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

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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

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Optical and Quantum Communications Group www.rle.mit.edu/qoptics October 25, 2016

6.453 Quantum Optical Communication Lecture 13 Jeffrey H. Shapiro

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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

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Parametric Amplifier with Gain G § Two-Mode Bogoliubov Transformation:

Type-II Phase-Matched Degenerate Parametric Amplifier

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Output State of the Parametric Amplifier § Quantum Characteristic-Function Analysis: § Important Special Case: Vacuum-State Inputs

utput state is entangled

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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

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Parametric Amplifier Output with Vacuum Inputs § Squeezed-Vacuum Representation: § Photon-Twins Representation:

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Photon-Twins Behavior § Semiclassical Theory for Deterministic : § Quantum Theory for Paramp Outputs from Vacuum Inputs:

a

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Reduced Density Operators for Paramp Outputs § Measure Observable :

implies

§ For the Parametric Amplifier with Vacuum-State Inputs

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§ Polarization-Combined Outputs from Anti-Phased Paramps

§ Low-gain operation:

Creating Polarization-Entangled Photon Pairs

Paramp A Paramp B Output 1 Output 2

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Creating Polarization-Entangled Photon Pairs § Dual-Paramp Output State in Low-Gain Limit: § Entangled Bi-Photon State Realized by Post-Selection:

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Polarization-Entangled Photon Pairs § Measure Outputs 1 and 2 in Conjugate-Pair Polarizations: § Polarization Entanglement:

Output k wave plates

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The Four Steps of Qubit Teleportation

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Coming Attractions: Lecture 14 § Lecture 14: Teleportation

§ Polarization entanglement and qubit teleportation § Quadrature entanglement and continuous-variable teleportation

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