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- 1. QUANTUM TELEPORTATION Seminar by Jaismon Francis
- 2. Introduction ● Classically, teleportation is impossible ● Teleportation is possible in quantum mechanics. ● In Quantum teleportation we dematerialize an object and recreate it somewhere else
- 3. In 1993 a group of six scientists discovered that teleportation is possible in quantum mechanics
- 4. Optical Ground Station (OGS), Tenerife, pointing in the direction of La Palma, where the quantum transmitter was located. The green laser beam was used as a beacon for the closed-loop optical tracking system which kept the transmitted and receiver telescopes aligned to each other. This photo was taken and digitally enhanced by Thomas Herbst, University of Vienna.
- 5. OVERVIEW ● We construct entangled states of two spin one-half particles that has zero total angular momentum. ● introduce Bell states, which are four entangled states that form a basis for the state space of two spin one-half particles. ● We explain how quantum teleportation of a spin state works with the help of an entangled pair.
- 6. Entangled States Most general state in state space of 2 spin ½ particles can be represented by Can one write the state as = v∗ ⊗ w∗? If no such v∗ and w∗ exist, we say that is an entangled state of the two particles Bob Alice
- 7. This image shows crystals used for storing entangled photons, which behave as though they are part of the same whole. Scientists used these crystals in their process of teleporting the state of a photon across more than 15 miles (25 kilometers) of optical fiber. Credit: Félix Bussières/University of Geneva
- 8. Bell basis states Bell states are a set of four entangled basis vectors in the state space of two spin one-half particles. Consider now the state NORMALIZED ORTHONORMAL
- 9. BELL BASIS
- 10. BELL BASIS RE WRITTEN
- 11. SIGMAS CAN BE REALIZED BY MACHINES The action of the Pauli matrices on spin states can be realized as time evolution via some Hamiltonian. We can check, for example, that any Pauli matrix can be written as the exponential of i times a Hermitian matrix (which would be proportional to the Hamiltonian 1 2 3 𝛔 machine
- 12. Quantum Teleportation Entangled Particle Source C Space B Space 0 1 2 3 1 2 3 A B 𝞼 machine C jaismonfrancis
- 13. C B Combined Space of Three Particles is C A B jaismonfrancis A
- 14. It is noteworthy that all the mathematical work above led to the key result which is neatly summarized as the following identity valid for arbitrary states
- 15. THANK YOU

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