Local models and hidden nonlocality in Quantum Theory

Preprint English OPEN
Guerini, Leonardo;
(2014)
  • Subject:
    arxiv: Quantum Physics

This Master's thesis has two central subjects: the simulation of correlations generated by local measurements on entangled quantum states by local hidden-variables models and the revelation of hidden nonlocality. We present and detail the Werner's local model and the hi... View more
  • References (21)
    21 references, page 1 of 3

    1 Preliminaries 5 1.1 Dirac's notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Basic de nitions and results . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Linear algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 Basic Probability Theory . . . . . . . . . . . . . . . . . . . . . . . . 10

    3 Nonlocality 22 3.1 The CHSH inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 The Horodecki Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.3 Local hidden variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4 Local models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    4 Werner's local model 32 4.1 Werner states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2 Bob's response function and the hidden variables . . . . . . . . . . . . . . 38 4.3 Alice's response function and a local model for an entangled state . . . . . 42 4.4 Barrett's local model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3 2 q 1 4 2 j01i h01j + 2 j10i h10j 4 q j00i h00j + 2 j01i h01j 4 2 q j00i h00j + q j10i h10j +

    [1] R. F. Werner, Phys. Rev. A 40, 4277 (1989).

    [2] J. S. Bell, Physics 1, 195 (1964).

    [3] S. Popescu, Phys. Rev. Lett. 74, 2619 (1995).

    [4] A. Einstein, B. Podolsky and N. Rosen, Phys. Rev. 47, 777 (1935).

    [5] J. F. Clauser, M. A. Horne, A. Shimony and R. A. Holt, Phys. Rev. Lett. 23, 880 (1969).

    [6] R. Horodecki, P. Horodecki, M. Horodecki, Phys. Lett. A 200, 340 (1995).

    [7] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani and S. Wehner, Rev. Mod. Phys. 86, 419 (2014).

  • Metrics
Share - Bookmark