From Quantum Optics to Quantum Technologies

Quantum optics is the study of the intrinsically quantum properties of light. During the second part of the 20th century experimental and theoretical progress developed together; nowadays quantum optics provides a testbed of many fundamental aspects of quantum mechanics such as coherence and quantum entanglement. Quantum optics helped trigger, both directly and indirectly, the birth of quantum technologies, whose aim is to harness non-classical quantum effects in applications from quantum key distribution to quantum computing. Quantum light remains at the heart of many of the most promising and potentially transformative quantum technologies. In this review, we celebrate the work of Sir Peter Knight and present an overview of the development of quantum optics and its impact on quantum technologies research. We describe the core theoretical tools developed to express and study the quantum properties of light, the key experimental approaches used to control, manipulate and measure such properties and their application in quantum simulation, and quantum computing.

[1]  S. Mukamel,et al.  Nonlinear spectroscopy of controllable many-body quantum systems , 2013, 1312.3365.

[2]  R. Brouri,et al.  Non-gaussian statistics from individual pulses of squeezed light , 2004, InternationalQuantum Electronics Conference, 2004. (IQEC)..

[3]  P. Knight,et al.  Quantum walk on the line as an interference phenomenon , 2003, quant-ph/0304201.

[4]  P. L. Knight,et al.  Decoherence in nonclassical motional states of a trapped ion , 1998, quant-ph/9803041.

[5]  S. Bose,et al.  Photon-blockade-induced Mott transitions and XY spin models in coupled cavity arrays , 2006, quant-ph/0606159.

[6]  H. S. Allen The Quantum Theory , 1928, Nature.

[7]  T. S. Monteiro,et al.  Cavity cooling a single charged levitated nanosphere. , 2015, Physical review letters.

[8]  Knight,et al.  Comparison of quantum-state diffusion and quantum-jump simulations of two-photon processes in a dissipative environment. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[9]  A. Houck,et al.  On-chip quantum simulation with superconducting circuits , 2012, Nature Physics.

[10]  D. Meyer From quantum cellular automata to quantum lattice gases , 1996, quant-ph/9604003.

[11]  F. Mintert,et al.  Ion-trap quantum logic using long-wavelength radiation. , 2001, Physical review letters.

[12]  Knight,et al.  Schrödinger-cat states in the resonant Jaynes-Cummings model: Collapse and revival of oscillations of the photon-number distribution. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[13]  M. Schreiber,et al.  Observation of many-body localization of interacting fermions in a quasirandom optical lattice , 2015, Science.

[14]  K. Jacobs,et al.  Preparation of nonclassical states in cavities with a moving mirror , 1997 .

[15]  Andrew M. Childs,et al.  Simulating Hamiltonian dynamics with a truncated Taylor series. , 2014, Physical review letters.

[16]  Cook,et al.  Possibility of direct observation of quantum jumps. , 1985, Physical review letters.

[17]  Klein,et al.  Observation of quantum collapse and revival in a one-atom maser. , 1987, Physical review letters.

[18]  King,et al.  Generation of nonclassical motional states of a trapped atom. , 1996, Physical review letters.

[19]  M. Nielsen Optical quantum computation using cluster States. , 2004, Physical review letters.

[20]  M. M. Miller,et al.  Fundamentals of Quantum Optics , 1968 .

[21]  P. Knight,et al.  Quantum jumps and atomic cryptograms , 1986, Nature.

[22]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[23]  A. Lvovsky Squeezed Light , 2014, A Guide to Experiments in Quantum Optics.

[24]  S. Girvin,et al.  Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture. , 2011, Physical review letters.

[25]  V. Degiorgio,et al.  About photon correlations , 2013 .

[26]  SCHEME TO PROBE THE DECOHERENCE OF A MACROSCOPIC OBJECT , 1997, quant-ph/9712017.

[27]  S. Mukamel,et al.  Nonlinear spectroscopy of trapped ions , 2014, 1410.1694.

[28]  B. Lanyon,et al.  Quasiparticle engineering and entanglement propagation in a quantum many-body system , 2014, Nature.

[29]  P. L. Knight,et al.  Nonclassicality of a photon-subtracted Gaussian field , 2004, quant-ph/0409218.

[30]  S. Scheel,et al.  Permanents in linear optical networks , 2004, quant-ph/0406127.

[31]  G. Vallone,et al.  Two-particle bosonic-fermionic quantum walk via integrated photonics. , 2011, Physical review letters.

[32]  Hong,et al.  Measurement of subpicosecond time intervals between two photons by interference. , 1987, Physical review letters.

[33]  Wineland,et al.  Laser cooling to the zero-point energy of motion. , 1989, Physical review letters.

[34]  D. E. Chang,et al.  Cavity opto-mechanics using an optically levitated nanosphere , 2009, Proceedings of the National Academy of Sciences.

[35]  M. Plenio,et al.  Quantifying Entanglement , 1997, quant-ph/9702027.

[36]  D. Deutsch Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[37]  F. Mintert,et al.  Spin resonance with trapped ions , 2003 .

[38]  T. Hänsch,et al.  Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms , 2002, Nature.

[39]  M. B. Plenio,et al.  Robust trapped-ion quantum logic gates by continuous dynamical decoupling , 2012 .

[40]  M. Kim,et al.  Reconstruction of the Jaynes-Cummings field state of ionic motion in a harmonic trap , 2017 .

[41]  M. B. Plenio,et al.  Fast quantum gates for cold trapped ions , 2000, quant-ph/0002092.

[42]  E. Solano,et al.  Digital quantum simulation of spin models with circuit quantum electrodynamics , 2015, 1502.06778.

[43]  C. Monroe,et al.  A “Schrödinger Cat” Superposition State of an Atom , 1996, Science.

[44]  J Casanova,et al.  Deep strong coupling regime of the Jaynes-Cummings model. , 2010, Physical review letters.

[45]  V. Vedral,et al.  Entanglement measures and purification procedures , 1997, quant-ph/9707035.

[46]  Jay M. Gambetta,et al.  Improved superconducting qubit coherence using titanium nitride , 2013, 1303.4071.

[47]  伏見 康治,et al.  Some formal properties of the density matrix , 1940 .

[48]  P. Knight,et al.  Quantum revivals of a two-level system driven by chaotic radiation , 1982 .

[49]  Sougato Bose,et al.  Quantum communication through spin chain dynamics: an introductory overview , 2007, 0802.1224.

[50]  R. Barends,et al.  Chiral ground-state currents of interacting photons in a synthetic magnetic field , 2016, Nature Physics.

[51]  S. Wehner,et al.  Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres , 2015, Nature.

[52]  Reid,et al.  Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification. , 1989, Physical review. A, General physics.

[53]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[54]  G. Milburn,et al.  Linear optical quantum computing with photonic qubits , 2005, quant-ph/0512071.

[55]  Klaus Molmer,et al.  Multiparticle Entanglement of Hot Trapped Ions , 1998, quant-ph/9810040.

[56]  Aaron C. E. Lee,et al.  Many-body localization in a quantum simulator with programmable random disorder , 2015, Nature Physics.

[57]  D. Stamper-Kurn,et al.  Observation of quantum-measurement backaction with an ultracold atomic gas , 2007, 0706.1005.

[58]  Andrew M. Steane Efficient fault-tolerant quantum computing , 1999, Nature.

[59]  A S Sørensen,et al.  Optomechanical transducers for long-distance quantum communication. , 2010, Physical review letters.

[60]  R. Barends,et al.  Coherent Josephson qubit suitable for scalable quantum integrated circuits. , 2013, Physical review letters.

[61]  Mann,et al.  Measurement of the Bell operator and quantum teleportation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[62]  Charles H. Bennett,et al.  Purification of noisy entanglement and faithful teleportation via noisy channels. , 1995, Physical review letters.

[63]  Peter L. Knight,et al.  Fluctuations and entropy in models of quantum optical resonance , 1988 .

[64]  W. Paul Electromagnetic traps for charged and neutral particles , 1990 .

[65]  M. Martin-Delgado,et al.  The localization of phonons in ion traps with controlled quantum disorder , 2010, 1002.3748.

[66]  Mahn‐Soo Choi,et al.  Recurrent Delocalization and Quasiequilibration of Photons in Coupled Systems in Circuit Quantum Electrodynamics. , 2016, Physical review letters.

[67]  S. Bose,et al.  PURIFICATION VIA ENTANGLEMENT SWAPPING AND CONSERVED ENTANGLEMENT , 1998, quant-ph/9812013.

[68]  Peter L. Knight,et al.  Fundamental physics with trapped ions , 1997 .

[69]  R. Barends,et al.  Digital quantum simulation of fermionic models with a superconducting circuit , 2015, Nature Communications.

[70]  Terry Rudolph,et al.  Why I am optimistic about the silicon-photonic route to quantum computing , 2016, 1607.08535.

[71]  M. Lukin,et al.  Controlling spin exchange interactions of ultracold atoms in optical lattices. , 2002, Physical review letters.

[72]  M. B. Plenio,et al.  Quantum gates and memory using microwave-dressed states , 2011, Nature.

[73]  P. Knight,et al.  Multiparticle generalization of entanglement swapping , 1998 .

[74]  Andrew W. Cross,et al.  Implementing a strand of a scalable fault-tolerant quantum computing fabric , 2013, Nature Communications.

[75]  Multilevel multiparty singlets as ground states and their role in entanglement distribution , 2006, quant-ph/0602139.

[76]  E. Jaynes,et al.  Comparison of quantum and semiclassical radiation theories with application to the beam maser , 1962 .

[77]  Andrew D. Greentree,et al.  Quantum phase transitions of light , 2006, cond-mat/0609050.

[78]  M. Bellini,et al.  Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light , 2004, Science.

[79]  D. E. Changa,et al.  Cavity opto-mechanics using an optically levitated nanosphere , 2009 .

[80]  L. Knoll,et al.  GENERATION OF ARBITRARY QUANTUM STATES OF TRAVELING FIELDS , 1999 .

[81]  Simon C. Benjamin,et al.  One-dimensional quantum computing with a ‘segmented chain’ is feasible with today’s gate fidelities , 2017, npj Quantum Information.

[82]  Ekert,et al.  "Event-ready-detectors" Bell experiment via entanglement swapping. , 1993, Physical review letters.

[83]  P. Knight,et al.  Entangled quantum systems and the Schmidt decomposition , 1995 .

[84]  Milburn,et al.  Quantum optical Fredkin gate. , 1989, Physical review letters.

[85]  E. Solano,et al.  Exact mapping of the 2+1 Dirac oscillator onto the Jaynes-Cummings model: Ion-trap experimental proposal , 2007, 0704.2315.

[86]  Kae Nemoto,et al.  Measurement-induced nonlinearity in linear optics , 2003, quant-ph/0305082.

[87]  E. Knill,et al.  A scheme for efficient quantum computation with linear optics , 2001, Nature.

[88]  Jeffrey H. Shapiro,et al.  Optical communication with two-photon coherent states-Part I: Quantum-state propagation and quantum-noise , 1978, IEEE Trans. Inf. Theory.

[89]  F. Nori,et al.  Quantum Simulation , 2013, Quantum Atom Optics.

[91]  I. Walmsley,et al.  Towards high-speed optical quantum memories , 2009, 0912.2970.

[92]  J Eisert,et al.  Positive Wigner functions render classical simulation of quantum computation efficient. , 2012, Physical review letters.

[93]  C. Monroe,et al.  Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects , 2012, 1208.0391.

[94]  Alexis Carrel,et al.  TISSUE CULTURE AND CELL PHYSIOLOGY , 1924 .

[95]  Arbitrary Dicke-State Control of Symmetric Rydberg Ensembles. , 2016, Physical review letters.

[96]  H. Bombin,et al.  Topological quantum distillation. , 2006, Physical review letters.

[97]  Benjamin J. Brown,et al.  Trapped-ion quantum error-correcting protocols using only global operations , 2014, 1407.1858.

[98]  Antonio-José Almeida,et al.  NAT , 2019, Springer Reference Medizin.

[99]  Jinhyoung Lee,et al.  Partial teleportation of entanglement in a noisy environment , 2000, quant-ph/0003060.

[100]  F. Mintert,et al.  High fidelity quantum gates of trapped ions in the presence of motional heating , 2015, 1510.05814.

[101]  Wolfgang Dür,et al.  Quantum Repeaters: The Role of Imperfect Local Operations in Quantum Communication , 1998 .

[102]  P. Knight,et al.  PHASE CONTROL OF SPONTANEOUS EMISSION , 1998 .

[103]  A. Crespi,et al.  Anderson localization of entangled photons in an integrated quantum walk , 2013, Nature Photonics.

[104]  Wolfgang Lange,et al.  Quantum Computing with Trapped Ions , 2009, Encyclopedia of Complexity and Systems Science.

[105]  Engineering two-mode interactions in ion traps , 1997, quant-ph/9708008.

[106]  Frustrated quantum spin models with cold Coulomb crystals. , 2011, Physical review letters.

[107]  S. Girvin,et al.  Charge-insensitive qubit design derived from the Cooper pair box , 2007, cond-mat/0703002.

[108]  R. Glauber Coherent and incoherent states of the radiation field , 1963 .

[109]  K. Berggren,et al.  Superconducting Nanowire Architectures for Single Photon Detection , 2016 .

[110]  G. Stutter,et al.  Resolved-Sideband Laser Cooling in a Penning Trap. , 2014, Physical review letters.

[111]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[112]  E. Schrödinger Die gegenwärtige Situation in der Quantenmechanik , 2005, Naturwissenschaften.

[113]  S. Deleglise,et al.  Reconstruction of non-classical cavity field states with snapshots of their decoherence , 2008, Nature.

[114]  R. Blatt,et al.  Quantum computations on a topologically encoded qubit , 2014, Science.

[115]  C. Caves Quantum Mechanical Noise in an Interferometer , 1981 .

[116]  Samuel L. Braunstein,et al.  Weak-force detection with superposed coherent states , 2002 .

[117]  A Retzker,et al.  Double well potentials and quantum phase transitions in ion traps. , 2008, Physical review letters.

[118]  Reck,et al.  Experimental realization of any discrete unitary operator. , 1994, Physical review letters.

[119]  J M Amini,et al.  Trapped-ion quantum logic gates based on oscillating magnetic fields. , 2008, Physical review letters.

[120]  Ilgaitis Prūsis,et al.  Nature of Photon , 2019 .

[121]  P. Knight,et al.  Vibrational coherent quantum computation , 2004, quant-ph/0405099.

[122]  L. M. K. Vandersypen,et al.  Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array , 2017, Nature.

[123]  J. Mitroy,et al.  All-order relativistic many-body theory of low-energy electron-atom scattering , 2014 .

[124]  Robert Jördens,et al.  A Mott insulator of fermionic atoms in an optical lattice , 2008, Nature.

[125]  F. Schmidt-Kaler,et al.  Two-dimensional spectroscopy for the study of ion coulomb crystals. , 2014, Physical review letters.

[126]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[127]  S. Scheel,et al.  MACROSCOPIC QUANTUM ELECTRODYNAMICS — CONCEPTS AND APPLICATIONS , 2008, 0902.3586.

[128]  M. B. Plenio,et al.  Robust creation of entanglement between ions in spatially separate cavities. , 2003 .

[129]  Barry C. Sanders,et al.  Quantum quincunx in cavity quantum electrodynamics , 2003 .

[130]  E. Sudarshan Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams , 1963 .

[131]  Light-shift-induced quantum gates for ions in thermal motion. , 2001, Physical review letters.

[132]  M. Martin-Delgado,et al.  Competing many-body interactions in systems of trapped ions , 2008, 0812.3812.

[133]  Mario Dagenais,et al.  Photon Antibunching in Resonance Fluorescence , 1977 .

[134]  M. Hohenstatt,et al.  Localized visible Ba + mono-ion oscillator , 1980 .

[135]  Knight,et al.  Generation of nonclassical light by dissipative two-photon processes. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[136]  Knight,et al.  Superpositions of coherent states: Squeezing and dissipation. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[137]  B. E. Kane A silicon-based nuclear spin quantum computer , 1998, Nature.

[138]  J. Gambetta,et al.  Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1 ms , 2012, 1202.5533.

[139]  S. Barnett,et al.  Thermofield analysis of squeezing and statistical mixtures in quantum optics , 1985 .

[140]  Stefano Mancini,et al.  Continuous-variable entanglement and quantum-state teleportation between optical and macroscopic vibrational modes through radiation pressure , 2003 .

[141]  Shota Yokoyama,et al.  Ultra-large-scale continuous-variable cluster states multiplexed in the time domain , 2013, Nature Photonics.

[142]  I. Sagnes,et al.  Near-optimal single-photon sources in the solid state , 2015, Nature Photonics.

[143]  Stephan Dürr,et al.  Optical π phase shift created with a single-photon pulse , 2015, Science Advances.

[144]  S. Stenholm The semiclassical theory of laser cooling , 1986 .

[145]  Gavin W. Morley,et al.  Matter-wave interferometry of a levitated thermal nano-oscillator induced and probed by a spin. , 2013, Physical review letters.

[146]  R. Feynman Simulating physics with computers , 1999 .

[147]  Julien Laurat,et al.  Generating Optical Schrödinger Kittens for Quantum Information Processing , 2006, Science.

[148]  Johnnie Gray,et al.  Unravelling quantum dot array simulators via singlet-triplet measurements , 2016, 1606.09263.

[149]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[150]  Shor,et al.  Good quantum error-correcting codes exist. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[151]  J. Cirac,et al.  Effective quantum spin systems with trapped ions. , 2004, Physical Review Letters.

[152]  Shih,et al.  New high-intensity source of polarization-entangled photon pairs. , 1995, Physical review letters.

[153]  Philippe Grangier,et al.  Increasing entanglement between Gaussian states by coherent photon subtraction. , 2006, Physical review letters.

[154]  Knight,et al.  Squeezing and superposition states. , 1987, Physical review. A, General physics.

[155]  C. Monroe,et al.  Scaling and suppression of anomalous heating in ion traps. , 2006, Physical review letters.

[156]  S. Haroche,et al.  A complementarity experiment with an interferometer at the quantum–classical boundary , 2001, Nature.

[157]  Hyunchul Nha,et al.  Proposed test of quantum nonlocality for continuous variables. , 2004, Physical review letters.

[158]  Simón Peres-horodecki separability criterion for continuous variable systems , 1999, Physical review letters.

[159]  Jaeyoon Cho,et al.  Fractional quantum Hall state in coupled cavities. , 2008, Physical review letters.

[160]  Trapped ions as vibrational beam splitters: SU(2) states in a two-dimensional ion trap. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[161]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[162]  E. Rico,et al.  Atomic quantum simulation of U(N) and SU(N) non-Abelian lattice gauge theories. , 2012, Physical review letters.

[163]  P. Knight,et al.  The Quantum jump approach to dissipative dynamics in quantum optics , 1997, quant-ph/9702007.

[164]  A Retzker,et al.  Ultrasensitive Magnetometer using a Single Atom. , 2014, Physical review letters.

[165]  P. Rabl,et al.  Microscopic model of electric-field-noise heating in ion traps , 2011, 1106.1949.

[166]  Pieter Kok,et al.  Efficient high-fidelity quantum computation using matter qubits and linear optics , 2005 .

[167]  S. Giampaolo,et al.  Adiabatic quantum simulation with a segmented ion trap: Application to long-distance entanglement in quantum spin systems , 2013, 1304.0261.

[168]  M. S. Kim,et al.  Efficient quantum computation using coherent states , 2001, quant-ph/0109077.

[169]  S. Bose,et al.  NOON states via a quantum walk of bound particles , 2016, 1607.01809.

[170]  John M. Martinis,et al.  State preservation by repetitive error detection in a superconducting quantum circuit , 2015, Nature.

[171]  P. Knight,et al.  The Rabi frequency in optical spectra , 1980 .

[172]  A. Bermudez,et al.  Synthetic gauge fields for vibrational excitations of trapped ions. , 2011, Physical review letters.

[173]  C. Gardiner,et al.  Cold Bosonic Atoms in Optical Lattices , 1998, cond-mat/9805329.

[174]  P. Knight,et al.  Proposal for teleportation of an atomic state via cavity decay , 1999, quant-ph/9908004.

[175]  S. Chumakov,et al.  The Jaynes–Cummings Model , 2009 .

[176]  Immanuel Bloch,et al.  Microscopic observation of magnon bound states and their dynamics , 2013, Nature.

[177]  K. Mølmer,et al.  QUANTUM COMPUTATION WITH IONS IN THERMAL MOTION , 1998, quant-ph/9810039.

[178]  Wineland,et al.  Observation of quantum jumps in a single atom. , 1986, Physical review letters.

[179]  Abolfazl Bayat,et al.  Entanglement entropy scaling in solid-state spin arrays via capacitance measurements , 2016, 1608.03970.

[180]  K. Thorne,et al.  Quantum Nondemolition Measurements , 1980, Science.

[181]  CH' , 2018, Dictionary of Upriver Halkomelem.

[182]  David C. Burnham,et al.  Observation of Simultaneity in Parametric Production of Optical Photon Pairs , 1970 .

[183]  A. Steane Multiple-particle interference and quantum error correction , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[184]  P. Knight,et al.  Concepts of quantum optics , 1983 .

[185]  J. Cirac,et al.  Creation of entangled states of distant atoms by interference , 1998, quant-ph/9810013.

[186]  M. Greiner,et al.  Quantum simulation of antiferromagnetic spin chains in an optical lattice , 2011, Nature.

[187]  J. Gea-Banacloche,et al.  Collapse and revival of the state vector in the Jaynes-Cummings model: An example of state preparation by a quantum apparatus. , 1990, Physical review letters.

[188]  David J. Wineland,et al.  Laser cooling of ions stored in harmonic and Penning traps , 1982 .

[189]  Vitus Händchen,et al.  Stable control of 10 dB two-mode squeezed vacuum states of light. , 2013, Optics express.

[190]  Kerry Vahala,et al.  Cavity opto-mechanics. , 2007, Optics express.

[191]  Franco Nori,et al.  Optomechanical-like coupling between superconducting resonators , 2014, 1403.4341.

[192]  R Laflamme,et al.  Entangled quantum key distribution over two free-space optical links. , 2008, Optics express.

[193]  G. J. Milburn,et al.  Pulsed quantum optomechanics , 2010, Proceedings of the National Academy of Sciences.

[194]  Knight,et al.  Quantum computing using dissipation to remain in a decoherence-free subspace , 2000, Physical review letters.

[195]  P. Grangier,et al.  Continuous variable quantum cryptography using coherent states. , 2001, Physical review letters.

[196]  Christoph Simon,et al.  Towards quantum superpositions of a mirror , 2004 .

[197]  Gerhard Klimeck,et al.  Quantum simulation of the Hubbard model with dopant atoms in silicon , 2015, Nature Communications.

[198]  H. Briegel,et al.  Measurement-based quantum computation , 2009, 0910.1116.

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

[200]  T. Rudolph,et al.  Resource-efficient linear optical quantum computation. , 2004, Physical review letters.

[201]  Scott Aaronson,et al.  The computational complexity of linear optics , 2010, STOC '11.

[202]  P. Knight,et al.  Introductory quantum optics , 2004 .

[203]  M. S. Kim,et al.  Recent developments in photon-level operations on travelling light fields , 2008, 0807.4708.

[204]  E. Knill,et al.  Realization of quantum error correction , 2004, Nature.

[205]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[206]  P. Grangier,et al.  Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment : A New Violation of Bell's Inequalities , 1982 .

[207]  Gavin W. Morley,et al.  Free Nano-Object Ramsey Interferometry for Large Quantum Superpositions. , 2015, Physical review letters.

[208]  P. Zoller,et al.  Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms , 2009, 0905.2610.

[209]  H. Weinfurter,et al.  Experimental Entanglement Swapping: Entangling Photons That Never Interacted , 1998 .

[210]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[211]  Marco G. Genoni,et al.  Quantifying the non-Gaussian character of a quantum state by quantum relative entropy , 2007, 0805.1645.

[212]  Dreyer,et al.  Observing the Progressive Decoherence of the "Meter" in a Quantum Measurement. , 1996, Physical review letters.

[213]  Jose Javier Sanchez-Mondragon,et al.  Periodic spontaneous collapse and revival in a simple quantum model , 1980 .

[214]  N. Cerf,et al.  Quantum key distribution using gaussian-modulated coherent states , 2003, Nature.

[215]  Ponderomotive control of quantum macroscopic coherence , 1996, quant-ph/9612005.

[216]  M. B. Plenio,et al.  Cavity-loss-induced generation of entangled atoms , 1999 .

[217]  Alexey V. Gorshkov,et al.  Non-local propagation of correlations in quantum systems with long-range interactions , 2014, Nature.

[218]  A. EINsTEIN,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete ' ? , 2011 .

[219]  Derek K. Jones,et al.  Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light , 2013, Nature Photonics.

[220]  Hong,et al.  Experimental realization of a localized one-photon state. , 1986, Physical review letters.

[221]  Michael J. Hartmann,et al.  Strongly interacting polaritons in coupled arrays of cavities , 2006, 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference.

[222]  M. Blencowe,et al.  Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper-pair box. , 2002, Physical review letters.

[223]  Cheng-Zhi Peng,et al.  Observation of eight-photon entanglement , 2011, Nature Photonics.

[224]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[225]  Simon C. Benjamin,et al.  Freely Scalable Quantum Technologies using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links , 2014, 1406.0880.

[226]  King,et al.  Demonstration of a fundamental quantum logic gate. , 1995, Physical review letters.

[227]  Collett,et al.  Quantum limits in interferometric detection of gravitational radiation. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[228]  B. J. Metcalf,et al.  Boson Sampling on a Photonic Chip , 2012, Science.