Machine Learning-Based Classification of Vector Vortex Beams.

Structured light is attracting significant attention for its diverse applications in both classical and quantum optics. The so-called vector vortex beams display peculiar properties in both contexts due to the nontrivial correlations between optical polarization and orbital angular momentum. Here we demonstrate a new, flexible experimental approach to the classification of vortex vector beams. We first describe a platform for generating arbitrary complex vector vortex beams inspired to photonic quantum walks. We then exploit recent machine learning methods-namely, convolutional neural networks and principal component analysis-to recognize and classify specific polarization patterns. Our study demonstrates the significant advantages resulting from the use of machine learning-based protocols for the construction and characterization of high-dimensional resources for quantum protocols.

[1]  Min Zhang,et al.  Joint atmospheric turbulence detection and adaptive demodulation technique using the CNN for the OAM-FSO communication. , 2018, Optics express.

[2]  L. Marrucci,et al.  Polarization pattern of vector vortex beams generated by q-plates with different topological charges. , 2012, Applied optics.

[3]  Gerbrand Ceder,et al.  Predicting crystal structure by merging data mining with quantum mechanics , 2006, Nature materials.

[4]  Ebrahim Karimi,et al.  Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram. , 2013, Optics letters.

[5]  D. Nolan,et al.  Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light. , 2011, Physical review letters.

[6]  Ying Li,et al.  Photonic polarization gears for ultra-sensitive angular measurements , 2013, Nature Communications.

[7]  Hailu Luo,et al.  Propagation model for vector beams generated by metasurfaces. , 2016, Optics express.

[8]  Johannes Courtial,et al.  Light’s Orbital Angular Momentum , 2004 .

[9]  Sergej Orlov,et al.  Nanointerferometric amplitude and phase reconstruction of tightly focused vector beams , 2013, Nature Photonics.

[10]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[11]  Sanjaya Lohani,et al.  Turbulence correction with artificial neural networks. , 2018, Optics letters.

[12]  L. Marrucci,et al.  Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. , 2006, Physical review letters.

[13]  Simone Severini,et al.  Experimental learning of quantum states , 2017, Science Advances.

[14]  Siyuan Yu,et al.  Integrated Compact Optical Vortex Beam Emitters , 2012, Science.

[15]  Ebrahim Karimi,et al.  Limitations to the determination of a Laguerre–Gauss spectrum via projective, phase-flattening measurement , 2014, 1401.3512.

[16]  Leif Katsuo Oxenløwe,et al.  High‐Dimensional Quantum Communication: Benefits, Progress, and Future Challenges , 2019, Advanced Quantum Technologies.

[17]  A. Willner,et al.  Optical communications using orbital angular momentum beams , 2015 .

[18]  Robert Fickler,et al.  Twisted photons: new quantum perspectives in high dimensions , 2017, Light: Science & Applications.

[19]  Ebrahim Karimi,et al.  Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface , 2014, Light: Science & Applications.

[20]  Masakazu Matsugu,et al.  Subject independent facial expression recognition with robust face detection using a convolutional neural network , 2003, Neural Networks.

[21]  G. Vallone,et al.  Free-space quantum key distribution by rotation-invariant twisted photons. , 2014, Physical review letters.

[22]  Charalambos Klitis,et al.  Direct fiber vector eigenmode multiplexing transmission seeded by integrated optical vortex emitters , 2017, Light: Science & Applications.

[23]  Mushegh Rafayelyan,et al.  Laguerre-Gaussian quasi-modal q-plates from nanostructured glasses , 2017 .

[24]  Timothy Doster,et al.  Machine learning approach to OAM beam demultiplexing via convolutional neural networks. , 2017, Applied optics.

[25]  Zach DeVito,et al.  Opt , 2017 .

[26]  Jian-Wei Pan,et al.  Quantum teleportation of multiple degrees of freedom of a single photon , 2015, Nature.

[27]  I K Fodor,et al.  A Survey of Dimension Reduction Techniques , 2002 .

[28]  Ebrahim Karimi,et al.  Light propagation in a birefringent plate with topological charge. , 2008, Optics letters.

[29]  Enrico Santamato,et al.  Statistical moments of quantum-walk dynamics reveal topological quantum transitions , 2016, Nature Communications.

[30]  Paolo Villoresi,et al.  Birth and evolution of an optical vortex. , 2016, Optics express.

[31]  Fabio Sciarrino,et al.  Calibration of Quantum Sensors by Neural Networks. , 2019, Physical review letters.

[32]  Nathan Wiebe,et al.  Pattern recognition techniques for Boson Sampling validation , 2017, Physical Review X.

[33]  Enrico Santamato,et al.  Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons , 2016, Nature Communications.

[34]  Ebrahim Karimi,et al.  Hypergeometric-Gaussian modes. , 2007, Optics letters.

[35]  Timothy Doster,et al.  De-multiplexing vortex modes in optical communications using transport-based pattern recognition. , 2018, Optics express.

[36]  Xianfeng Chen,et al.  Superhigh-Resolution Recognition of Optical Vortex Modes Assisted by a Deep-Learning Method. , 2019, Physical review letters.

[37]  N. Spagnolo,et al.  Experimental Engineering of Arbitrary Qudit States with Discrete-Time Quantum Walks. , 2018, Physical review letters.

[38]  J. O'Brien,et al.  Witnessing eigenstates for quantum simulation of Hamiltonian spectra , 2016, Science Advances.

[39]  A. Zeilinger,et al.  Multi-photon entanglement in high dimensions , 2015, Nature Photonics.

[40]  Daniel W. Davies,et al.  Machine learning for molecular and materials science , 2018, Nature.

[41]  Leif Katsuo Oxenløwe,et al.  Orbital Angular Momentum States Enabling Fiber-based High-dimensional Quantum Communication , 2018, Physical Review Applied.

[42]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[43]  Isaac Nape,et al.  Creation and Detection of Vector Vortex Modes for Classical and Quantum Communication , 2017, Journal of Lightwave Technology.

[44]  Tsuyoshi Murata,et al.  {m , 1934, ACML.

[45]  Marti A. Hearst Trends & Controversies: Support Vector Machines , 1998, IEEE Intell. Syst..

[46]  Xianzhong Chen,et al.  Vector Vortex Beam Generation with a Single Plasmonic Metasurface , 2016 .

[47]  Andrew Forbes,et al.  Implementing quantum walks using orbital angular momentum of classical light. , 2012, Physical review letters.

[48]  Fabio Sciarrino,et al.  Air-core fiber distribution of hybrid vector vortex-polarization entangled states , 2019, Advanced Photonics.

[49]  L. Marrucci,et al.  The polarizing Sagnac interferometer: a tool for light orbital angular momentum sorting and spin-orbit photon processing. , 2010, Optics express.

[50]  D. Gauthier,et al.  High-dimensional quantum cryptography with twisted light , 2014, 1402.7113.

[51]  C. Branciard,et al.  Indefinite Causal Order in a Quantum Switch. , 2018, Physical review letters.

[52]  Z. Hradil Quantum-state estimation , 1996, quant-ph/9609012.

[53]  A. Zeilinger,et al.  Communication with spatially modulated light through turbulent air across Vienna , 2014, 1402.2602.

[54]  Lorenzo Marrucci,et al.  Spin–orbit photonics , 2015, Nature Photonics.

[55]  Shuangchun Wen,et al.  Generation of arbitrary vector vortex beams on hybrid-order Poincaré sphere , 2017 .

[56]  S. Barnett,et al.  Philosophical Transactions of the Royal Society A : Mathematical , 2017 .

[57]  Nathan Wiebe,et al.  Experimental statistical signature of many-body quantum interference , 2018 .

[58]  Guang-Can Guo,et al.  Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons , 2010, 1002.0638.

[59]  R. Boyd,et al.  High-dimensional intracity quantum cryptography with structured photons , 2016, 1612.05195.

[60]  Mario Krenn,et al.  Active learning machine learns to create new quantum experiments , 2017, Proceedings of the National Academy of Sciences.

[61]  S. Barnett,et al.  Measuring the orbital angular momentum of a single photon. , 2002, Physical review letters.

[62]  Zhi-Qiang Jiao,et al.  Mapping Twisted Light into and out of a Photonic Chip. , 2018, Physical review letters.

[63]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[64]  Toby Walsh,et al.  Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Three , 2011 .

[65]  J. Rarity,et al.  Experimental quantum Hamiltonian learning , 2017, Nature Physics.

[66]  J. P. Woerdman,et al.  Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[67]  Jonathan Leach,et al.  Direct measurement of a 27-dimensional orbital-angular-momentum state vector , 2013, Nature Communications.

[68]  A. Zeilinger,et al.  Twisted light transmission over 143 km , 2016, Proceedings of the National Academy of Sciences.

[69]  Jorge Cadima,et al.  Principal component analysis: a review and recent developments , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[70]  Ebrahim Karimi,et al.  Quantum walks and wavepacket dynamics on a lattice with twisted photons , 2014, Science Advances.

[71]  Ruediger Schack,et al.  Unknown Quantum States and Operations, a Bayesian View , 2004, quant-ph/0404156.

[72]  Roger G. Melko,et al.  Reconstructing quantum states with generative models , 2018, Nature Machine Intelligence.

[73]  D. Gross,et al.  Focus on quantum tomography , 2013 .

[74]  Nathan Wiebe,et al.  Experimental Phase Estimation Enhanced By Machine Learning , 2017, Physical Review Applied.

[75]  M. Lavery,et al.  Efficient sorting of orbital angular momentum states of light. , 2010, Physical review letters.

[76]  Robert Fickler,et al.  Quantum Entanglement of High Angular Momenta , 2012, Science.

[77]  W. Marsden I and J , 2012 .

[78]  N. Spagnolo,et al.  Quantum state engineering using one-dimensional discrete-time quantum walks , 2017, 1710.10518.

[79]  Andrew G. Glen,et al.  APPL , 2001 .

[80]  Ebrahim Karimi,et al.  Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications , 2011 .