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In this lecture course, which is a logical continuation of the course “Theoretical Quantum Optics”, you will study about main types of nonclassical correlations in quantum systems and about their applications to protocols of quantum communication. In particular, we will consider quantum entanglement, Bell nonlocality, and related quantum correlations. You will get the knowledge about two main architectures of quantum computational devices and quantum communication protocols: those ones based on discrete and continuous variables. Apart of fundamental knowledge, you will get practical skills for analysis of quantum circuits and security analysis of quantum communication protocols.

Weyl-Wigner-Groenewold-Moyal (WWGM) formalism.

s-parameterized phase-space representations.

Combined quantum-classical theory.

Two-level systems.

No-cloning theorem.

Quantum-state discrimination.

Einstein-Podolsky-Rosen argumentation.

Separable and inseparable states.

Peres-Horodecki criterion.

Entanglement witness.

Entanglement of continuous-variable systems.

Two-mode squeezed vacuum states.

Gaussian distributions.

Phase-space representation

. Uncertainty relations.

Gaussian operations.

Bell inequalities in the CHSH form.

Violations of Bell inequalities.

Local realistic theories.

Non-signaling bounds.

Hierarchy of quantum correlations.

Experimental implementation.

Loopholes.

Continuous-variable quantum teleportation.

Fidelity of quantum states.

Teleportation of qubit.

Entanglement swapping.

Classical information.

Quantum information.

Holevo’s bound

Cryptography.

Basic QKD protocols.

Analysis of basic QKD protocols.

Practical issues of QKD.

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).
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, Cambridge, 2010).
- A. Perelomov, Generalized coherent states and their applications, (Springer, Berlin, 1986).
- 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).
- G. Adesso, S. Ragy, and A. R. Lee, Continuous Variable Quantum Information: Gaussian States and Beyond, Open Syst. Inf. Dyn. 21, 1440001 (2014); see also arXiv:1401.4679 [quant-ph].
- R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009); see also arXiv:quant- ph/0702225.
- N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Bell Nonlocality, Rev. Mod. Phys. 86, 419 (2014); see also arXiv:1303.2849 [quant-ph].
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Quantum Cryp- tography, Rev. Mod. Phys. 74, 145 (2002); see also arXiv:quant- ph/0101098.
- F. Xu, X. Ma, Q. Zhang, H.-K. Lo, and J.-W. Pan, Secure quantum key distribution with realistic devices, Rev. Mod. Phys. 92, 025002 (2020); see also arXiv:1903.09051 [quant-ph].
- S. Pirandola, et al., Advances in Quantum Cryptography, Adv. Opt. Photon. 12, 1012 (2020); see also arXiv:1906.01645 [quant-ph].