## Optical Methods of Quantum Information

Prof. I.V. Sokolov,

upper level courses

I. Quantum cryptography

No-cloning theorem as the basis of quantum cryptography. Secret key distribution in Bennett - Brassard (84) protocol of polarization coding. Estimate of Eve's (evasedropper) possibilities in the 'receive - resend' approach and with the use of optical amplifier. Secret key distribution in Bennett (92) protocol of phase coding. Compensation of polarization distortion in optical fiber waveguides. Estimate of the secret key distribution rate in real experiment.

II. Quantum information channels: teleportation and dense coding

Basics of quantum teleportation. Entangles states as the states of well-defined relative motion of subsystems. Quantum systems with binary basis and representation of qubit with the use of spin, Bloch or Poincaret spheres. Schematic of quantum teleportation of qubits. Generation of polarization entangled twin photons via parametric downconversion. Entangled states detection in coincidence scheme. Experimental observation of teleportation of qubits. Generation of the entangled states of bright light beams and their detection with the use of wave mixing. Schematic and experimental observation of quantum teleportation of continious variables. Dense coding in the entangled states basis. Experimental observation of dense coding with the use of polarization entangled twin photons.

III. Basics of quantum computation

Notion of quantum parallelism. Qubit, effective spin rotations as operations with qubit. Basic operations of classical and quantum computer. Hadamard transformation, C-not gate, Toffoli gate. Fast and slow algorithms of computation. Shor's algorithm of factorization, Fourier - Hadamard transformation, Deutsch's problem. Experimental demonstration of C-not operation with the use of cold ions in Paul trap. Nuclear magnetic resonance experiments.