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Quantum information with continuous variables

Registro delle lezioni

Anno accademico 2021/2022
Docente Giacomo De Palma, Vittorio Giovannetti

Lecture

  • 02 Nov 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    Hilbert spaces and Dirac notation. Spectral representation of self-adjoint operators. Position operator and continuous spectrum. Positive semidefinite operators. Trace.

  • 05 Nov 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    Pure quantum states. Density operator. Quantum measurements. Projective measurements and quantum observables. Compatibility of quantum measurements. Measurements with outcome in R^n. Measurement of the position operator. Tensor product and composite quantum systems.

  • 09 Nov 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    Partial trace. Quantum Hamiltonians and unitary evolution. Schrödinger and Heisenberg representations. Momentum operator and Fourier transform. Quadratures and canonical commutation relations. Symplectic form. Quantum harmonic oscillator: ladder operators, spectrum of the Hamiltonian, Fock basis. Displacement operators.

  • 11 Nov 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    Quadratic Hamiltonians and their action on the quadratures. Symplectic group. Williamson theorem for positive-definite matrices and symplectic eigenvalues. Normal form of quadratic Hamiltonians. Quantum Gaussian states.

  • 16 Nov 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    First and second moments and their transformation with respect to Gaussian unitary operations. The Robertson-Schrödinger uncertainty principle. Quantum Gaussian states and their covariance matrix. Coherent states.

  • 18 Nov 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    Overcompleteness of coherent states and heterodyne measurement. Characteristic function of a trace-class operator and Fourier-Weyl relation. Wigner function.

  • 23 Nov 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    Characteristic and Wigner functions of Gaussian states. Relations among Husimi Q representation, Wigner quasiprobability distribution and Glauber–Sudarshan P representation. Polar decomposition of symplectic matrices.

  • 25 Nov 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    Isomorphism between 2m x 2m orthogonal symplectic matrices and m x m unitary matrices. Action on coherent states. Phase-shifters and beamsplitters. Quantum Gaussian attenuator. One and two mode squeezing. Two-mode squeezed vacuum states.

  • 30 Nov 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    Separable and entangled states. Covariance matrix of two-mode squeezed vacuum state and correlations of the outcomes of the quadrature measurements and the heterodyne measurements. Classical capacity of the quantum Gaussian attenuator with heterodyne measurement and coherent states as codewords (idea of the proof).

  • 02 Dic 2021 (2h 00m)

    Giacomo De Palma - Corso (attività didattica) - Mista

    Quantum key distribution. Private and key capacity of the quantum Gaussian attenuator (idea of the proof).

  • 18 Maggio 2022 (2h 00m)

    Vittorio Giovannetti - Corso (attività didattica) - Mista

    LEZIONE 1: CPT formalism (Gaussian channels - single mode models) < -- importata da Lezione 5 di Information Methods for Quantum Technologies

  • 20 Maggio 2022 (2h 00m)

    Vittorio Giovannetti - Corso (attività didattica) - Mista

    LEZIONE 2: Gaussian channels (multimode case) <--- importata da Lezione 6 di Information methods for quantum technologies

  • 13 Giu 2022 (2h 00m)

    Vittorio Giovannetti - Corso (attività didattica) - Mista

    LEZIONE 3: Schumacher compression and holevo bound -- importata a LEZIONE 15 del corso di Information Methods for Quantum Technologies.

  • 15 Giu 2022 (2h 00m)

    Vittorio Giovannetti - Corso (attività didattica) - Mista

    LEZIONE 4: quantum capacities -- importato da LEZIONE 16 del corso di Information Methods for Quantum Technologies

  • 20 Giu 2022 (2h 00m)

    Vittorio Giovannetti - Corso (attività didattica) - Mista

    LEZIONE 5: importata da Lezione 17 del corso di Information Methods for quantum technologies

  • 22 Giu 2022 (2h 00m)

    Vittorio Giovannetti - Corso (attività didattica) - Mista

    LEZIONE 6: mutuata da Lezione 18 di Information Methods for Quantum Tech.

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