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Statistical properties of quantum systems significantly differ from their classical counterparts. Such differences play a crucial role in a many fundamental and applied investigations. The latter are especially important for developing new quantum technologies, including quantum computation, quantum communication, and quantum metrology. Electromagnetic radiation in the optical branch of the spectrum is a convenient physical system for conducting experiments related to fundamental quantum phenomena. In this lecture course you will study nonclassical properties of quantum systems, theory of quantum measurements, and mathematical methods needed for making research in the field of quantum optics and quantum information. Skills and knowledge obtained in this lecture course are important for successful attending another lecture course—"Theory of Quantum Information".

States of classical systems.

Coding by discrete variables.

Classical entropy.

Quantum states.

Hilbert space of states.

Quantum observables.

Dirac notation.

Density operator of pure states.

POVM measurements.

Unitary evolution.

Mixed quantum states.

Von Neumann entropy.

Quantization of electromagnetic field.

Coherent states.

Optical elements.

Balanced homodyne detection.

Photodetection theory.

Eight-port homodyne detection.

s-parameterized distributions.

Born’s rule in phase-space representation.

Expected values of observables.

Transformations of quantum states.

Linear losses.

Detection efficiency.

Boson sampling.

Sub-Poissonian statistics of photocounts.

Quadrature squeezing.

Nonclassicality of quantum states.

The final mark is formed by combining the marks for the assignments (40 points max) and the exam (60 points max).

- L. Mandel, E. Wolf, Optical coherence and quantum optics, (Cambridge University Press, 1995).
- D. F. Walls and G.J. Milburn, Quantum Optics, (Springer-Verlag, Berlin, 2008).
- W. Vogel and D.-G. Welsch, Quantum Optics, (Wiley–VCH, Berlin, 2006).
- W.P. Schleich, Quantum optics in phase space, (Wiley–WCH, Berlin, 2001).
- A. Perelomov, Generalized coherent states and their applications, (Springer, Berlin, 1986).
- 6. A. A. Semenov, V. K. Usenko, E. V. Shchukin, and B. I. Lev, Nonclassi- cality of quantum states and its application in quantum cryptography, Ukr. J. Phys. Reviews 3, 151 (2006).