Universal state inversion and concurrence in arbitrary dimensions
Open accessAbstract
Wootters [Phys. Rev. Lett. 80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. Wootters's concurrence is defined with the help of the superoperator that flips the spin of a qubit. We generalize the spin-flip superoperator to a ``universal inverter,'' which acts on quantum systems of arbitrary dimension, and we introduce the corresponding generalized concurrence for joint pure states of ${D}_{1}\ifmmode\times\else\texttimes\fi{}{D}_{2}$ bipartite quantum systems. We call this generalized concurrence the I concurrence to emphasize its relation to the universal inverter. The universal inverter, which is a positive, but not completely positive superoperator, is closely related to the completely positive universal-NOT superoperator, the quantum analogue of a classical NOT gate. We present a physical realization of the universal-NOT superoperator.
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Global Quantum Concurrence (CQ) as defined in Eq. (30) is widely used in this type of circuit and provides an approximation of the entanglement levels of qubit states for each execution and density matrix.
“Eq. (30) is widely used in this type of circuit and provides an approximation of the entanglement levels of qubit states for each execution and density matrix [47], [52].”
From Mathematical proof of the Fisher-Escolà <i>Q</i> statistical distribution in quantum consciousness modeling (2025) · cites this paper as [52]
Up to scaling, there is a unique operator satisfying the requirements for I-concurrence.
“Up to scaling, there is a unique operator satisfying these requirements [67], namely”
From Measures and dynamics of entangled states (2005) · cites this paper as [67]
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<i>Quantum Computation and Quantum Information</i>
Nielsen, M. A., Chuang, I., & Grover, L. K. (2002) · American Journal of Physics · doi:10.1119/1.1463744 · Cited by 21,895 · see citing works
Quantum computation and quantum information
Law, J. (2001) · ACM SIGSOFT Software Engineering Notes · doi:10.1145/505482.505499 · Cited by 20,449 · see citing works
Entanglement of Formation of an Arbitrary State of Two Qubits
Wootters, W. K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2245 · Cited by 8,290 · see citing works
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 · see citing works
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 3,051 · see citing works
Entanglement 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 · see citing works
Quantum Dynamical Semigroups and Applications
(2007) · Lecture Notes in Physics · doi:10.1007/3-540-70861-8 · Cited by 1,182 · see citing works
Reduction criterion of separability and limits for a class of distillation protocols
Horodecki, M., & Horodecki, P. (1999) · Physical Review A · doi:10.1103/physreva.59.4206 · Cited by 887 · see citing works
Quantum Dynamical Semigroups and Applications
Alicki, R., & Lendi, K. (1987) · Springer eBooks · doi:10.1007/3-540-18276-4 · Cited by 567 · see citing works
Introduction to Quantum Computation and Information
Lo, H.-K., Spiller, T. P., & Popescu, S. (1998) · WORLD SCIENTIFIC eBooks · doi:10.1142/9789812385253 · Cited by 488 · see citing works
Fidelity and concurrence of conjugated states
Uhlmann, A. (2000) · Physical Review A · doi:10.1103/physreva.62.032307 · Cited by 421 · see citing works
Derka, R., Bužek, V., & EKERT, A. K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.1571 · Cited by 251 · see citing works
Self-citationOptimal manipulations with qubits: Universal-NOT gate
Bužek, V., Hillery, M. S., & Werner, R. F. (1999) · Physical Review A · doi:10.1103/physreva.60.r2626 · Cited by 235 · see citing works
Self-citationBraunstein, S. L., Bužek, V., & Hillery, M. (2001) · Physical Review A · doi:10.1103/physreva.63.052313 · Cited by 108 · see citing works
Self-citationQuantum Error Correction and Reversible Operations
Caves, C. M. (1999) · Journal of Superconductivity · doi:10.1023/a:1007720606911 · Cited by 61 · see citing works
Self-citationLendi, K. (1987) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/20/1/011 · Cited by 42 · see citing works
Bužek, V., Hillery, M. S., & Werner, F. (2000) · Journal of Modern Optics · doi:10.1080/095003400148150 · Cited by 34 · see citing works
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Research works printed but not linked: 2
- [14][14] P. Rungta, W. J. Munro, K. Nemoto, P. Deuar, G. J. Milburn, C. M. Caves, In Directions in Quantum Optics: A Collection of Papers Dedicated to the Memory of Dan Walls, edited by H. J. Carmichael, R. J. Glauber, M. O. Scully (Springer-Verlag, Berlin, 2000), pages 149-164. -
- [18][18] S. Yu, unpublished, e-print quant-ph/0001053 . · arXiv
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Amico, L., Fazio, R., Osterloh, A., & Vedral, V. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.517 · Cited by 3,745 · see citing works
Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401 · see citing works
Liu, B.-H., Li, L., Huang, Y.-F., Li, C.-F., Guo, G.-C., Laine, E.-M., Breuer, H.-P., & Piilo, J. (2011) · Nature Physics · doi:10.1038/nphys2085 · Cited by 574 · see citing works
Measures and dynamics of entangled states
Mintert, F., Carvalho, A. R. R., Kuś, M., & Buchleitner, A. (2005) · Physics Reports · doi:10.1016/j.physrep.2005.04.006 · Cited by 420 · see citing works
Byrd, M. S., & Khaneja, N. (2003) · Physical Review A · doi:10.1103/physreva.68.062322 · Cited by 268 · see citing works
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Fields, C., Glazebrook, J. F., & Marcianò, A. (2022) · Quanta · doi:10.12743/quanta.v11i1.206 · Cited by 37 · see citing works
Escolà-Gascón, Á., & Benito-León, J. (2025) · Computational and Structural Biotechnology Journal · doi:10.1016/j.csbj.2025.04.025 · Cited by 4 · see citing works
- Authors
- Rungta, P., Bužek, V., Caves, C. M., Hillery, M., & Milburn, G. J.
- Affiliations
- University of New Mexico (US)
- Hunter College (US)
- The University of Queensland (AU)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2001-09-18
- Volume
- 64
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2106985682
- Cited by
- 848
- References
- 17
- Citations by year
- 2026: 32 · 2025: 49 · 2024: 46 · 2023: 72 · 2022: 42 · 2021: 38 · 2020: 37 · 2019: 37 · 2018: 31 · 2017: 25 · 2016: 28 · 2015: 29 · 2014: 34 · 2013: 26 · 2012: 20
- FWCI
- 16.33
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- concurrence, entanglement of formation, bipartite quantum systems, arbitrary dimensions, quantum NOT gate, entanglement measures
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