Quantum Entanglement and Distillation in Information Processing Shao-Ming Fei

Quantum Entanglement Pure state: v ector on Separable! bipartitetripartite multipartite

a) PPT criterion: Separability: no general criteria b) Reduction: Mixed state: density matrix Separable! Realignment, Covariance matrix criterion, …

Measure: Bipartite Entanglement of Formation (EoF) Pure state

Measurable bounds for EoF M. Li, S.M. Fei, Phys. Rev. A 82 (2010) Lower Bound for EoF K. Chen, S. Albeverio, S.M. Fei, Phys. Rev. Lett. 95(2005) S.M. Fei, X. Li-Jost, Phys. Rev. A 73(2006) Mixed state

Relative Entropy, Negativity, …….. Lower Bound for Concurrence K. Chen, S. Albeverio, S.M. Fei, Phys. Rev. Lett. 95(2005) X.H. Gao, S.M. Fei and K. Wu, Phys. Rev. A 74 (Rapid Comm.)(2006) M. Li, S.M. Fei and Z.X. Wang, J. Phys. A 42 (2009) X.S. Li, X.H. Gao and S.M. Fei, Phys. Rev. A 83 (2011) Concurrence

Two-qubit: A. Buchleitner et.al. Nature 440(2006)1022 Experimental measurement of entanglement

Three qubits Two qubits Theorem (multi-qubit):

S.M. Fei, M.J. Zhao, K. Chen and Z.X. Wang, Phys. Rev. A 80 (2009) N-partite M-dimensional case: SU(M) generators

Entanglement as resource in quantum formation processing Quantum computation Quantum teleportation Dense coding Quantum cryptography Quantum error correction Quantum repeater Phase transition

1 qubit2 bit1 qubit AliceBob Entanglement enhanced

AliceBob Entanglement enhanced

1 qubit AliceBob 2 bit Entanglement enhanced

1 qubit2 bit1 qubit AliceBob Entanglement enhanced

Optimal Teleportation M. Li, S.M. Fei and Z.X. Wang, Phys. Rev. A 8 (2008) M.J. Zhao, Z.G. Li, S.M. Fei and Z.X. Wang, J. Phys. A 43, (2010) Fully entangled fraction: M. Horodecki, P. Horodecki and R. Horodecki, Phys. Rev. A 60, 1888 (1999) S. Albeverio, S.M. Fei, Phys. Lett. A 276(2000)8 S. Albeverio, S.M. Fei and W.L. Yang, Phys. Rev. A 66 (2002)

$ ~ ? Bipartite system with one subsystem undergoes a noisy channel Evolution of quantum entanglement: Z.G. Li, S.M. Fei, Z.D. Wang and W.M. Liu, Phys. Rev. A,79 (2009) Two-qubit: Buchleitner et. al., Nature Physics 4, 99 (2008)

Kraus operator E.g. generalized amplitude damping channel

Atom-Cavity System zero detuning Evolution of quantum entanglement: (Hamiltonian ~ master equation) J.H. Eberly and T. Yu, Science 316 (2007) 555

L.L. Lan, X.B. Wang and S.M. Fei, Int. J. Quant. Inform. 8 (2010)1239

Entanglement of Assistance (EoA) A B C Z.G. Li, S.M. Fei, S. Albeverio, W.M. Liu, Phys. Rev. A 80 (2009) Evolution of EoA Z.G. Li, M.J. Zhao, S.M. Fei and W. M. Liu, Phys. Rev. A 81 (2010)

Distillation: U U Entangled, but not distillable: bound entangled Measurement

Separable PPT (positive partial transpose) All PPT entangled states are bound entangled! Non PPT distillable ? no answer yet Violation of reduction criterion distillable Distillability from Bell inequalities

M. Li, S.M. Fei, Phys. Rev. Lett. 104 (2010)

Improving capacity of noisy channels 12 max. entangled $ 21 bound entangled $

bound entangled!

on 1 and 3 by Alice Alice measures 1 Bob measures 2 => |0> Maximally Entangled !

Quantum Discord (quantum correlation besides entanglement) Quantum mutual information project measurement performed on subsystem B Quantum conditional entropy Associated quantum mutual information Classical correlation Quantum discord S. Luo, Phys. Rev. A 77 (2008)

Undergoes the phase flip channel Concurrence (dashed line) and quantum discord (solid line) under phase flip channel for B. Li, Z.X. Wang, S.M. Fei, Phys. Rev. A 83 (2011)

H. Dong, D. Z. Xu, C. P. Sun, Coherent excitation transferring via dark state in light-harvesting process, arXiv: Entanglement in Biological structure