Abstract
In this paper, we propose a concurrence vector for a multipartite qudit pure state based on its coefficient matrices and define its norm as the generalized concurrence. Moreover, we prove that this generalized concurrence is a good measure according to the three necessary conditions that any measure of entanglement has to satisfy, i.e. it equals zero if and only if the state is separable, it remains invariant under local unitary transformations, and it is not increasing under local operations and classical communication. This generalized concurrence is very practical and convenient for computation.
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References
Peres A.: Quantum Theory: Concepts and Methods. Kluwer, Dordrecht (1993)
Bennett C.H., Wiesner S.J.: Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)
Bennett C.H., Brassard G., Crepeau C., Jozsa R., Peres A., Wootters W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993)
Bennett C.H., DiVincenzo D.P., Smolin J.A., Wootters W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824–3851 (1996)
Hill S., Wootters W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022–5025 (1997)
Wootters W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)
Audenaert K., Verstraete F., Moor De.: Variational characterizations of separability and entanglement of formation. Phys. Rev. A 64, 052304 (2001)
Rungta P., Buzek V., Caves C.M., Hillery M., Milburn G.J.: Universal state inversion and concurrence in arbitrary dimensions. Phys. Rev. A 64, 042315 (2001)
Wootters W.K.: Entanglement of formation and concurrence. Quantum Inf. Comput. 1, 27–44 (2001)
Albeverio S., Fei S.M.: A note on invariants and entanglements. J. Opt. B: Quantum Semiclass. Opt. 3, 223–227 (2001)
Akhtarshenas S.J.: Concurrence vectors in arbitrary multipartite quantum systems. J. Phys. A: Math. Gen. 38, 6777–6784 (2005)
Huang Y., Wen J., Qiu D.: Practical full and partial separability criteria for multipartite pure states based on the coefficient matrix method. J. Phys. A: Math. Theor. 42, 425306 (2009)
Vedral V., Plenio M.B., Rippin M.A., Knight P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275–2279 (1997)
Shimoni Y., Shapira D., Biham O.: Characterization of pure quantum states of multiple qubits using the Groverian entanglement measure. Phys. Rev. A 69, 062303 (2004)
Vidal G., Werner R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)
Facchi P., Florio G., Pascazio S.: Probability-density-function characterization of multipartite entanglement. Phys. Rev. A 74, 042331 (2006)
Linden N., Popescu S.: On multi-particle entanglement. Fortschr. Phys. 46, 567–578 (1998)
Long Y., Qiu D., Long D.: An entanglement measure based on two order minors. J. Phys. A: Math. Theor. 42, 265301 (2009)
Higuchi A., Sudbery A.: How entangled can two couples get. Phys. Lett. A 273, 213–217 (2000)
Brown I.D., Stepney S., Sudbery A., Braunstein S.L.: Searching for highly entangled multi-qubit states. J. Phys. A: Math. Gen. 38, 1119–1131 (2005)
Uhlmann A.: Optimizing entropy relative to a channel or subalgebra. Open Syst. Inf. Dyn. 5, 209–227 (1998)
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Huang, Y., Qiu, D. Concurrence vectors of multipartite states based on coefficient matrices. Quantum Inf Process 11, 235–254 (2012). https://doi.org/10.1007/s11128-011-0247-9
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DOI: https://doi.org/10.1007/s11128-011-0247-9