Lecture 13 Jeffrey H. Shapiro Optical and Quantum Communications - PDF document

October 25, 2016 6.453 Quantum Optical Communication Lecture 13 Jeffrey H. Shapiro Optical and Quantum Communications Group www.rle.mit.edu/qoptics 6.453 Quantum Optical Communication - Lecture 13 § Announcements § Pick up lecture notes, slides § Two-Mode Linear Systems § Parametric amplifier statistics § Entanglement § Four-Mode Quantum Systems § Polarization entanglement § Qubit teleportation 2 www.rle.mit.edu/qoptics 1

Parametric Amplifier with Gain G Type-II Phase-Matched Degenerate Parametric Amplifier § Two-Mode Bogoliubov Transformation: 3 www.rle.mit.edu/qoptics Output State of the Parametric Amplifier § Quantum Characteristic-Function Analysis: § Important Special Case: Vacuum-State Inputs output state is entangled 4 www.rle.mit.edu/qoptics 2

Parametric Amplifier Output with Vacuum Inputs § Individual Output Modes are in Classical States: § Each output is a phase-insensitive-amplified zero-input field § Joint Output State is Non-Classical: § The (diagonal) basis modes are in squeezed vacuum states 5 www.rle.mit.edu/qoptics Parametric Amplifier Output with Vacuum Inputs § Squeezed-Vacuum Representation: § Photon-Twins Representation: 6 www.rle.mit.edu/qoptics 3

Photon-Twins Behavior § Semiclassical Theory for Deterministic : a § Quantum Theory for Paramp Outputs from Vacuum Inputs: 7 www.rle.mit.edu/qoptics Reduced Density Operators for Paramp Outputs § Measure Observable : implies § For the Parametric Amplifier with Vacuum-State Inputs 8 www.rle.mit.edu/qoptics 4

Creating Polarization-Entangled Photon Pairs § Polarization-Combined Outputs from Anti-Phased Paramps Output 2 Paramp A Output 1 Paramp B § Low-gain operation: 9 www.rle.mit.edu/qoptics Creating Polarization-Entangled Photon Pairs § Dual-Paramp Output State in Low-Gain Limit: § Entangled Bi-Photon State Realized by Post-Selection: 10 www.rle.mit.edu/qoptics 5

Polarization-Entangled Photon Pairs § Measure Outputs 1 and 2 in Conjugate-Pair Polarizations: wave plates Output k § Polarization Entanglement: 11 www.rle.mit.edu/qoptics The Four Steps of Qubit Teleportation 12 www.rle.mit.edu/qoptics 6

Coming Attractions: Lecture 14 § Lecture 14: Teleportation § Polarization entanglement and qubit teleportation § Quadrature entanglement and continuous-variable teleportation 13 www.rle.mit.edu/qoptics 7

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