QM Lecture 12 Quantum Entanglement 

Lecture-12     Quantum Entanglement   

CONTENTS

    I.    The Quantum Theory and Bell’s discovery

           I.1 The Realistic, Orthodox and Agnostic points of view of QM

                          The condition of completeness, criterion of reality, and principle of locality

           I.2    The EPR paper on the (lack of) Completeness of the Quantum Theory

           I.3 The Bohm experimental version to settle the EPR paradox

    II.   Detailed illustration of entanglement process: The Annihilation of the Positronium

           The positronium states

                   Case: Disintegration of the spin-zero state of the positronium

           Polarization of the photons

                   Counter-clockwise (right-hand) circularly polarized (RHC) plane-waves

                   Clockwise (left-hand) circularly polarized (LHC) plane-waves

                          |RHCñ  and |LHCñ   photon quantum state

                        Conservation of parity in the positronium decay

                   Laws of conservation and symmetries

                   Example of symmetry.  The hydrogen ion molecule

           The inversion operator

                   Inversion operation in classical and quantum systems  

                   The inversion operator   is also known as the parity operator

           Conservation of parity

                   Decay of the positronium into an odd-parity two-photon state |F ⟩ 

                   Joint and Conditional Probabilities

    III. Entanglement from independent particle sources

    IV.  The Bell's Theorem

APPENDIX-1: Tensor Product of State-Spaces

              APPENDIX-2: THE EPR Paper on the (lack of) Completeness and Locality of the Quantum Theory.