# Quantum Teleportation

- Page ID
- 142672

- 298: A Single Page Summary of Quantum Teleportation
- Quantum teleportation is a form of information transfer that requires pre-existing entanglement and a classical communication channel to send information from one location to another.

- 305: Quantum Teleportation - Another Look
- A graphic representation of the teleportation procedure is accompanied by a quantum circuit for its implementation.

- 313: GHZ Entanglement - A Tensor Algebra Analysis
- This tutorial analyses experimental results on a GHZ entanglement reported by Anton Zeilinger and collaborators in the 3 February 2000 issue of Nature (pp. 515‐519) using tensor algebra. The GHZ experiment employs three‐photon entanglement to provide a stunning attack on local realism.

- 316: A Surgical Refutation of the Local Realism Heresy
- Three photons are created in a single event (Nature, February 3, 2000 pp. 515-519) and move apart in the horizontal y-z plane. The goal of this exercise is to demonstrate that an analysis of measurements in the diagonal and circular polarization basis reveals the impossibility of assigning definite values to the polarization states of the photons prior to and independent of measurement.

- 318: Quantum v. Realism
- This tutorial demonstrates the conflict between quantum theory and realism in an experiment described in Physical Review Letters on October 31, 2003 by Zhao, et al. titled ʺExperimental Violation of Local Realism by Four‐Photon GHZ Entanglement.ʺ It draws on the methodology outlined by N. David Mermin in two articles in the general physics literature: Physics Today, June 1990; American Journal of Physics, August 1990.

- 323: Hardy's Paradox - An Algebraic Analysis
- Hardy created a two-photon thought experiment for which a local hidden-variable (EPR) model for the photon states is not consistent with all the predictions of quantum theory.

- 329: An Extension of Bohm's EPR Experiment
- In 1951 David Bohm proposed a gedanken experiment that further illuminated the conflict between local realism and quantum mechanics first articulated by Einstein, Podolsky and Rosen (EPR). In this thought experiment a spin‐1/2 pair is prepared in a singlet state and the individual particles travel in opposite directions on the y‐axis to a pair of observers set up to measure spin in either the x‐ or z‐direction. In this summary tensor algebra will be used to analyze Bohmʹs thought experiment

- 332: Positronium Annihilation
- Positronium is an analog of the hydrogen atom in which the proton is replaced by a positron, the electron's anti-particle. The electron-positron pair undergoes annihilation in 10^−10 seconds producing two γ-ray photons. Positronium's effective mass is 1/2, yielding a ground state energy (excluding the magnetic interactions between the spin 1/2 anti-particles)

- 339: Entanglement Reveals a Conflict Between Local Realism and Quantum Theory
- A tensor algebra approach is used to demonstrate the challenge to the local realistic position of reality that quantum mechanical entanglement creates.

- 340: A Summary of Feynman's "Simulating Physics with Computers"
- This tutorial is based on "Simulating Physics with Computers" by Richard Feynman, published in the International Journal of Theoretical Physics (volume 21, pages 481-485), and Julian Brown's Quest for the Quantum Computer (pages 91-100). Feynman used the experiment outlined below to establish that a local classical computer could not simulate quantum physics.

- 342: Yet Another Assault on Local Realism
- The purpose of this tutorial is to review Nick Herbert's "simple proof of Bell's theorem" as presented in Chapter 12 of Quantum Reality.

- 343: Yet Another Assault on Local Realism - A Matrix/Tensor Algebra Approach
- The purpose of this tutorial is to review Nick Herbertʹs ʺsimple proof of Bellʹs theoremʺ as presented in Chapter 12 of Quantum Reality using matrix and tensor algebra.

- 344: Jim Baggott's Bell Theorem Analysis
- The purpose of this tutorial is to review Jim Baggott's analysis of Bell's theorem as presented in Chapter 4 of The Meaning of Quantum Theory using matrix and tensor algebra.

- 345: Another Bell Theorem Analysis
- The purpose of this tutorial is to review Jim Baggott's analysis of Bell's theorem as presented in Chapter 4 of The Meaning of Quantum Theory using matrix and tensor algebra.

- 346: Another Bell Theorem Analysis - Shorter Version
- The purpose of this tutorial is to review Jim Baggott's analysis of Bell's theorem as presented in Chapter 4 of The Meaning of Quantum Theory using matrix and tensor algebra.

- 349: Analysis of the Stern-Gerlach Experiment
- As will be demonstrated in this tutorial, the Stern-Gerlach experiment illustrates several key quantum concepts.

- 350: Hardy's Paradox
- Hardy's paradox is based on analysis of the double Mach-Zehnder interferometer shown below. A positron enters one interferometer and an electron the other. One arm of each interferometer intersect allowing for electron-positron interaction.

- 351: Bell State Exercises
- The Bell states are maximally entangled superpositions of two-particle states. Consider two spin-1/2 particles created in the same event. There are four maximally entangled wave functions representing their collective spin states. Each particle has two possible spin orientations and therefore the composite state is represented by a 4-vector in a four-dimensional Hilbert space.

- 354: A Brief Description of Aspect's Experiment
- The purpose of this tutorial is restricted to a brief computational summary of the EPR experiment reported by Aspect, Grangier and Roger, ʺExperimental Realization of Einstein‐Podolsky‐Rosen‐Bohm Gedanken Experiment: A New Violation of Bellʹs Inequalities,ʺ in Phys. Rev. Lett. 49, 91 (1982).

- 356: A Brief Introduction to Entanglement Swapping
- The Bell states are the four maximally entangled two-qubit entangled basis for a four-dimensional Hilbert space and play an essential role in quantum information theory and technology, including teleportation and entanglement swapping.

- 357: An Entanglement Swapping Protocol
- In the field of quantum information, interference, superpositions and entangled states are essential resources. Entanglement, a non-factorable superposition, is routinely achieved when two photons are emitted from the same source, perhaps a parametric down converter (PDC). Entanglement swapping involves the transfer (teleportation) of entanglement to two photons that were produced independently and never previously interacted.

- 358: Quantum Correlations Simplified
- According to Richard Feynman it takes a quantum computer to simulate quantum pheonomenon.

- 359: Simulating Quantum Correlations with a Quantum Computer
- According to Richard Feynman it takes a quantum computer to simulate quantum phenomena. In this tutorial we begin with a traditional quantum analysis of a well-know thought experiment involving correlated spin-1/2 particles. After that the operation of a quantum circuit designed to simulate the thought experiment is analyzed. It will be shown that the quantum analysis and the simulation lead to the same result for the expectation value for the experiment.

- 360: Quantum Computer Simulation of Photon Correlations
- A two-stage atomic cascade emits entangled photons (A and B) in opposite directions with the same circular polarization according to observers in their path. The experiment involves the measurement of photon polarization states in the vertical/horizontal measurement basis, and allows for the rotation of the right-hand detector through an angle θ, in order to explore the consequences of quantum mechanical entanglement.

- 361: Quantum Correlations Illustrated with Photons
- A two-stage atomic cascade emits entangled photons (A and B) in opposite directions with the same circular polarization according to observers in their path. The experiment involves the measurement of photon polarization states in the vertical/horizontal measurement basis, and allows for the rotation of the right-hand detector through an angle θ, in order to explore the consequences of quantum mechanical entanglement.

- 362: Examining the Local States of an Entangled Bipartate Superposition
- When a bipartite system is in an entangled superposition, its subsystems are not in superpositions but are instead mixed states with each subsystem in a definite, but unknown state. An entangled spin is always in its local state, the state described by its reduced density operator, because this is the state actually detected by an observer of the spin. The entangled state is a global superposition of spin correlations, not a superposition of local spin states.

- 363: A Brief Introduction to the Quantum Computer
- A quantum computer exploits quantum mechanical effects such as superpositions, entanglement and interference to perform new types of calculations that are impossible on a classical computer. Whereas classical computers perform operations on classical bits, which can be in one of two discrete states, 0 or 1, quantum computers perform operations on quantum bits, or qubits, which can be put into any superposition of two quantum states, |0> and |1>.

- 364: A Very Simple Example of Parallel Quantum Computation
- This tutorial deals with quantum function evaluation and parallel computation.