The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
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
Flagged first, then by citations
Cited by
Sorted by citations
Items 501–600 of 1,010
Genuine multipartite entanglement in quantum phase transitions
de Oliveira, T. R., Rigolin, G., & de Oliveira, M. C. (2006) · Physical Review A · doi:10.1103/physreva.73.010305 · Cited by 101
Distinguishability of Quantum States by Separable Operations
Duan, R., Feng, Y., Xin, Y., et al. (2009) · IEEE Transactions on Information Theory · doi:10.1109/tit.2008.2011524 · Cited by 99
Ground-state entanglement in the XXZ model
Gu, S.-J., Tian, G.-S., & Lin, H.-Q. (2005) · Physical Review A · doi:10.1103/physreva.71.052322 · Cited by 101
Chiral route to spontaneous entanglement generation
Gonzalez-Ballestero, C., González-Tudela, A., García-Vidal, F. J., & Moreno, E. (2015) · Physical Review B · doi:10.1103/physrevb.92.155304 · Cited by 103
Transport of orbital-angular-momentum entanglement through a turbulent atmosphere
Pors, B.-J., Monken, C. H., Eliel, E. R., & Woerdman, J. P. (2011) · Optics Express · doi:10.1364/oe.19.006671 · Cited by 93
Quantum‐Memory‐Assisted Entropic Uncertainty Relations
Wang, D., Ming, F., Hu, M., & Ye, L. (2019) · Annalen der Physik · doi:10.1002/andp.201900124 · Cited by 98
Quantum concepts in optical polarization
Goldberg, A. Z., de la Hoz, P., Bjork, G. G., Klimov, A. B., Grassl, M., Leuchs, G., & Sánchez-Soto, L. L. (2020) · Advances in Optics and Photonics · doi:10.1364/aop.404175 · Cited by 100
Generation, manipulation, and detection of two-qubit entanglement in waveguide QED
Gonzalez-Ballestero, C., Moreno, E., & García-Vidal, F. J. (2014) · Physical Review A · doi:10.1103/physreva.89.042328 · Cited by 97
Cold trapped ions as quantum information processors
Šašura, M., & Bužek, V. (2002) · Journal of Modern Optics · doi:10.1080/09500340110115497 · Cited by 95
Ordering two-qubit states with concurrence and negativity
Miranowicz, A., & Grudka, A. (2004) · Physical Review A · doi:10.1103/physreva.70.032326 · Cited by 98
Maximally discordant mixed states of two qubits
Galve, F., Giorgi, G. L., & Zambrini, R. (2011) · Physical Review A · doi:10.1103/physreva.83.012102 · Cited by 97
Entanglement or separability: the choice of how to factorize the algebra of a density matrix
Thirring, W., Bertlmann, R. A., Köhler, P., & Narnhofer, H. (2011) · The European Physical Journal D · doi:10.1140/epjd/e2011-20452-1 · Cited by 97
Entanglement estimation from Bell inequality violation
Bartkiewicz, K., Horst, B., Lemr, K., & Miranowicz, A. (2013) · Physical Review A · doi:10.1103/physreva.88.052105 · Cited by 95
Smith, B. J., & Raymer, M. G. (2006) · Physical Review A · doi:10.1103/physreva.74.062104 · Cited by 97
Entanglement versus chaos in disordered spin chains
dos Santos, L. F., Rigolin, G., & Escobar, C. O. (2004) · Physical Review A · doi:10.1103/physreva.69.042304 · Cited by 95
Black Holes, Qubits and OctonionsPreprint
Borsten, L., Dahanayake, D., Duff, M. J., Ebrahim, H., & Rubens, W. (2008) · Cited by 114
Two-Point Versus Multipartite Entanglement in Quantum Phase Transitions
Anfossi, A., Giorda, P., Montorsi, A., & Traversa, F. L. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.056402 · Cited by 99
Ordering states with entanglement measures
Virmani, S., & Plenio, M. B. (2000) · Physics Letters A · doi:10.1016/s0375-9601(00)00157-2 · Cited by 96
Entanglement, Quantum Phase Transitions, and Density Matrix Renormalization
Osborne, T. J., & Nielsen, M. A. (2002) · Quantum Information Processing · doi:10.1023/a:1019601218492 · Cited by 95
Efficient reversible entanglement transfer between light and quantum memories
Cao, M., Hoffet, F., Qiu, S., Sheremet, A. S., & Laurat, J. (2020) · Optica · doi:10.1364/optica.400695 · Cited by 94
Monogamy of entanglement of formation
de Oliveira, T. R., Cornelio, M. F., & Fanchini, F. F. (2014) · Physical Review A · doi:10.1103/physreva.89.034303 · Cited by 95
Separability criteria and bounds for entanglement measures
Breuer, H. (2006) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/39/38/010 · Cited by 91
Strong Monogamy Conjecture for Multiqubit Entanglement: The Four-Qubit Case
Regula, B., Martino, S. D., Lee, S., & Adesso, G. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.110501 · Cited by 94
Quantum computing for neutrino-nucleus scattering
Roggero, A., Li, A. C. Y., Carlson, J., Gupta, R., & Perdue, G. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.074038 · Cited by 103
Continuity bounds for entanglement
Nielsen, M. A. (2000) · Physical Review A · doi:10.1103/physreva.61.064301 · Cited by 97
Macroscopic entanglement jumps in model spin systems
Bose, I., & Chattopadhyay, E. (2002) · Physical Review A · doi:10.1103/physreva.66.062320 · Cited by 94
Tavis-Cummings model beyond the rotating wave approximation: Quasidegenerate qubits
Agarwal, S., Rafsanjani, S. M. H., & Eberly, J. H. (2012) · Physical Review A · doi:10.1103/physreva.85.043815 · Cited by 95
4 Qubit Quantum State Tomography
Altepeter, J. B., James, D. F. V., & Kwiat, P. G. (2004) · Lecture notes in physics · doi:10.1007/978-3-540-44481-7_4 · Cited by 103
Geometric phases in quantum information
Sjöqvist, E. (2015) · International Journal of Quantum Chemistry · doi:10.1002/qua.24941 · Cited by 94
Multipartite entangled states in particle mixing
Blasone, M., Dell’Anno, F., Siena, S. D., Mauro, M. D., & Illuminati, F. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.096002 · Cited by 106
Quantum correlations and entanglement in far-from-equilibrium spin systems
Hazzard, K. R. A., van den Worm, M., Foss‐Feig, M., Manmana, S. R., Torre, E. G. D., Pfau, T., Kästner, M., & Rey, A. M. (2014) · Physical Review A · doi:10.1103/physreva.90.063622 · Cited by 101
Quantum correlations in terms of neutrino oscillation probabilities
Alok, A. K., Banerjee, S., & Sankar, S. U. (2016) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2016.05.001 · Cited by 105
Entanglement detection beyond the computable cross-norm or realignment criterion
Zhang, C., Zhang, Y.-S., Zhang, S., & Guo, G. (2008) · Physical Review A · doi:10.1103/physreva.77.060301 · Cited by 97
Entanglement versus quantum discord in two coupled double quantum dots
Fanchini, F. F., Castelano, L. K., & Caldeira, A. O. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/7/073009 · Cited by 96
Nambu, Y., Usami, K., Tsuda, Y., Matsumoto, K., & Nakamura, K. T. (2002) · Physical Review A · doi:10.1103/physreva.66.033816 · Cited by 91
Quantum steering ellipsoids, extremal physical states and monogamy
Milne, A., Jevtic, S., Jennings, D. H., Wiseman, H. M., & Rudolph, T. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/8/083017 · Cited by 92
Ergotropy from coherences in an open quantum system
Çakmak, B. (2020) · Physical review. E · doi:10.1103/physreve.102.042111 · Cited by 92
Minimally entangled typical thermal state algorithms
Stoudenmire, E. M., & White, S. R. (2010) · eScholarship (California Digital Library) · Cited by 92
Chen, Q., Shi, B., Zhang, Y.-S., & Guo, G. (2008) · Physical Review A · doi:10.1103/physreva.78.053810 · Cited by 90
Multipartite entangled states in coupled quantum dots and cavity QED
Wang, X., Feng, M., & Sanders, B. C. (2003) · Physical Review A · doi:10.1103/physreva.67.022302 · Cited by 91
Classical correlation and quantum discord mediated by cavity in two coupled qubits
Wang, C., Li, C.-X., Nie, L.-Y., et al. (2010) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/44/1/015503 · Cited by 92
Increase of entanglement by local PT -symmetric operations
Chen, S.-L., Chen, G.-Y., & Chen, Y.-N. (2014) · Physical Review A · doi:10.1103/physreva.90.054301 · Cited by 92
Strings, black holes, and quantum information
Каллош, Р., & Linde, A. D. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.104033 · Cited by 92
Entanglement limits duality and vice versa
Qian, X., Vamivakas, A. N., & Eberly, J. H. (2018) · Optica · doi:10.1364/optica.5.000942 · Cited by 91
Quantum entanglement and Bell inequality violation at colliders
Barr, A. J., Fabbrichesi, M. E., Roberto Floreanini, B., Emidio Gabrielli, A., & Marzola, L. (2024) · Progress in Particle and Nuclear Physics · doi:10.1016/j.ppnp.2024.104134 · Cited by 159
Characterization of two-qubit perfect entanglers
Rezakhani, A. T. (2004) · Physical Review A · doi:10.1103/physreva.70.052313 · Cited by 91
Single-photon bus connecting spin-wave quantum memories
Simon, J., Tanji, H., Ghosh, S., & Vuletić, V. (2007) · Nature Physics · doi:10.1038/nphys726 · Cited by 92
Top cited articles in thermodynamic research
Fu, H., & Ho, Y. (2015) · Journal of Engineering Thermophysics · doi:10.1134/s1810232815010075 · Cited by 91
Entanglement dynamics for uniformly accelerated two-level atoms
Hu, J., & Yu, H. (2015) · Physical Review A · doi:10.1103/physreva.91.012327 · Cited by 91
Phase diagram of the antiferromagnetic XXZ model on the triangular lattice
Sellmann, D., Zhang, X., & Eggert, S. (2015) · Physical Review B · doi:10.1103/physrevb.91.081104 · Cited by 94
Entanglement, avoided crossings, and quantum chaos in an Ising model with a tilted magnetic field
Karthik, J., Sharma, A., & Lakshminarayan, A. (2007) · Physical Review A · doi:10.1103/physreva.75.022304 · Cited by 93
A complete basis of generalized Bell states
Васильевич, С. Д., & Leuchs, G. (2009) · New Journal of Physics · doi:10.1088/1367-2630/11/1/013006 · Cited by 94
Entanglement of solid-state qubits by measurement
Ruskov, R., & Korotkov, A. N. (2003) · Physical review. B, Condensed matter · doi:10.1103/physrevb.67.241305 · Cited by 90
Pulsed Sagnac polarization-entangled photon source with a PPKTP crystal at telecom wavelength
Jin, R.-B., Shimizu, R., Wakui, K., Fujiwara, M., Yamashita, T., Miki, S., Terai, H., Wang, Z., & Sasaki, M. (2014) · Optics Express · doi:10.1364/oe.22.011498 · Cited by 89
Finite-temperature mutual information in a simple phase transition
Wilms, J., Vidal, J., Verstraete, F., & Dusuel, S. (2012) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2012/01/p01023 · Cited by 85
Long quantum channels for high-quality entanglement transfer
Banchi, L., Apollaro, T. J. G., Cuccoli, A., et al. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/12/123006 · Cited by 89
Souza, A. M., Reis, M. S., Soares-Pinto, D. O., Oliveira, I. S., & Sarthour, R. S. (2008) · Physical Review B · doi:10.1103/physrevb.77.104402 · Cited by 90
Protecting Coherence and Entanglement by Quantum Feedback Controls
Zhang, J., Wu, R.-B., Li, C., & Tarn, T. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2009.2039238 · Cited by 91
Nonequilibrium thermal entanglement
Quiroga, L., Rodríguez, F. J., Ramírez, M. E., & París, R. (2007) · Physical Review A · doi:10.1103/physreva.75.032308 · Cited by 89
Entanglement measure for rank-2 mixed states
Osborne, T. J. (2005) · Physical Review A · doi:10.1103/physreva.72.022309 · Cited by 86
Two-Particle Nonlocal Aharonov-Bohm Effect from Two Single-Particle Emitters
Splettstoesser, J., Moskalets, M. V., & Büttiker, Μ. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.076804 · Cited by 89
Complementarity and entanglement in bipartite qudit systems
Jakob, M., & Bergou, J. A. (2007) · Physical Review A · doi:10.1103/physreva.76.052107 · Cited by 88
Distribution of entanglement in large-scale quantum networks
Perseguers, S., Lapeyre, G. J., Cavalcanti, D., Lewenstein, M., & Acín, A. (2013) · Reports on Progress in Physics · doi:10.1088/0034-4885/76/9/096001 · Cited by 106
Measure of multipartite entanglement with computable lower bounds
Hong, Y., Gao, T., & Yan, F. (2012) · Physical Review A · doi:10.1103/physreva.86.062323 · Cited by 91
Deterministic entanglement swapping with an ion-trap quantum computer
Riebe, M., Monz, T., Kim, K., Villar, A. S., Schindler, P., Chwalla, M., Hennrich, M., & Blatt, R. (2008) · Nature Physics · doi:10.1038/nphys1107 · Cited by 90
Non-Markovian effects in waveguide-mediated entanglement
Gonzalez-Ballestero, C., García-Vidal, F. J., & Moreno, E. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/7/073015 · Cited by 90
Piccitto, G., Russomanno, A., & Rossini, D. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.064305 · Cited by 96
Al-Qasimi, A., & James, D. F. V. (2011) · Physical Review A · doi:10.1103/physreva.83.032101 · Cited by 87
Demonstration of Einstein–Podolsky–Rosen steering with enhanced subchannel discrimination
Sun, K., Ye, X.-J., Xiao, Y., Xu, X.-Y., Wu, Y.-C., Xu, J.-S., Chen, J.-L., Li, C.-F., & Guo, G.-C. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0067-1 · Cited by 86
A Characterization of Global Entanglement
Love, P. J., van den Brink, A. M., Smirnov, A. Y., Amin, M. H. S., Grajcar, M., Il’ichev, E. V., Izmalkov, A., & Zagoskin, A. M. (2007) · Quantum Information Processing · doi:10.1007/s11128-007-0052-7 · Cited by 87
Ma, F.-W., Liu, S., & Kong, X.-M. (2011) · Physical Review A · doi:10.1103/physreva.84.042302 · Cited by 88
Quantum decoherence in noninertial frames
Wang, J., & Jing, J. (2010) · Physical Review A · doi:10.1103/physreva.82.032324 · Cited by 87
Optimal entanglement generation from quantum operations
Leifer, M., Henderson, L., & Linden, N. (2003) · Physical Review A · doi:10.1103/physreva.67.012306 · Cited by 87
Witnessing entanglement in quantum magnets using neutron scattering
Scheie, A. O., Laurell, P., Samarakoon, A., Lake, B., Nagler, S. E., Granroth, G. E., Okamoto, S., Alvarez, G., & Tennant, D. M. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.103.224434 · Cited by 91
Constraining new physics in entangled two-qubit systems: top-quark, tau-lepton and photon pairs
Fabbrichesi, M. E., Roberto Floreanini, B., & Emidio Gabrielli, A. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11307-2 · Cited by 122
Entanglement and quantum phase transition in the one-dimensional anisotropic XY model
Ma, F.-W., Liu, S.-X., & Kong, X.-M. (2011) · Physical Review A · doi:10.1103/physreva.83.062309 · Cited by 86
Yang, L., Zhou, J., & Guo, H. M. (2009) · Physical Review A · doi:10.1103/physreva.79.012309 · Cited by 86
Quantum entanglement of unitary operators on bipartite systems
Wang, X., & Zanardi, P. (2002) · Physical Review A · doi:10.1103/physreva.66.044303 · Cited by 83
Multipartite entanglement in a one-dimensional time-dependent Ising model
Lakshminarayan, A., & Subrahmanyam, V. (2005) · Physical Review A · doi:10.1103/physreva.71.062334 · Cited by 89
Entanglement monogamy and entanglement evolution in multipartite systems
Bai, Y.-K., Ye, M.-Y., & Wang, Z. D. (2009) · Physical Review A · doi:10.1103/physreva.80.044301 · Cited by 86
ENTANGLEMENT MONOTONES AND MAXIMALLY ENTANGLED STATES IN MULTIPARTITE QUBIT SYSTEMS
Osterloh, A., & Siewert, J. (2006) · International Journal of Quantum Information · doi:10.1142/s0219749906001980 · Cited by 95
A comparative study of relative entropy of entanglement, concurrence and negativity
Miranowicz, A., & Grudka, A. (2004) · Journal of Optics B: Quantum and Semiclassical Optics · doi:10.1088/1464-4266/6/12/009 · Cited by 86
Exploring multipartite quantum correlations with the square of quantum discord
Bai, Y.-K., Zhang, N., Ye, M.-Y., & Wang, Z. D. (2013) · Physical Review A · doi:10.1103/physreva.88.012123 · Cited by 84
Steered quantum coherence as a signature of quantum phase transitions in spin chains
Hu, M., Gao, Y.-Y., & Fan, H. (2020) · Physical Review A · doi:10.1103/physreva.101.032305 · Cited by 82
Operational Interpretation for Global Multipartite Entanglement
Boixo, S., & Monràs, A. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.100503 · Cited by 85
Classification of Multipartite Entanglement of All Finite Dimensionality
Gour, G., & Wallach, N. R. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.060502 · Cited by 83
Robustness of quantum correlations against decoherence
Hu, M., & Fan, H. (2011) · Annals of Physics · doi:10.1016/j.aop.2011.11.001 · Cited by 84
Concurrence vectors in arbitrary multipartite quantum systems
Akhtarshenas, S. J. (2005) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/38/30/011 · Cited by 75
Localizable entanglement in antiferromagnetic spin chains
Jin, B.-Q., & Korepin, V. E. (2004) · Physical Review A · doi:10.1103/physreva.69.062314 · Cited by 85
Decoherence of geometric phase gates
Nazir, A., Spiller, T. P., & Munro, W. J. (2002) · Physical Review A · doi:10.1103/physreva.65.042303 · Cited by 82
Quantum-speed-limit time for multiqubit open systems
Liu, C., Xu, Z.-Y., & Zhu, S. (2015) · Physical Review A · doi:10.1103/physreva.91.022102 · Cited by 83
Evaluating the noise resilience of variational quantum algorithms
Fontana, E., Fitzpatrick, N., Ramo, D. M., Duncan, R., & Rungger, I. (2021) · Physical Review A · doi:10.1103/physreva.104.022403 · Cited by 99
Fabbrichesi, M. E., Roberto Floreanini, B., Emidio Gabrielli, A., & Marzola, L. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-11935-8 · Cited by 120
Three-tangle for mixtures of generalized GHZ and generalized W states
Eltschka, C., Osterloh, A., Siewert, J., & Uhlmann, A. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/4/043014 · Cited by 84
The geometry of entanglement: metrics, connections and the geometric phase
Lévay, P. (2004) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/37/5/024 · Cited by 85
Thermal entanglement in an exactly solvable Ising-XXZdiamond chain structure
Rojas, O., Rojas, M., Ananikian, N. S., & de Souza, S. M. (2012) · Physical Review A · doi:10.1103/physreva.86.042330 · Cited by 83
Direct Generation of Polarization-Entangled Photon Pairs in a Poled Fiber
Zhu, E. Y., Tang, Z., Qian, L., Helt, L. G., Liscidini, M., Sipe, J. E., Corbari, C., Canagasabey, A., Ibsen, M., & Kazansky, P. G. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.213902 · Cited by 85
Entanglement induced by spontaneous emission in spatially extended two-atom systems
Ficek, Z., & Tanasgrave, R. (2003) · Journal of Modern Optics · doi:10.1080/09500340308234584 · Cited by 83
Entanglement of Formation of an Arbitrary State of Two Rebits
Caves, C. M., Fuchs, C. A., & Rungta, P. (2001) · Foundations of Physics Letters · doi:10.1023/a:1012215309321 · Cited by 88
Entangling power of the quantum baker's map
Scott, A. J., & Caves, C. M. (2003) · CERN Document Server (European Organization for Nuclear Research) · Cited by 83
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
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 ›
Are you an author, or do you see a problem with this page? Request a review
