Contents -- List of figures -- Notions of Quantum Information -- Foundations of quantum physics -- The state space -- Evolution of a quantum system -- Quantum measurements -- Projective measurements -- Compound systems -- The Einstein-Podolsky-Rosen paradox -- The non-cloning theorem -- The principle of uncertainty - Heisenberg -- The irreversibility of the measurements -- Qubits -- Qutrits -- Qubit registers -- Quantum circuits -- Single qubit gates -- Multiple qubit gates -- Qubit measurement -- The qubit as a physical system -- Quantum parallelism -- Quantum algorithms -- Deutsch’s algorithm -- Deutsch-Jozsa’s algorithm -- Bernstein-Vazirani’s algorithm -- Simon’s algorithm -- Grover’s algorithm -- Quantum Fourier transform and its applications -- Shor’s algorithm Determination of the period -- Quantum errors -- Quantum error correction -- The encoding block -- The block of errors -- Shor’s error correction scheme (,) -- Quantum Cryptography -- Introduction to cryptography -- Quantum cryptography -- Quantum key distribution -- The Ekert protocol -- The Bennett-Brassard BB84 protocol -- The Bennett B92 protocol -- The Bechmann-Pasquinucci and Peres protocol for qutrits -- Raw Key Extraction -- Error Estimation -- Key Reconciliation -- Privacy Amplification -- Other schemes of quantum key distribution -- The degree of security -- Entangled Quantum States -- Bi-partite systems -- Tri-partite systems -- N-partite entanglement -- Quantum Secret Sharing -- Multi-party Quantum Secret Sharing -- Quantum communication -- Mixed states Density operator -- Properties of density operator -- Reduced density operator -- Shannon classical entropy -- Properties of Shannon entropy -- Types of Shannon entropy -- Von Neumann quantum entropy -- Properties of von Neumann entropy -- Types of von Neumann entropy -- Quantum communication -- Classical communication channels -- Quantum communication channels -- Depolarization -- Quantum amortization phase -- Amplitude amortization -- Quantum data compression -- Schmidt decomposition -- Mixed-state entanglement and distillation -- Communication using entangled states -- Bell states and Pauli operators -- Quantum dense coding -- Quantum teleportation -- Communication using quantum entanglement swapping -- Bibliography.