Quantum Information Theory
Master
Course


60
07/01/2022 to 30/03/2022
Course Description
1. Intro, Mathematical Instruments (a) Intro to QINFO. (b) from Bit to Qubit. (c) Basics of Linear Algebra. 2. States: (a) Density operators and Ensembles (b) The Schmidt Decomposition (c) Reduced density operators and Purification (existence, how different purifications are connected) (d) The Bloch Sphere. 3. Measurements (a) POVMs: properties and representations (b) Naimark Theorem (b) Impossibility of discriminating among non orthogonal states (d) Helstrom Theorem (c) Quantum State Tomography. 4. Distances for quantum states: (a) Kolmogorov distance for probability distributions (b) Properties of TD and its operational meaning (c) Fidelity and its connection with the TD (d) Uhlmann Theorem. 5. Open quantum system dynamics (a) Basic Properties (b) Kraus and Stinespring representations (c) CP vs P (d) Contractivity, noninvertibility (e) Local, LOCC and separable maps (f) Qubit channels. 6. Entanglement Theory (a) Pure state entanglement (b) Mixed state entanglement (c) Locality and Realism (d) EPR paradox and the hidden variable hypothesis, Bell inequality (CHSH),Tsirelson bound, PRBoxes (e) The GHZ state and multipartite entanglement (f) Separability criteria (g) Partial transpose e Reduction criteria (PPT states), Majorization criterion,Entanglement Witnesses (h) Entanglement Measures. 7. Possible and Impossible Machines (a) Possible Machines: Quantum Teleportation, Superdense Coding, Entanglement Swapping (b) Impossible Machines: QBell telephone, Qcopier (No cloning theorem), Classical Teleportation, JointMeasurement Machine. 8. Quantum Computation (a) Classical model of computation: The Turing Machine, Universal and Probabilistici TMs, Complexity classes, The ChurchTuring Thesis, The Gate Array Model, Universal Gate sets,Reversible vs Nonreversible gates (b) The Landauer Principle and the second principle of thermodynamics (c) Quantum Gates: Onequbit gates, Generalized Euler decomposition, Universal sets and Approximate universal sets for one qubit,Twoqubit gates: CNOT, CU from CNOT, U(N) from CNOT gates, GottesmanKnill theorem (d) Quantum Supremacy (e) Quantum Parallelism. 9. Quantum Algorithms (a) DeutchJozsa Algorithm (b) BerensteinVazirani Algorithm (c) Simon Algorithm (d) Quantum Fourier Transfrom (e) Period Finding Algorithm (f) Shor Algorithm (g) Grover Algorithm.10. Quantum Error Correction (a) Intro (b) 3 qubit code for BitFlip errors and PhaseFlip errors (c) 9 qubit code for all 1qubit errors (c) KnillLaflamme theorem. 11. Quantum Cryptography (a) Private key vs. public key algorithms, Onetime Pad, Shor algorithm vs RSA (b) Quantum Key distribution protocols: BB84 protocol, B92 protocol, Ekert protocol.
Subject area
Digital communications IA electronics
Physics
Field area
Digital
Industry and Space
Educationalinfo
Competences
Introductory course on quantum information theory
Prerequisites
at least a Bachelor
Duration
45h
ECTS
60
Validation mode
Oral Examination
Maximum number of students
30
Organizer
Partner
Scuola Normale Superiore
Faculty
Scuola Normale Superiore
Department
Classe di Scienze