A useful strong lower bound on two-qubit concurrence

A new strong lower bound on concurrence for two-qubit states is derived. Its equality with the concurrence itself for the pure- and X-states is proved analytically; while extensive numerical computations show that equality for a general mixed state may also exist. Being a very simple function and easy to calculate, it is more convenient and practical than the exact value in some cases, including entanglement investigations in spin chains. We study thermal localizable entanglement in spin chains as an example, to demonstrate the convenience of this bound.

[1]  Transport of entanglement through a Heisenberg¿XY spin chain , 2004, quant-ph/0409048.

[2]  Lov K. Grover.  Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[3]  Ting Yu,et al.  Evolution from entanglement to decoherence of bipartite mixed "X" states , 2005, Quantum Inf. Comput..

[4]  A. Uhlmann.  Entropy and Optimal Decompositions of States Relative to a Maximal Commutative Subalgebra , 1997, quant-ph/9704017.

[5]  N. Gisin.  Bell's inequality holds for all non-product states , 1991 .

[6]  Charles H. Bennett,et al.  Quantum cryptography without Bell's theorem. , 1992, Physical review letters.

[7]  Xiaoguang Wang.  Entanglement in the quantum Heisenberg XY model , 2001 .

[8]  M. Popp,et al.  Localizable Entanglement , 2004 .

[9]  W. Wootters.  Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[10]  Pérès.  Separability Criterion for Density Matrices. , 1996, Physical review letters.

[11]  Deutsch,et al.  Quantum Privacy Amplification and the Security of Quantum Cryptography over Noisy Channels. , 1996, Physical review letters.

[12]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[13]  Vladimir E. Korepin,et al.  Localizable entanglement in antiferromagnetic spin chains , 2003 .

[14]  M. Ban.  Entanglement, phase correlation and dephasing of two-qubit states , 2008 .

[15]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[16]  Claus Kiefer,et al.  Decoherence: Concepts and examples , 1999 .

[17]  Michal Horodecki,et al.  Entanglement measures , 2001, Quantum Inf. Comput..

[18]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[19]  J I Cirac,et al.  Entanglement versus correlations in spin systems. , 2004, Physical review letters.

[20]  Lov K. Grover,et al.  Quantum computation , 1999, Proceedings Twelfth International Conference on VLSI Design. (Cat. No.PR00013).

[21]  W. Wootters,et al.  Entanglement of a Pair of Quantum Bits , 1997, quant-ph/9703041.

[22]  V. Korepin,et al.  Localizable entanglement in antiferromagnetic spin chains (9 pages) , 2004 .

[23]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[24]  J. Silva-Valencia,et al.  Concurrence of finite Ising chains with the Dzyaloshinsky–Moriya interaction , 2010 .

[25]  M. Jafarpour,et al.  A Probability Measure for Entanglement of Pure Two-Qubit Systems and a Useful Interpretation for Concurrence , 2011 .

[26]  E. Rains.  RIGOROUS TREATMENT OF DISTILLABLE ENTANGLEMENT , 1998, quant-ph/9809078.

[27]  G. Vidal,et al.  Computable measure of entanglement , 2001, quant-ph/0102117.

[28]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[29]  M. Jafarpour,et al.  Entanglement and squeezing of multi-qubit systems using a two-axis countertwisting Hamiltonian with an external field , 2008 .

[30]  D. Teresi,et al.  Thermal localizable entanglement in a simple multipartite system , 2009 .

[31]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[32]  F. Verstraete,et al.  Numerical Computation of Localizable Entanglement in Spin Chains , 2006 .

[33]  M. Plenio,et al.  Quantifying Entanglement , 1997, quant-ph/9702027.