Physics

Elements of classical information theory: the universal Turing machine, the circuit model, set of universal logic gates, computational complexity, complexity classes (P, NP, NPC, BPP), the Landaeur principle, the paradox of Maxwell demonsand its resolution, "What is information and how is it quantified?": Shannon entropy, the compression of classical information, Shannon noiseless coding theorem, discrete vector spaces, communication on noisy channels, classical Hamming bound, the noisy channel coding theorem, parity check coding, mutual entropy, conditional entropy, mutual information Elements of classical cryptography: historical introduction, private key cryptography, public key cryptography: RSA protocol Quantum mechanics and quantum information elements: pure states and mixed states, the density operator, qubit, density matrix of a single qubit, representation through Bloch sphere, reduced density matrix, the density operator: compound systems, purification of mixed states , entanglement: definition for pure and mixed states, Bell states, the evolution of open systems, Kraus representation, axiomatic approach to quantum operations, Kraus theorem, single qubit map examples: depolarizing channel, bit flip channel, phase-flip channel, amplitude damping, entanglement: the Schmidt decomposition, partial transposition criterion, measure theory: generalized measures and POVM measures, no-cloning theorem, estimation of a quantum state, quantum teleportation, entanglement swapping, von Neumann entropy, Schumacher's theorem of compression, the Holevo bound Quantum cryptography: BB84 protocol, Ekert protocol, notes on quantum memory and quantum repeater Quantum computing: one qubit operators, two qubit logic gates: CNOT and CPHASE, generation and measurement of Bell states, universal quantum gate sets, Deutch-Jozsa algorithm, Quantum Fourier Transform, Shor algorithm, Grover algorithm, quantum error correction: 3 qubit error correcting code: bit flip and phase flip, Shor error correcting code, Quantum Hamming Bound Fundamentals of quantum mechanics: Einstein-Podolsky-Rosen article, Bell inequality (CHSH): experimental realization and loophole (detection loophole, locality loophole), GHZ states, study of the quantum-to-classical transition, quantum contextuality Experimental implementation of quantum information: De Vincenzo's criteria, Experimental quantum optics: generation of single photon states, different coding of qubits by single photon states, detection of single photon states, generation of photon pairs, Hong-Ou-Mandel effect, measurement of Bell states in polarization with linear optics, CNOT logic gate with linear optics, quantum teleportation, generation of GHZ states, boson sampling, quantum information with trapped ions, QED

Quantum Mechanics (non-relativistic)

- Principles of quantum computation and information, Volume 1 and 2 Giuliano Benenti, Giulio Casati, e Giuliano Strini World Scientific - Quantum Computation and Quantum Information Michael Nielsen and Isaac Chuang Cambridge press - John Preskill Lecture Notes http://www.theory.caltech.edu/~preskill/ph219/index.html#lecture

Lesson attendance is optional but highly recommended.

The final exam consists of an oral test. Typically, the oral exam includes questions and / or exercises on the program. During the course students can carry out two exemptions (2/3 of the overall assessment), in this case the oral exam focuses on an in-depth analysis of a topic covered during the course (1/3 of the overall assessment). As an alternative to the exemptions, the student can only be assessed on an oral exam covering the whole program. The evaluation criteria of the exam take into account: - the correctness of the concepts presented during the exemptions / oral exam - the clarity and rigor of the presentation in the in-depth presentation - the analytical development capacity of the theory during the exemptions / oral exam - problem solving aptitudes (method and results) during exemptions / oral exam