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6.453 Quantum Optical Communication
Spring 2009
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September 25, 2008
6.453 Quantum Optical Communication
Lecture 7
Jeffrey H. Shapiro
Optical and Quantum Communications Group
www.rle.mit.edu/qoptics
6.453 Quantum Optical Communication — Lecture 7
! Announcements
! Turn in problem set 3
! Pick up problem set 3 solutions, problem set 4, lecture notes, slides
! Quantum Harmonic Oscillator
! Quadrature-measurement statistics and phase space
! Characteristics functions and the Wigner distribution
! Positive operator-valued measurement of
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Quadrature-Measurement Statistics: Summary
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Quadrature-Measurement Statistics of
and
! Coherent State
! Number State
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Quadrature-Measurement Statistics of
! Amplitude-Squeezed State
! Phase-Squeezed State
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Classical Random Variable Review
! Probability Density Function:
! Characteristic Function:
! Fourier Relationship
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Quadrature-Measurement Statistics
! Characteristic Function for the Quadrature Measurement
! Wigner Characteristic Function
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Quadrature-Measurement Statistics of
! Wigner Characteristic Function of the Number State
! Quadrature-Measurement Probability Density Function
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Quadrature-Measurement Statistics of
! Example:
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Wigner Distribution in
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Space
! Inverse Transform of the Wigner Characteristic Function
! Vacuum-State Wigner Distribution:
! One-Photon Wigner Distribution:
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Measuring the
Operator
! Definition: Measurement of the
Operator
! yields an outcome that is a complex number
! joint probability density for getting this outcome is
! Consistency Checks:
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Measuring the
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Operator: Summary
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Coming Attractions: Lectures 8 and 9
! Lecture 8:
Quantum Harmonic Oscillator
! Reconciling the
measurement with the notion of observables
Single-Mode Photodetection
! Direct Detection — semiclassical versus quantum
! Homodyne Detection — semiclassical versus quantum
! Lecture 9:
Single-Mode Photodetection
! Heterodyne Detection — semiclassical versus quantum
! Realizing the
measurement
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