Figures 16.2 Preparation of a singlet state 576 16.3 Particle trajectories for two Gaussian slit systems after Bohm's model,and the corresponding quantum potential 580 16.4 Trajectories for a potential barrier(E=V/2)after Bohm's model,and the corresponding quantum potential 16.5 The three-dimensional Hilbert space proposed by Bell 16.6 Scheme of the experiment proposed for proving the second Bell theorem 589 Experiment proposed by CHSH Optimal orientation for a,a,b,and b'for testing the CHSH inequality 16.9 Typical dependence of f()upon ne for cases I-III 595 16.10 Partial Grotrian diagram of atomic calcium for Freedman and Clauser's experiment 599 16.11 Schematic diagram of apparatus and associated electronics of the experiment by Freedman and Clauser 599 16.12 Freedman-Clauser experiment and Aspect and co- -workers'experiment 600 16.13 Alley-Shih and Ou-Mandel's experiment 602 16.14 Measured coincidence counting rate as a function of the polarizer angle 01. with 62 fixed at 45 % 16.15 Experimental set-up in order to solve detection loopholes 16.16 "Entanglement"with vacuum 606 16.17 Yurke and Stoler's experimen 6 16.18 611 16.19 ent sw apping 612 16.20 Orientations for the proof of Stapp's theorem 614 16.21 The GHSZ proposed experiment 616 16.22 Conditional entanglement 619 16,23 Necessary criterion for separability 623 17.1 Information difference in bits versus angle 6 for the information-theoretic Bell inequality 635 17.2 Informational distance by quadrilateral inequality Schematic representation of quantum non-separability 17.4 Diagram for entangled and disentangled states 17.5 Representation of all density matrices De compression of information Teleportation 17.8 Realization of teleportation with photons 17.9 The CNOT gate 652 17.10 Implementation of a CNOT gate by means of a polarization interferometer 17.11 The quantum computation device as an equivalent of a Mach-Zender interferometer 653 17.12 Generation of Bell states by means of a Hadamard gate followed by a CNOT gate 17.13 Preparation of a GHSZ state 17.14 Toffoli gate 657xv Figures 16.2 Preparation of a singlet state 576 16.3 Particle trajectories for two Gaussian slit systems after Bohm’s model, and the corresponding quantum potential 580 16.4 Trajectories for a potential barrier (E = V/2) after Bohm’s model, and the corresponding quantum potential 581 16.5 The three-dimensional Hilbert space proposed by Bell 585 16.6 Scheme of the experiment proposed for proving the second Bell theorem 589 16.7 Experiment proposed by CHSH 590 16.8 Optimal orientation for a, a , b, and b for testing the CHSH inequality 592 16.9 Typical dependence of f (θ) upon nθ for cases I-III 595 16.10 Partial Grotrian diagram of atomic calcium for Freedman and Clauser’s experiment 599 16.11 Schematic diagram of apparatus and associated electronics of the experiment by Freedman and Clauser 599 16.12 Freedman–Clauser experiment and Aspect and co-workers’ experiment 600 16.13 Alley-Shih and Ou-Mandel’s experiment 602 16.14 Measured coincidence counting rate as a function of the polarizer angle θ1, with θ2 fixed at 45◦ 604 16.15 Experimental set-up in order to solve detection loopholes 605 16.16 “Entanglement” with vacuum 606 16.17 Yurke and Stoler’s experiment 608 16.18 Entanglement swapping 611 16.19 Variation of entanglement swapping 612 16.20 Orientations for the proof of Stapp’s theorem 614 16.21 The GHSZ proposed experiment 616 16.22 Conditional entanglement 619 16.23 Necessary criterion for separability 623 17.1 Information difference in bits versus angle θ for the information-theoretic Bell inequality 635 17.2 Informational distance by quadrilateral inequality 635 17.3 Schematic representation of quantum non-separability 636 17.4 Diagram for entangled and disentangled states 637 17.5 Representation of all density matrices 638 17.6 Decompression of information 639 17.7 Teleportation 644 17.8 Realization of teleportation with photons 646 17.9 The CNOT gate 652 17.10 Implementation of a CNOT gate by means of a polarization interferometer 653 17.11 The quantum computation device as an equivalent of a Mach–Zender interferometer 653 17.12 Generation of Bell states by means of a Hadamard gate followed by a CNOT gate 655 17.13 Preparation of a GHSZ state 655 17.14 Toffoli gate 657