quantum entanglement and distillation in information processing shao-ming fei 2011.04.18
TRANSCRIPT
a) PPT criterion:
Separability: no general criteria
b) Reduction:
Mixed state: density matrix
Separable!
Realignment, Covariance matrix criterion, …
Measurable bounds for EoF M. Li, S.M. Fei, Phys. Rev. A 82 (2010) 044303
Lower Bound for EoFK. Chen, S. Albeverio, S.M. Fei, Phys. Rev. Lett. 95(2005)210501
S.M. Fei, X. Li-Jost, Phys. Rev. A 73(2006)024302
Mixed state
Relative Entropy, Negativity, ……..
Lower Bound for ConcurrenceK. Chen, S. Albeverio, S.M. Fei, Phys. Rev. Lett. 95(2005)040504
X.H. Gao, S.M. Fei and K. Wu, Phys. Rev. A 74 (Rapid Comm.)(2006)050303M. Li, S.M. Fei and Z.X. Wang, J. Phys. A 42 (2009) 145303
X.S. Li, X.H. Gao and S.M. Fei, Phys. Rev. A 83 (2011) 034303
Concurrence
S.M. Fei, M.J. Zhao, K. Chen and Z.X. Wang, Phys. Rev. A 80 (2009) 032320
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
Optimal Teleportation
M. Li, S.M. Fei and Z.X. Wang, Phys. Rev. A 8 (2008) 032332M.J. Zhao, Z.G. Li, S.M. Fei and Z.X. Wang, J. Phys. A 43, (2010) 275203
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)8S. Albeverio, S.M. Fei and W.L. Yang, Phys. Rev. A 66 (2002) 012301
$
~ ?
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) 024303
Two-qubit: Buchleitner et. al., Nature Physics 4, 99 (2008)
Atom-Cavity System
zero detuning
Evolution of quantum entanglement:(Hamiltonian ~ master equation)
J.H. Eberly and T. Yu, Science 316 (2007) 555
Entanglement of Assistance (EoA)
A
B CZ.G. Li, S.M. Fei, S. Albeverio, W.M. Liu, Phys. Rev. A 80 (2009) 034301
Evolution of EoAZ.G. Li, M.J. Zhao, S.M. Fei and W. M. Liu, Phys. Rev. A 81 (2010) 042312
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
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) 042303
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) 022321
H. Dong, D. Z. Xu, C. P. Sun, Coherent excitation transferring via dark state in light-harvesting process, arXiv:1102.0960
Entanglement in Biological structure