowski, K., & Sommers, H.-J. (2000) · CERN Document Server (European Organization for Nuclear Research) · Cited by 245
Bell States of Atoms with Ultralong Lifetimes and Their Tomographic State Analysis
Roos, C. F., Lancaster, G. P. T., Riebe, M., Häffner, H., Hänsel, W., Gulde, S., Becher, C., Eschner, J., Schmidt-Kaler, F., & Blatt, R. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.220402 · Cited by 241
Popp, M., Verstraete, F., Martin-Delgado, M. A., & Cirac, J. I. (2005) · Physical Review A · doi:10.1103/physreva.71.042306 · Cited by 256
Tunable ion–photon entanglement in an optical cavity
Stute, A., Casabone, B., Schindler, P., Monz, T., Schmidt, P. O., Brandstätter, B., Northup, T. E., & Blatt, R. (2012) · Nature · doi:10.1038/nature11120 · Cited by 243
Concurrence of Mixed Multipartite Quantum States
Mintert, F., Kuś, M., & Buchleitner, A. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.260502 · Cited by 243
Coherent and collective quantum optical effects in mesoscopic systemsPreprint
Brandes, T. (2005) · Cited by 286
Quantifying entanglement with witness operators
Brandão, F. G. S. L. (2005) · Physical Review A · doi:10.1103/physreva.72.022310 · Cited by 243
Quantum Data HidingPreprint
Divincenzo, D. P., Leung, D., & Terhal, B. M. (2001) · Cited by 282
Experimental demonstration of quantum correlations over more than 10 km
Tittel, W., Brendel, J., Gisin, B., Herzog, T., Zbinden, H., & Gisin, N. (1998) · Physical Review A · doi:10.1103/physreva.57.3229 · Cited by 259
Local description of quantum inseparability
Sanpera, A., Tarrach, R., & Vidal, G. (1998) · Physical Review A · doi:10.1103/physreva.58.826 · Cited by 246
Quantum teleportation of entangled coherent states
Wang, X. (2001) · Physical Review A · doi:10.1103/physreva.64.022302 · Cited by 236
Discrete Entanglement Distribution with Squeezed Light
Kraus, B., & Cirac, J. I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.013602 · Cited by 232
Quantum coherence and uncertainty in the anisotropic XY chain
Karpat, G., Çakmak, B., & Fanchini, F. F. (2014) · Physical Review B · doi:10.1103/physrevb.90.104431 · Cited by 235
Gaussian measures of entanglement versus negativities: Ordering of two-mode Gaussian states
Adesso, G., & Illuminati, F. (2005) · Physical Review A · doi:10.1103/physreva.72.032334 · Cited by 234
Entanglement, quantum phase transition, and scaling in the XXZ chain
Gu, S.-J., Lin, H.-Q., & Li, Y. (2003) · Physical Review A · doi:10.1103/physreva.68.042330 · Cited by 237
Measurements in two bases are sufficient for certifying high-dimensional entanglement
Bavaresco, J., Valencia, N. H., Klöckl, C., Pivoluska, M., Erker, P., Friis, N., Malik, M., & Huber, M. (2018) · Nature Physics · doi:10.1038/s41567-018-0203-z · Cited by 242
Quantum and classical thermal correlations in the XY spin- 1 2 chain
Maziero, J., Guzman, H. C., Céleri, L. C., Sarandy, M. S., & Serra, R. M. (2010) · Physical Review A · doi:10.1103/physreva.82.012106 · Cited by 228
Spin squeezing and pairwise entanglement for symmetric multiqubit states
Wang, X., & Sanders, B. C. (2003) · Physical Review A · doi:10.1103/physreva.68.012101 · Cited by 233
Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states
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Metadata
- Authors
- Wootters, W. K.
- Affiliations
- Williams College (US)
- Corresponding author
- Wootters, William K.
- ORCID
- Wootters, William K.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1998-03-09
- Volume
- 80
- Issue
- 10
- Pages
- 2245-2248
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2011208902
- Cited by
- 8,290
- References
- 21
- Citations by year
- 2026: 320 · 2025: 387 · 2024: 339 · 2023: 340 · 2022: 349 · 2021: 371 · 2020: 328 · 2019: 336 · 2018: 325 · 2017: 301 · 2016: 406 · 2015: 339 · 2014: 381 · 2013: 368 · 2012: 381
- FWCI
- 62.08
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- 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
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- entanglement of formation, two-qubit states, mixed states, density matrix, quantum entanglement
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