Transcript Pure state
Quantum Entanglement and Distillation in Information Processing Shao-Ming Fei 2011.04.18 Quantum Entanglement Pure state: vector on bipartite tripartite multipartite Separable! Mixed state: density matrix Separable! Separability: no general criteria a) PPT criterion: b) Reduction: Realignment, Covariance matrix criterion, … Measure: Bipartite Entanglement of Formation (EoF) Pure state Mixed state Lower Bound for EoF K. Chen, S. Albeverio, S.M. Fei, Phys. Rev. Lett. 95(2005)210501 S.M. Fei, X. Li-Jost, Phys. Rev. A 73(2006)024302 Measurable bounds for EoF M. Li, S.M. Fei, Phys. Rev. A 82 (2010) 044303 Concurrence Lower Bound for Concurrence K. 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)050303 M. 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 Relative Entropy, Negativity, …….. Experimental measurement of entanglement Two-qubit: A. Buchleitner et.al. Nature 440(2006)1022 Theorem (multi-qubit): Two qubits Three qubits N-partite M-dimensional case: SU(M) generators S.M. Fei, M.J. Zhao, K. Chen and Z.X. Wang, Phys. Rev. A 80 (2009) 032320 Entanglement as resource in quantum formation processing Quantum computation Quantum teleportation Dense coding Quantum cryptography Quantum error correction Quantum repeater Phase transition Entanglement enhanced 1 qubit Alice 2 bit 1 qubit Bob Entanglement enhanced Alice Bob 1 2 01 10 Entanglement enhanced 1 qubit Alice 2 bit 1 qubit Bob Entanglement enhanced 1 qubit Alice 2 bit 1 qubit Bob Optimal Teleportation 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) 012301 Fully entangled fraction: M. Li, S.M. Fei and Z.X. Wang, Phys. Rev. A 8 (2008) 032332 M.J. Zhao, Z.G. Li, S.M. Fei and Z.X. Wang, J. Phys. A 43, (2010) 275203 Evolution of quantum entanglement: Bipartite system with one subsystem undergoes a noisy channel $ ~ ? Two-qubit: Buchleitner et. al., Nature Physics 4, 99 (2008) Z.G. Li, S.M. Fei, Z.D. Wang and W.M. Liu, Phys. Rev. A,79 (2009) 024303 Kraus operator E.g. generalized amplitude damping channel Evolution of quantum entanglement: (Hamiltonian ~ master equation) Atom-Cavity System zero detuning 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) Z.G. Li, S.M. Fei, S. Albeverio, W.M. Liu, Phys. Rev. A 80 (2009) 034301 Evolution of EoA Z.G. Li, M.J. Zhao, S.M. Fei and W. M. Liu, Phys. Rev. A 81 (2010) 042312 A B C Distillation: U U Measurement Entangled, but not distillable: bound entangled Separable PPT (positive partial transpose) All PPT entangled states are bound entangled! Non PPT distillable ? no answer yet Violation of reduction criterion Distillability from Bell inequalities distillable M. Li, S.M. Fei, Phys. Rev. Lett. 104 (2010) 240502 Improving capacity of noisy channels $ 1 2 1 max. entangled 3 4 2 bound entangled 3 4 $ 1 2 1 2 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) 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 Entanglement in Biological structure H. Dong, D. Z. Xu, C. P. Sun, Coherent excitation transferring via dark state in light-harvesting process, arXiv:1102.0960