Measurement of the Wigner distribution and the density matrix of a light mode using optical homodyne tomography: Application to squeezed states and the vacuum
Abstract
We have measured probability distributions of quadrature-field amplitude for both vacuum and quadrature-squeezed states of a mode of the electromagnetic field. From these measurements we demonstrate the technique of optical homodyne tomography to determine the Wigner distribution and the density matrix of the mode. This provides a complete quantum mechanical characterization of the measured mode.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For continuous variables, tomography has been implemented in both quantum and atom optics.
“For continuous variables, tomography has been implemented in both quantum [23] and atom [24] optics.”
From Nonmaximally Entangled States: Production, Characterization, and Utilization (1999) · cites this paper as [23]
Cites
On the Quantum Correction For Thermodynamic Equilibrium
Wigner, E. (1932) · Physical Review · doi:10.1103/physrev.40.749 · Cited by 9,283 · see citing works
Distribution functions in physics: Fundamentals
Hillery, M. S., O’Connell, R. F., Scully, M. O., & Wigner, E. P. (1984) · Physics Reports · doi:10.1016/0370-1573(84)90160-1 · Cited by 2,932 · see citing works
The Mathematics of Computerized Tomography
Natterer, F. (1986) · Vieweg+Teubner eBooks · doi:10.1007/978-3-663-01409-6 · Cited by 1,774 · see citing works
Distribution Functions in Physics: Fundamentals
Hillery, M. S., O’Connell, R. F., Scully, M. O., & Wigner, E. P. (1997) · Springer eBooks · doi:10.1007/978-3-642-59033-7_28 · Cited by 1,687 · see citing works
Vogel, K., & Risken, H. (1989) · Physical Review A · doi:10.1103/physreva.40.2847 · Cited by 1,314 · see citing works
Phase properties of the quantized single-mode electromagnetic field
Pegg, D. T., & Barnett, S. M. (1989) · Physical Review A · doi:10.1103/physreva.39.1665 · Cited by 879 · see citing works
Noise in homodyne and heterodyne detection
Yuen, H. P., & Chan, V. W. S. (1983) · Optics Letters · doi:10.1364/ol.8.000177 · Cited by 745 · see citing works
Yuen, H. P., & Shapiro, J. H. (1980) · IEEE Transactions on Information Theory · doi:10.1109/tit.1980.1056132 · Cited by 641 · see citing works
Squeezed-light – enhanced polarization interferometer
Grangier, P., Slusher, R. E., Yurke, B., & LaPorta, A. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.2153 · Cited by 495 · see citing works
The concept of transition in quantum mechanics
Park, J. L. (1970) · Foundations of Physics · doi:10.1007/bf00708652 · Cited by 301 · see citing works
Slusher, R. E., Grangier, P., LaPorta, A., Yurke, B., & Potasek, M. J. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.2566 · Cited by 283 · see citing works
Operational approach to the phase of a quantum field
Noh, J. W., Fougères, A., & Mandeļ, L. (1992) · Physical Review A · doi:10.1103/physreva.45.424 · Cited by 240 · see citing works
Observation of zero-point noise squeezing via a Josephson-parametric amplifier
Movshovich, R., Yurke, B., Kaminsky, P. G., Smith, A. D., Silver, A. H., Simon, R. W., & Schneider, M. V. (1990) · Physical Review Letters · doi:10.1103/physrevlett.65.1419 · Cited by 149 · see citing works
Bifurcation in the phase probability distribution of a highly squeezed state
Schleich, W. P., Horowicz, R. J., & Varró, S. (1989) · Physical Review A · doi:10.1103/physreva.40.7405 · Cited by 134 · see citing works
Phase distribution of a quantum state without using phase states
Vogel, W., & Schleich, W. P. (1991) · Physical Review A · doi:10.1103/physreva.44.7642 · Cited by 79 · see citing works
Sub-shot-noise correlation of total photon number using macroscopic twin pulses of light
Smithey, D. T., Beck, M., Belsley, M., & Raymer, M. G. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2650 · Cited by 77 · see citing works
Self-citationGenerating and detecting short-duration pulses of squeezed light
Yurke, B., Grangier, P., Slusher, R. E., & Potasek, M. J. (1987) · Physical Review A · doi:10.1103/physreva.35.3586 · Cited by 76 · see citing works
Measurement of quantum states and the Wigner function
Royer, A. (1989) · Foundations of Physics · doi:10.1007/bf00737764 · Cited by 68 · see citing works
The empirical determination of quantum states
Band, W., & Park, J. L. (1970) · Foundations of Physics · doi:10.1007/bf00708723 · Cited by 68 · see citing works
The Wigner distribution function—50th birthday
O’Connell, R. F. (1983) · Foundations of Physics · doi:10.1007/bf01889413 · Cited by 53 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Quantum dynamics of single trapped ions
Leibfried, D., Blatt, R., Monroe, C., & Wineland, D. (2003) · Reviews of Modern Physics · doi:10.1103/revmodphys.75.281 · Cited by 2,739 · see citing works
James, D. F. V., Kwiat, P. G., Munro, W. J., & White, A. G. (2001) · Physical Review A · doi:10.1103/physreva.64.052312 · Cited by 2,176 · see citing works
“(University of Oregon), made a homodyne measurement of the Wigner function of a single mode of light [9].”
BackgroundMicrowave photonics with superconducting quantum circuits
Gu, X. Q., Kockum, A. F., Miranowicz, A., Liu, Y.-X., & Nori, F. (2017) · Physics Reports · doi:10.1016/j.physrep.2017.10.002 · Cited by 1,294 · see citing works
A “Schrödinger Cat” Superposition State of an Atom
Monroe, C. R., Meekhof, D. M., King, B. E., & Wineland, D. J. (1996) · Science · doi:10.1126/science.272.5265.1131 · Cited by 1,296 · see citing works
NMR techniques for quantum control and computation
Vandersypen, L. M. K., & Chuang, I. L. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.76.1037 · Cited by 1,217 · see citing works
Digital computation of the fractional Fourier transform
Ozaktas, H. M., Arikan, O., Kutay, M. A., & Bozdagt, G. (1996) · IEEE Transactions on Signal Processing · doi:10.1109/78.536672 · Cited by 1,187 · see citing works
Quantum computing with trapped ions
HAFFNER, H., ROOS, C., & BLATT, R. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.09.003 · Cited by 1,154 · see citing works
Continuous-variable optical quantum-state tomography
Lvovsky, A. I., & Raymer, M. G. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.299 · Cited by 1,125 · see citing works
Self-citationCondensation of Semiconductor Microcavity Exciton Polaritons
Deng, H., Weihs, G., Santori, C., Bloch, J., & Yamamoto, Y. (2002) · Science · doi:10.1126/science.1074464 · Cited by 890 · see citing works
Unraveling hadron structure with generalized parton distributions
Belitsky, A. V., & Radyushkin, A. V. (2005) · Physics Reports · doi:10.1016/j.physrep.2005.06.002 · Cited by 878 · see citing works
Synthesizing arbitrary quantum states in a superconducting resonator
Hofheinz, M., Wang, H., Ansmann, M., Bialczak, R. C., Lucero, E. A., Neeley, M., O’Connell, A. D., Sank, D., Wenner, J., Martinis, J. M., et al. (2009) · Nature · doi:10.1038/nature08005 · Cited by 875 · see citing works
Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light
Zavatta, A., Viciani, S., & Bellini, M. (2004) · Science · doi:10.1126/science.1103190 · Cited by 783 · see citing works
Negativity of the Wigner function as an indicator of non-classicality
Kenfack, A., & yczkowski, K. (2004) · Journal of Optics B: Quantum and Semiclassical Optics · doi:10.1088/1464-4266/6/10/003 · Cited by 779 · see citing works
Direct measurement of the quantum wavefunction
Lundeen, J. S., Sutherland, B. R., Patel, A., Stewart, C., & Bamber, C. (2011) · Nature · doi:10.1038/nature10120 · Cited by 730 · see citing works
Efficient quantum state tomography
Cramer, M., Plenio, M. B., Flammia, S. T., Somma, R. D., Gross, D., Bartlett, S. D., Landon-Cardinal, O., Poulin, D., & Liu, Y.-K. (2010) · Nature Communications · doi:10.1038/ncomms1147 · Cited by 677 · see citing works
Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications
Reid, M. D., Drummond, P. D., Bowen, W. P., Cavalcanti, E. G., Lam, P. K., Bachor, H., Andersen, U. L., & Leuchs, G. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.1727 · Cited by 650 · see citing works
Quantum State Reconstruction of the Single-Photon Fock State
Lvovsky, A. I., Hansen, H., Aichele, T., Benson, O. J., Mlynek, J., & Schiller, S. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.050402 · Cited by 641 · see citing works
Nobel Lecture: Controlling photons in a box and exploring the quantum to classical boundary
Haroche, S. (2013) · Reviews of Modern Physics · doi:10.1103/revmodphys.85.1083 · Cited by 623 · see citing works
Experimental Determination of the Motional Quantum State of a Trapped Atom
Leibfried, D., Meekhof, D. M., King, B. E., Monroe, C., Itano, W. M., & Wineland, D. J. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.4281 · Cited by 688 · see citing works
Reconstruction of non-classical cavity field states with snapshots of their decoherence
Deléglise, S., Dotsenko, I., Sayrin, C., Bernu, J., Brune, M., Raimond, J. M., & Haroche, S. (2008) · Nature · doi:10.1038/nature07288 · Cited by 613 · see citing works
Measurement of the quantum states of squeezed light
Breitenbach, G., Schiller, S., & Mlynek, J. (1997) · Nature · doi:10.1038/387471a0 · Cited by 546 · see citing works
Nonmaximally Entangled States: Production, Characterization, and Utilization
White, A. G., James, D. F. V., Eberhard, P. H., & Kwiat, P. G. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.3103 · Cited by 511 · see citing works
Preparation of nonclassical states in cavities with a moving mirror
Bose, S., Jacobs, K. A., & Knight, P. L. (1997) · Physical Review A · doi:10.1103/physreva.56.4175 · Cited by 497 · see citing works
Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits
Nation, P. D., Johansson, J. R., Blencowe, M. P., & Nori, F. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1 · Cited by 492 · see citing works
Filho, R. L. D. M., & Vogel, W. (1996) · Physical Review A · doi:10.1103/physreva.54.4560 · Cited by 476 · see citing works
Interference of light and Bell's theorem
Белинский, А. В., & Клышко, Д. Н. (1993) · Physics-Uspekhi · doi:10.1070/pu1993v036n08abeh002299 · Cited by 464 · see citing works
Generating single microwave photons in a circuit
Houck, A., Schuster, D., Gambetta, J., Schreier, J. A., Johnson, B., Chow, J. M., Frunzio, L., Majer, J., Devoret, M., Girvin, S. M., et al. (2007) · Nature · doi:10.1038/nature06126 · Cited by 447 · see citing works
Bengtsson, I., & Życzkowski, K. (2006) · doi:10.2277/0521814510 · Cited by 502 · see citing works
Unknown quantum states: The quantum de Finetti representation
Caves, C. M., Fuchs, C. A., & Schack, R. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1494475 · Cited by 427 · see citing works
Symplectic tomography as classical approach to quantum systems
Mancini, S., Man'ko, V. I., & Tombesi, P. (1996) · Physics Letters A · doi:10.1016/0375-9601(96)00107-7 · Cited by 435 · see citing works
Unraveling hadron structure with generalized parton distributions
Belitsky, A. V. (2016) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 421 · see citing works
Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence
Parkins, A. S., Marte, P., Zoller, P., & Kimble, H. J. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.3095 · Cited by 396 · see citing works
Method for Direct Measurement of the Wigner Function in Cavity QED and Ion Traps
Lutterbach, L. G., & Davidovich, L. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.2547 · Cited by 395 · see citing works
Discrete phase space based on finite fields
Gibbons, K. S., Hoffman, M. J., & Wootters, W. K. (2004) · Physical Review A · doi:10.1103/physreva.70.062101 · Cited by 386 · see citing works
Quantum Memory for Squeezed Light
Appel, J., Figueroa, E. V., Korystov, D., Lobino, M., & Lvovsky, A. I. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.093602 · Cited by 383 · see citing works
Tomography of quantum detectors
Lundeen, J. S., Feito, A., Coldenstrodt-Ronge, H. B., Pregnell, K. L., Silberhorn, C., Ralph, T. C., Eisert, J., Plenio, M. B., & Walmsley, I. A. (2008) · Nature Physics · doi:10.1038/nphys1133 · Cited by 350 · see citing works
Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators
Flammia, S. T., Gross, D., Liu, Y.-K., & Eisert, J. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/9/095022 · Cited by 356 · see citing works
Nonlocality of the Einstein-Podolsky-Rosen state in the Wigner representation
Banaszek, K., & Wódkiewicz, K. (1998) · Physical Review A · doi:10.1103/physreva.58.4345 · Cited by 357 · see citing works
Complex wave-field reconstruction using phase-space tomography
Raymer, M. G., Beck, M., & McAlister, D. F. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.1137 · Cited by 349 · see citing works
Self-citationFan, H.-Y., Lu, H.-L., & Fan, Y. (2005) · Annals of Physics · doi:10.1016/j.aop.2005.09.011 · Cited by 346 · see citing works
Direct Measurement of the Wigner Function of a One-Photon Fock State in a Cavity
Bertet, P., Auffèves, A., Maioli, P., Osnaghi, S., Meunier, T., Brune, M., Raimond, J. M., & Haroche, S. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.200402 · Cited by 344 · see citing works
Maximum-likelihood estimation of the density matrix
Banaszek, K., D’Ariano, G. M., Paris, M. G. A., & Sacchi, M. F. (1999) · Physical Review A · doi:10.1103/physreva.61.010304 · Cited by 342 · see citing works
Direct Probing of Quantum Phase Space by Photon Counting
Banaszek, K., & Wódkiewicz, K. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.4344 · Cited by 340 · see citing works
Testing Quantum Nonlocality in Phase Space
Banaszek, K., & Wódkiewicz, K. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.2009 · Cited by 338 · see citing works
Photon Temporal Modes: A Complete Framework for Quantum Information Science
Brecht, B., Reddy, D. V., Silberhorn, C., & Raymer, M. G. (2015) · Physical Review X · doi:10.1103/physrevx.5.041017 · Cited by 341 · see citing works
Self-citationOptical State Truncation by Projection Synthesis
Pegg, D. T., Phillips, L. S., & Barnett, S. M. (1998) · Physical Review Letters · doi:10.1103/physrevlett.81.1604 · Cited by 322 · see citing works
Operator ordering in quantum optics theory and the development of Dirac s symbolic method
Fan, H.-Y. (2003) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/5/4/201 · Cited by 327 · see citing works
Symplectic tomography as classical approach to quantum systems
MANCINI, S., TOMBESI, P., & I, M. V. (1996) · CERN Document Server (European Organization for Nuclear Research) · Cited by 326 · see citing works
Quark imaging in the proton via quantum phase-space distributions
Belitsky, A. V., Ji, X., & Yuan, F. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.69.074014 · Cited by 325 · see citing works
Dunn, T. J., Walmsley, I. A., & Mukamel, S. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.884 · Cited by 324 · see citing works
Quantum systems with finite Hilbert space
Vourdas, A. (2004) · Reports on Progress in Physics · doi:10.1088/0034-4885/67/3/r03 · Cited by 321 · see citing works
Multiphoton quantum optics and quantum state engineering
Dell’Anno, F., Siena, S. D., & Illuminati, F. (2006) · Physics Reports · doi:10.1016/j.physrep.2006.01.004 · Cited by 306 · see citing works
Procedure for Direct Measurement of General Quantum States Using Weak Measurement
Lundeen, J. S., & Bamber, C. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.070402 · Cited by 309 · see citing works
Iterative maximum-likelihood reconstruction in quantum homodyne tomography
Lvovsky, A. I. (2004) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/6/6/014 · Cited by 304 · see citing works
The quantum phase problem: a critical review
Lynch, R. (1995) · Physics Reports · doi:10.1016/0370-1573(94)00095-k · Cited by 303 · see citing works
Unbalanced homodyning for quantum state measurements
Wallentowitz, S., & Vogel, W. (1996) · Physical Review A · doi:10.1103/physreva.53.4528 · Cited by 301 · see citing works
Optimal filtering in fractional Fourier domains
Kutay, M. A., Özaktaş, H. M., Ankan, O., & Onural, L. (1997) · IEEE Transactions on Signal Processing · doi:10.1109/78.575688 · Cited by 299 · see citing works
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Reports on Progress in Physics · doi:10.1088/0034-4885/78/4/042001 · Cited by 310 · see citing works
Measurement of the Wigner function of an ensemble of helium atoms
Kurtsiefer, C., Pfau, T., & Mlynek, J. (1997) · Nature · doi:10.1038/386150a0 · Cited by 280 · see citing works
Vanner, M. R., Pikovski, I., Cole, G. D., Kim, M. S., Brukner, Č., Hammerer, K., Milburn, G. J., & Aspelmeyer, M. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1105098108 · Cited by 279 · see citing works
Positive distribution description for spin states
Dodonov, V. V., & Man’ko, V. I. (1997) · Physics Letters A · doi:10.1016/s0375-9601(97)00199-0 · Cited by 275 · see citing works
State estimation for large ensembles
Gill, R. D., & Massar, S. (2000) · Physical Review A · doi:10.1103/physreva.61.042312 · Cited by 273 · see citing works
An introduction to the tomographic picture of quantum mechanics
Ibort, A., Man’ko, V. I., Marmo, G., Simoni, A., & Ventriglia, F. (2009) · Physica Scripta · doi:10.1088/0031-8949/79/06/065013 · Cited by 259 · see citing works
Open-system dynamics of entanglement:a key issues review
Aolita, L., de Melo, F., & Davidovich, L. (2015) · Refubium (Universitätsbibliothek der Freien Universität Berlin) · doi:10.17169/refubium-20820 · Cited by 258 · see citing works
Direct sampling of electric-field vacuum fluctuations
Riek, C., Seletskiy, D. V., Moskalenko, A. S., Schmidt, J. F., Krauspe, P., Eckart, S., Eggert, S., Burkard, G., & Leitenstorfer, A. (2015) · Science · doi:10.1126/science.aac9788 · Cited by 257 · see citing works
Quantum-State Tomography and Discrete Wigner Function
Leonhardt, U. (1995) · Physical Review Letters · doi:10.1103/physrevlett.74.4101 · Cited by 276 · see citing works
Quantum-state control in optical lattices
Deutsch, I., & Jessen, P. (1998) · Physical Review A · doi:10.1103/physreva.57.1972 · Cited by 242 · see citing works
Quark Wigner distributions and orbital angular momentum
Lorcé, C., & Pasquini, B. (2011) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.84.014015 · Cited by 243 · see citing works
Man’ko, V. I., & Man’ko, O. V. (1997) · Journal of Experimental and Theoretical Physics · doi:10.1134/1.558326 · Cited by 240 · see citing works
Schiller, S., Breitenbach, G., Pereira, S. F., Müller, T., & Mlynek, J. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.2933 · Cited by 231 · see citing works
D’Ariano, G. M., Paris, M. G. A., & Sacchi, M. F. (2003) · Advances in imaging and electron physics · doi:10.1016/s1076-5670(03)80065-4 · Cited by 227 · see citing works
Brif, C., & Mann, A. (1999) · Physical Review A · doi:10.1103/physreva.59.971 · Cited by 223 · see citing works
Electron quantum optics in ballistic chiral conductors
Bocquillon, E., Freulon, V., Parmentier, F. D., Berroir, J., Plaçais, B., Wahl, C., Rech, J., Jonckheere, T., Martin, T., Grenier, C., et al. (2013) · Annalen der Physik · doi:10.1002/andp.201300181 · Cited by 210 · see citing works
Detection of the density matrix through optical homodyne tomography without filtered back projection
D’Ariano, G. M., Macchiavello, C., & Paris, M. G. A. (1994) · Physical Review A · doi:10.1103/physreva.50.4298 · Cited by 218 · see citing works
Quantum-Optical Catalysis: Generating Nonclassical States of Light by Means of Linear Optics
Lvovsky, A. I., & Mlynek, J. (2002) · Physical Review Letters · doi:10.1103/physrevlett.88.250401 · Cited by 215 · see citing works
Quantum tomography of an electron
Jullien, T., Roulleau, P., Roche, B., Cavanna, A., Jin, Y., & Glattli, D. C. (2014) · Nature · doi:10.1038/nature13821 · Cited by 214 · see citing works
Discrete Wigner function and quantum-state tomography
Leonhardt, U. (1996) · Physical Review A · doi:10.1103/physreva.53.2998 · Cited by 214 · see citing works
Pulsed squeezed light: Simultaneous squeezing of multiple modes
Wasilewski, W., Lvovsky, A. I., Banaszek, K., & Radzewicz, C. (2006) · Physical Review A · doi:10.1103/physreva.73.063819 · Cited by 212 · see citing works
Nonclassical effects in phase space
Lütkenhaus, N., & Barnett, S. M. (1995) · Physical Review A · doi:10.1103/physreva.51.3340 · Cited by 208 · see citing works
Quantum State Tomography of an Itinerant Squeezed Microwave Field
Mallet, F., Castellanos-Beltran, M. A., Ku, H. S., Glancy, S., Knill, E. H., Irwin, K. D., Hilton, G. C., Vale, L. R., & Lehnert, K. W. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.220502 · Cited by 204 · see citing works
Reliable Quantum State Tomography
Christandl, M., & Renner, R. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.120403 · Cited by 200 · see citing works
Experimental State Tomography of Itinerant Single Microwave Photons
Eichler, C., Bozyigit, D., Lang, C., Steffen, L., Fink, J. M., & Wallraff, A. J. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.220503 · Cited by 200 · see citing works
Impossibility of Measuring the Wave Function of a Single Quantum System
D’Ariano, G. M., & Yuen, H. P. (1996) · Physical Review Letters · doi:10.1103/physrevlett.76.2832 · Cited by 200 · see citing works
Realistic optical homodyne measurements and quasiprobability distributions
Leonhardt, U., & Paul, H. (1993) · Physical Review A · doi:10.1103/physreva.48.4598 · Cited by 200 · see citing works
On Quantum Statistical Inference
Barndorff-Nielsen, O. E., Gill, R. D., & Jupp, P. E. (2003) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/1467-9868.00415 · Cited by 197 · see citing works
Continuous-variable quantum key distribution system: Past, present, and future
Zhang, Y., Bian, Y., Li, Z., Yu, S., & Guo, H. M. (2024) · Applied Physics Reviews · doi:10.1063/5.0179566 · Cited by 203 · see citing works
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
Bocko, M. F., & Onofrio, R. (1996) · Reviews of Modern Physics · doi:10.1103/revmodphys.68.755 · Cited by 194 · see citing works
Wigner function and probability distribution for shifted and squeezed quadratures
Mancini, S., Man’ko, V. I., & Tombesi, P. (1995) · Quantum and Semiclassical Optics Journal of the European Optical Society Part B · doi:10.1088/1355-5111/7/4/016 · Cited by 195 · see citing works
Direct measurement of the Wigner function by photon counting
Banaszek, K., Radzewicz, C., Wódkiewicz, K., & Krasiński, J. S. (1999) · Physical Review A · doi:10.1103/physreva.60.674 · Cited by 193 · see citing works
Quantum-state mapping between multilevel atoms and cavity light fields
Parkins, A. S., Marte, P., Zoller, P., Carnal, O., & Kimble, H. J. (1995) · Physical Review A · doi:10.1103/physreva.51.1578 · Cited by 192 · see citing works
Measurement of number-phase uncertainty relations of optical fields
Smithey, D. T., Beck, M., Cooper, J., & Raymer, M. G. (1993) · Physical Review A · doi:10.1103/physreva.48.3159 · Cited by 190 · see citing works
Self-citationQuantum states in probability representation and tomography
Man’ko, O. V., & Man’ko, V. I. (1997) · Journal of Russian Laser Research · doi:10.1007/bf02559668 · Cited by 190 · see citing works
Measuring the quantum state of light
Leonhardt, U., & Paul, H. (1995) · Progress in Quantum Electronics · doi:10.1016/0079-6727(94)00007-l · Cited by 189 · see citing works
Homodyne detection of the density matrix of the radiation field
D’Ariano, G. M., Leonhardt, U., & Paul, H. (1995) · Physical Review A · doi:10.1103/physreva.52.r1801 · Cited by 189 · see citing works
Diluted maximum-likelihood algorithm for quantum tomography
Řeháček, J., Hradil, Z., Knill, E. H., & Lvovsky, A. I. (2007) · Physical Review A · doi:10.1103/physreva.75.042108 · Cited by 187 · see citing works
Continuous‐variable quantum information processing
Andersen, U. L., Leuchs, G., & Silberhorn, C. (2009) · Laser & Photonics Review · doi:10.1002/lpor.200910010 · Cited by 187 · see citing works
DEFORMATION QUANTIZATION: QUANTUM MECHANICS LIVES AND WORKS IN PHASE-SPACE
ZACHOS, C. K. (2002) · International Journal of Modern Physics A · doi:10.1142/s0217751x02006079 · Cited by 182 · see citing works
Laurat, J., Keller, G., Huguenin, J. A. O., Fabre, C., Coudreau, T., Serafini, A., Adesso, G., & Illuminati, F. (2005) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/7/12/021 · Cited by 179 · see citing works
Paternostro, M., Kim, M. S., & Byoung Seung, H. A. M. (2003) · Physical Review A · doi:10.1103/physreva.67.023811 · Cited by 177 · see citing works
Quantum state transfer between motion and light
Parkins, A. S., & Kimble, H. J. (1999) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/1/4/323 · Cited by 179 · see citing works
- Authors
- Smithey, D. T., Beck, M., Raymer, M. G., & Faridani, A.
- Affiliations
- University of Oregon (US)
- Oregon State University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1993-03-01
- Volume
- 70
- Issue
- 9
- Pages
- 1244-1247
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2059108078
- Cited by
- 1,538
- References
- 20
- Citations by year
- 2026: 29 · 2025: 27 · 2024: 52 · 2023: 29 · 2022: 42 · 2021: 40 · 2020: 57 · 2019: 76 · 2018: 42 · 2017: 35 · 2016: 38 · 2015: 42 · 2014: 46 · 2013: 51 · 2012: 65
- FWCI
- 70.39
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- optical homodyne tomography, Wigner function, density matrix, squeezed states, vacuum state, quantum state characterization, light mode
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
