Abstract
In this paper we explore the non-monotonic nature of entanglement of formation with respect to concurrence for pure bipartite states. For pure bipartite system, one of the basic physical reason of this non-monotonicity character is due to the existence of incomparable states, i.e., the pure bipartite states which are not convertible to each other by LOCC with certainty.
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References
Cirone M.A.: Entanglement correlations, Bell inequalities and the concurrence. Phys. Lett. A 339, 269–274 (2005)
Wootters W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)
Wootters W.K.: Entanglement of formation and concurrence. Quant. Inform. Comput. 1, 27–44 (2001)
Ghosh B., Majumdar A.S., Nayak N.: Environment-assisted entanglement enhancement. Phys. Rev. A 74, 052315 (2006)
Datta A., Ghosh B., Majumdar A.S., Nayak N.: Information transfer through a one-atom micromaser. Europhys. Lett. 67, 934–940 (2004)
Bennett C.H., Brassard G., Popescu S., Schumacher B., Smolin J.A., Wootters W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)
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)
Chen K., Albeverio S., Fei S-M.: Concurrence of arbitrary dimensional bipartite quantum states. Phys. Rev. Lett. 95, 040504 (2005)
Mintert F., Kus M., Buchleitner A.: Concurrence of mixed bipartite quantum states in arbitrary dimensions. Phys. Rev. Lett. 92, 167902 (2004)
Gour G.: Mixed-state entanglement of assistance and the generalized concurrence. Phys. Rev. A 72, 042318 (2005)
Heydari H.: Concurrence classes for general pure multipartite states. J. Phys. A: Math. Gen. 38, 8667–8679 (2005)
Heydari H.: Concurrence classes for an arbitrary multi-qubit state based on a positive operator valued measure. J. Phys. A: Math. Gen. 38, 11007–11017 (2005)
Mintert F., Kus M., Buchleitner A.: Concurrence of mixed multipartite quantum states. Phys. Rev. Lett. 95, 260502 (2005)
Popescu S., Rohrlich D.: Thermodynamics and the measure of entanglement. Phys. Rev. A 56, R3319–R3321 (1997)
Terhal B.M., Vollbrecht K.G.H.: Entanglement of formation for isotropic states. Phys. Rev. Lett. 85, 2625–2628 (2000)
Chen K., Albeverio S., Fei S.M.: Entanglement of formation of bipartite quantum states. Phys. Rev. Lett. 95, 210501 (2005)
Rungta P., Caves C.M.: Concurrence-based entanglement measures for isotropic states. Phys. Rev. A 67, 012307 (2003)
Nielsen M.A.: Conditions for a class of entanglement transformations. Phys. Rev. Lett. 83, 436–439 (1999)
Chattopadhyay I., Sarkar D.: Character of locally inequivalent classes of states and entropy of entanglement. Phys. Rev. A 77, 050305(R) (2008)
Vidal G., Werner R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)
Horodecki P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232, 333–339 (1997)
Ishizaka S.: Binegativity and geometry of entangled states in two qubits. Phys. Rev. A 69, 020301 (2004)
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Chattopadhyay, I., Sarkar, D. Entanglement of formation is non-monotonic with concurrence: a simple proof. Quantum Inf Process 7, 243–249 (2008). https://doi.org/10.1007/s11128-008-0085-6
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DOI: https://doi.org/10.1007/s11128-008-0085-6