MIT OpenCourseWarehttp://ocw.mit.edu 6.453 Quantum Optical Communication Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.September 25, 2008Optical and Quantum Communications Groupwww.rle.mit.edu/qoptics6.453 Quantum Optical CommunicationLecture 7Jeffrey H. Shapiro2www.rle.mit.edu/qoptics6.453 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 of3www.rle.mit.edu/qopticsQuadrature-Measurement Statistics: Summary4www.rle.mit.edu/qopticsQuadrature-Measurement Statistics of and! Coherent State! Number State5www.rle.mit.edu/qopticsQuadrature-Measurement Statistics of! Amplitude-Squeezed State ! Phase-Squeezed State6www.rle.mit.edu/qopticsClassical Random Variable Review! Probability Density Function:! Characteristic Function:! Fourier Relationship7www.rle.mit.edu/qopticsQuadrature-Measurement Statistics! Characteristic Function for the Quadrature Measurement! Wigner Characteristic Function8www.rle.mit.edu/qopticsQuadrature-Measurement Statistics of! Wigner Characteristic Function of the Number State! Quadrature-Measurement Probability Density Function9www.rle.mit.edu/qopticsQuadrature-Measurement Statistics of! Example:10www.rle.mit.edu/qopticsWigner Distribution in Space! Inverse Transform of the Wigner Characteristic Function! Vacuum-State Wigner Distribution:! One-Photon Wigner Distribution:11www.rle.mit.edu/qopticsMeasuring 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:12www.rle.mit.edu/qopticsMeasuring the Operator: Summary13www.rle.mit.edu/qopticsComing Attractions: Lectures 8 and 9! Lecture 8:Quantum Harmonic Oscillator! Reconciling the measurement with the notion of observablesSingle-Mode Photodetection! Direct Detection — semiclassical versus quantum! Homodyne Detection — semiclassical versus quantum! Lecture 9:Single-Mode Photodetection! Heterodyne Detection — semiclassical versus quantum! Realizing the
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