1 Quantum Imaging with Continuous Variables Luigi A．Lugiato，Alessandra Gatti，and Enrico Brambilla 1．1 Introduction 1．2 The Concepts of Squeezing and of Entanglement with Continuous Variables， and Their Intrinsic Connection 1．2．1 Prototype Model Ⅰ 1．2．2 Prototype Model Ⅱ 1．3 Intrinsic Relation Between Squeezing and Entanglement 1．4 Spatially Multimode Parametric Down-Conversion： Some Topics in Quantum Imaging 1．4．1 Spatially Multimode Versus Single-Mode Squeezing：Optical Parametric Down-Conversion of Type-Ⅰ 1．4．2 Near-FieldlFar-Field Duality in Type-Ⅰ OPAs 1．4．3 Detection of Weak Amplitude or Phase Objects Beyond the Standard Quantum Limit 1．4．4 Image Amplification by Parametric Down-Conversion （Type-Ⅰ） References 2 Spatial Entanglement in Optical Parametric Down-Conversion Alessandra Gatti，Enrico Brambilla，Ottavia Jedrkiewicz，and Luigi 2．1 Introduction 2．2 Simultaneous Near-Field and Far-Field Spatial Quantum Correlation in the High-Gain Regime of Type-Ⅱ Parametric Down-Conversion 2．2．1 Propagation Equations for the Signal-Idler Fields and Input-Output Relations 2．2．2 Near-and Far-Field Correlations in the Stationary and Plane-Wave Pump Approximation 2．2．3 Near-and Far-Field Correlations： Numerical Results in the General Case 2．2．4 Far-Field Correlations 2．2．5 Near-Field Correlations 2．3 Detection of Sub-Shot-Noise Spatial Correlations in High-Gain Parametric Down-Conversion 2．3．1 Detection of the Spatial Features of the Far-Field PDC Radiation by Means of the CCD 2．3．2 Experimental Set-Up for Spatial-C．orrelations Measurements 2．3．3 Detection of Quantum Spatial Correlations： Spatial Analogue of Photon Antibunching in Time 2．4 Multiphoton， Multimode Polarization Entanglement in Parametric Down-Conversion 3 Quantum Imaging in the Cntinuous-Wave Regime Using Degenerate Optical Cavities Agnes Maitre，Nicolas Treps，and Claude Fabre 3．1 Introduction 3．2 Classical Imaging Properties of Degenerate ODtical Cavities 3．2．2 Cavity Round-Trip Transform 3．2．3 Image Transmission Through an ODtical Cavity 3．3 Theory of Optical Parametric Oscillation in a Degenerate Cavity 3．3．2 Quantum Properties 3．4 Experimental Results 3．4．1 Classical Effects： Observation of Optical Patterns 3．4．2 Observation of Quantum Correlations in Images 4 Quantum Imaging by Synthesis of Multimode Quantum Light Nicolas Treps，Hans A．Bachor，Ping Koy Lam，and Claude Fabre 4．1 Introduction 4．2 Quantum Noise in an Arravlike Detection 4．3 Implementing a Sub-Shot-Noise Array Detection 4．4 The Quantum Laser Pointer 4．5 Optical Read-Out 4．6 Measuring a Signal in an Optimal Way 4．7 Conclusion References 5 Ghost Imaging Alessandra，Gatti， Enrico Brambilla，Morten Bache，and Luigi A．Lugiato 5．1 Introduction 5．2 General Theory of Ghost Imaging with Entangled Beams 5．3 Wave-Particle Aspect 5．4 Spatial Average in Ghost Diffraction： Increase of Spatial Bandwidth and of Speed in Retrieval 5．5 Ghost Imaging with Homodyne Detection 5．6 Debate： Is Quantum Entanglement R，eally Necessary for Ghost Imaging？ 5．7 Ghost Imaging by Split Thermallike Beams： Theory（15-17） 5．7．1 Analogy Between Thermal and Entangled Beams in Ghost Imaging （15-17） 5．7．2 Resolution Aspects 5．7．3 Relations with the Classic Hanburry-Brown and Twiss Correlation Technique （37） 5．7．4 Correlation Aspects 5．7．5 Visibility Aspects 5．7．6 Some Historical Considerations 5．7．7 Rule-of-Thumb Comparison Between Entangled and “Thermal” Ghost Imaging 5．8 Ghost Imaging with Split Thermal Beams： Experiment 5．8．1 High-R，esolution Ghost Imaging （23） 5．8．2 The Ghost Diffraction Experiment： Complementarity Between Coherence and Correlation （24） References 6 Quantum Limits of Optical Super-Resolution Mikhail I Kolobov 6．1 Super-Resolution in Classical Optics 6．2 Quantum Theory of Super-Resolution 6．2．1 Quantum Theory of Optical Imaging 6．2．2 Quantum Theory of Optical Fourier Microscopy 6．3 Quantum Limits in Reconstruction of Optical Objects 6．3．1 Reconstruction of Classical Noise-Free Objects 6．3．2 Reconstruction of Objects with Quantum Fluctuations 6．3．3 Point-Spread Function for Super-Resolving Reconstruction of Objects 6．4 Squeezed-Light Source for Microscopy with Super-Resolution 7 Noiseless Amplification of Optical Images Mikhail I．Kolobov and Eric Lantz 7．1 Introduction 7．2 Traveling-Wave Scheme for Amplification of Images 7．3 Optimum Phase Matching for Parametric Amplification 7．4 Quantum Fluctuations in the Amplified Image and Conditions for Noiseless Amplification 7．5 Experimental Demonstration of Temporally Noiseless Image Amplification 7．6 Experiment on Spatially Noiseless Amplification of Images References 8 Opticallmage Processing in Second-Harmonic Generation Pierre Scotto， Pere Colet， Adriatn Jacobo， afnd Maxi San Miguel 8．1 Introduction 8．2 Image Processing in Second-Harmonic Generation at a Classical 8．2．1 Frequency Up-Conversion of an Image 8．2．2 Contrast Enhancement and Contour Recognition 8．2．3 Noise Filtering Properties 8．3 Quantum Image Processing in Type-Ⅰ Second-Harmonic Generation 8．3．1 Field-Operator Dynamics 8．3．2 Quantum Image Processing 8．4 Quantum Image Processing in Type-Ⅱ Second-Harmonic Generation 8．4．1 Propagation Equations 8．4．2 Linearly y-Polarized Pump： Frequency Addition Regime 8．4．3 45°-Linearly Polarized Pump： Noiseless Up-Conversion and Amplification References 9 Transverse Distribution of Quantum Fluctuations in Free-Space Spatial Solitons Eric Lantz，Nicolas Treps， and Claude Fabrre 9．1 Introduction 9．2 General Method 9．2．1 Propagation Equations for the Fluctuations 9．2．2 Green's Function Approach 9．2．3 Correlations Between the Photocurrents 9．3 Spatial Solitons： Mean Values 9．3．1 X（3） Scalar Spatial Soliton 9．3．2 X（3） Vector Spatial Soliton 9．3．3 X（2） Spatial Soliton 9．4 Squeezing on the Total Beam 9．4．1 X（3） Scalar Spatial Soliton 9．4．2 X（3） Vector Soliton： Total Beam Squeezing and Correlation Between Polarizations 9．4．3 X（2） Spatial Solitons 9．5 Local Quantum Fluctuations 9．5．1 X（3） Scalar Spatial Soliton 9．5．2 Intensity Squeezing by Spatial Filtering 9．5．3 X（3） Vector Soliton 9．6 Quantum Correlations Between Field Quadratures at Different Points 9．6．1 X（3） Scalar Spatial Soliton 9．6．2 Vector Solitons 9．6．3 X（2）Spatial Solitons 9．7 Conclusion References 10 Quantum Fluctuations in Cavity Solitons Gian-Luca Oppo and John Jeffers 10．1 Introduction 10．2 Cavity Solitons in Degenerate Optical Parametric Oscillators 10．2．1 Spatial Equations and Domain Walls with Oscillatory Tails 10．2．2 Cavity Solitons Formed by Locked Domain Walls 10．3 Quantum Fluctuations in DOPO 10．3．1 Wigner Representation 10．3．2 Q-Representation 10．4 Arrays of CS Induced by Quantum Fluctuations 10．5 Quantum Features in the Near and the Far Field of CS 10．5．1 Quantum Correlations of CS in the Near Field 10．5．2 Quantum Correlations of CS in the Far Field 10．6 Conclusions and Acknowledgments References 11 Quantum Holographic Teleportation and Dense Coding of Optical Images Ivan V． Sokolov 11．1 Introduction 11．2 Continuous-Variable Squeezing and Entanglement for Spatially Multimode Light Fields 11．2．1 Spatial Scales of Quantum Correlations in Squeezed Light 11．2．2 Spatially Multimode Entanglement 11．3 Quantum Holographic Teleportation of Optical Images 11．3．1 Basics of Quantum Teleportation 11．3．2 Optical Scheme for Quantum Teleportation of Images 11．3．3 Quantum Statistics of the Teleported Field 11．3．4 Global and Reduced Fidelity of Holographic Teleportation 11．3．5 Quantum Holographic Teleportation and Holography 11．4 Quantum Dense Coding of Optical Images 11．4．1 Basics of Quantum Dense Coding 11．4．2 Optical Scheme for Quantum Dense Coding of Images 11．4．3 Shannon Mutual Information for Images 11．4．4 Channel Capacity 11．5 Conclusions and Outlook A Properties of Spatially Multimode Squeezing B Homodyne Detection with Spatial Resolution References 12 Orbital Angular Momentum of Light Stephen M． Barnett and Roberta Zambrini 12．1 Introduction 12．2 Angular Momentum in Electromagnetism 12．2．1 Spin and Orbital Angular Momentum 12．2．2 Angular Momentum in Paraxial Optics 12．2．3 Mechanical Effects 12．3 Beams Carrying Orbital Angular Momentum 12．3．1 Phase Singularities and Spatial Properties 12．3．2 Laguerre-Gaussian and Bessel Beams 12．3．3 Generation and Conversion 12．3．4 Other Field Spatial Profiles 12．3．5 Fractional Orbital Angular Momentum 12．4 Quantum Optical Angular Momentum 12．4．1 States of Spin and Orbital Angular Momentum 12．4．2 Measuring Orbital Angular Momentum 12．5 Angle and Angular Momentum 12．5．1 Uncertainty Relation for Angle and Angular Momentum 12．5．2 Intelligent and Minimum Uncertainty Product States 12．5．3 Communications 12．5．4 Rotation Measurements 12．6 Orbital Angular Momentum in Quantum Nonlinear Optics 12．6．1 Phase Matching 12．6．2 Second-Harmonic Generation of Laguerre-Gaussian Beams 12．6．3 Down-Conversion and Entanglement 12．6．4 High-Order Nonlinearity 12．7 Conclusion References Index
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