메뉴 건너뛰기




Volumn 11, Issue 3, 2012, Pages 853-872

A measure of non-Gaussianity for quantum states

Author keywords

Non Gaussianity measure; Photon added thermal states; Q function; Quasiprobability; Wehrl entropy

Indexed keywords

GAUSSIANS; NONGAUSSIANITY; OSCILLATOR MODES; PHASE SPACES; Q-FUNCTIONS; QUANTUM STATE; QUASIPROBABILITY; THERMAL STATE;

EID: 84861092245     PISSN: 15700755     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11128-011-0314-2     Document Type: Article
Times cited : (74)

References (49)
  • 2
    • 27144459059 scopus 로고    scopus 로고
    • Quantum information with continuous variables
    • Braunstein, S.L., van Loock, P.: Quantum information with continuous variables. Rev. Mod. Phys. 77, 531 (2005)
    • (2005) Rev. Mod. Phys. , vol.77 , pp. 531
    • Braunstein, S.L.1    Van Loock, P.2
  • 3
    • 34547491739 scopus 로고    scopus 로고
    • Entanglement in continuous-variable systems: Recent advances and current perspectives
    • Adesso, G., Illuminati, F.: Entanglement in continuous-variable systems: recent advances and current perspectives. J. Phys. A Math. Theor. 40, 7821 (2007)
    • (2007) J. Phys. A Math. Theor. , vol.40 , pp. 7821
    • Adesso, G.1    Illuminati, F.2
  • 4
    • 0000588867 scopus 로고    scopus 로고
    • Peres-Horodecki separability criterion for continuous variable systems
    • Simon, R.: Peres-Horodecki separability criterion for continuous variable systems. Phys. Rev. Lett. 84, 2726 (2000)
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 2726
    • Simon, R.1
  • 5
    • 84861098357 scopus 로고    scopus 로고
    • Separability criterion for Gaussian states
    • Braunstein, S.L., Pati, A.K. (eds.) Kluwer, Dordrecht
    • Simon, R.: Separability criterion for Gaussian states. In: Braunstein, S.L., Pati, A.K. (eds.) Quantum Information with Continuous Variables, Kluwer, Dordrecht (2001)
    • (2001) Quantum Information with Continuous Variables
    • Simon, R.1
  • 6
    • 4244042893 scopus 로고
    • Gaussian-Wigner distributions in quantum mechanics and optics
    • Simon, R., Sudarshan, E.C.G., Mukunda, N.: Gaussian-Wigner distributions in quantum mechanics and optics. Phys. Rev. A 36, 3868 (1987)
    • (1987) Phys. Rev. A , vol.36 , pp. 3868
    • Simon, R.1    Sudarshan, E.C.G.2    Mukunda, N.3
  • 8
    • 4243059985 scopus 로고
    • Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
    • Bennett, C., Brasasard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 1895
    • Bennett, C.1    Brasasard, G.2    Crepeau, C.3    Jozsa, R.4    Peres, A.5    Wootters, W.K.6
  • 10
    • 27144502413 scopus 로고    scopus 로고
    • Computable measure of nonclassicality for light
    • Asbóth, J.K., Calsamiglia, J., Ritsch, H.: Computable measure of nonclassicality for light. Phys. Rev. Lett. 94, 173602 (2005)
    • (2005) Phys. Rev. Lett. , vol.94 , pp. 173602
    • Asbóth, J.K.1    Calsamiglia, J.2    Ritsch, H.3
  • 11
    • 0002367030 scopus 로고    scopus 로고
    • Observable signs of nonclassical light
    • Klyshko, D.N.: Observable signs of nonclassical light. Phys. Lett. A 213, 7 (1996)
    • (1996) Phys. Lett. A , vol.213 , pp. 7
    • Klyshko, D.N.1
  • 12
    • 2342541032 scopus 로고    scopus 로고
    • Direct observation of nonclassical photon statistics in parametric down-conversion
    • Waks, E., Diamanti, E., Sanders, B.C., Bartlett, S.D., Yamamoto, Y.: Direct observation of nonclassical photon statistics in parametric down-conversion. Phys. Rev. Lett. 92, 113602 (2004)
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 113602
    • Waks, E.1    Diamanti, E.2    Sanders, B.C.3    Bartlett, S.D.4    Yamamoto, Y.5
  • 13
    • 33645064569 scopus 로고    scopus 로고
    • Highly nonclassical photon statistics in parametric down-conversion
    • Waks, E., Sanders, B.C., Diamanti, E., Yamamoto, Y.: Highly nonclassical photon statistics in parametric down-conversion. Phys. Rev. A 73, 033814 (2006)
    • (2006) Phys. Rev. A , vol.73 , pp. 033814
    • Waks, E.1    Sanders, B.C.2    Diamanti, E.3    Yamamoto, Y.4
  • 16
    • 33744811141 scopus 로고    scopus 로고
    • Non-Gaussian states from continuous-wave Gaussian light sources
    • Mølmer, K.: Non-Gaussian states from continuous-wave Gaussian light sources. Phys. Rev. A 73, 063804 (2006)
    • (2006) Phys. Rev. A , vol.73 , pp. 063804
    • Mølmer, K.1
  • 17
    • 0001459897 scopus 로고
    • Moment hierarchies and cumulants in quantum optics
    • Schack, R., Schenzle, A.: Moment hierarchies and cumulants in quantum optics. Phys. Rev. A 41, 3847 (1990)
    • (1990) Phys. Rev. A , vol.41 , pp. 3847
    • Schack, R.1    Schenzle, A.2
  • 18
    • 46249088961 scopus 로고    scopus 로고
    • Highly non-Gaussian states created via cross-Kerr nonlinearity
    • Tyc, T., Korolkova, N.: Highly non-Gaussian states created via cross-Kerr nonlinearity. New J. Phys. 10, 023041 (2008)
    • (2008) New J. Phys. , vol.10 , pp. 023041
    • Tyc, T.1    Korolkova, N.2
  • 19
    • 34547682223 scopus 로고    scopus 로고
    • Continuous-variable quantum teleportation with non-Gaussian resources
    • Dell' Anno, F., De Siena, S., Albano, L., Illuminati, F.: Continuous-variable quantum teleportation with non-Gaussian resources. Phys. Rev. A 76, 022301 (2007)
    • (2007) Phys. Rev. A , vol.76 , pp. 022301
    • Dell Anno, F.1    De Siena, S.2    Albano, L.3    Illuminati, F.4
  • 20
    • 45749107541 scopus 로고    scopus 로고
    • Continuous variable quantum teleportation with sculptured and noisy non-Gaussian resources
    • Dell' Anno, F., De Siena, S., Albano, L., Illuminati, F.: Continuous variable quantum teleportation with sculptured and noisy non-Gaussian resources. Eur. Phys. J. ST 160, 115 (2008)
    • (2008) Eur. Phys. J. ST , vol.160 , pp. 115
    • Dell Anno, F.1    De Siena, S.2    Albano, L.3    Illuminati, F.4
  • 21
    • 80053115862 scopus 로고    scopus 로고
    • Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments
    • Sabapathy, K.K., Ivan, J.S., Simon, R.: Robustness of non-Gaussian entanglement against noisy amplifier and attenuator environments. Phys. Rev. Lett. 107, 130501 (2011)
    • (2011) Phys. Rev. Lett. , vol.107 , pp. 130501
    • Sabapathy, K.K.1    Ivan, J.S.2    Simon, R.3
  • 22
    • 35548993718 scopus 로고    scopus 로고
    • Measure of the non-Gaussian character of a quantum state
    • Genoni, M.G., Paris, M.G.A., Banaszek, K.: Measure of the non-Gaussian character of a quantum state. Phys. Rev. A 76, 042327 (2007)
    • (2007) Phys. Rev. A , vol.76 , pp. 042327
    • Genoni, M.G.1    Paris, M.G.A.2    Banaszek, K.3
  • 23
    • 58149115024 scopus 로고    scopus 로고
    • Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
    • Genoni, M.G., Paris, M.G.A., Banaszek, K.: Quantifying the non-Gaussian character of a quantum state by quantum relative entropy. Phys. Rev. A 78, 060303 (2008)
    • (2008) Phys. Rev. A , vol.78 , pp. 060303
    • Genoni, M.G.1    Paris, M.G.A.2    Banaszek, K.3
  • 24
    • 84861098358 scopus 로고    scopus 로고
    • ar-Xiv:0812.2800. The contents of the present paper have been around in unpublished preprint form since 2008, and have influenced several authors. The new input since then has been our realization that scaling on the Q function is indeed a physical process [28]
    • Solomon Ivan, J., Kumar, M.S., Simon, R.: A measure of non-Gaussianity for quantum states. ar-Xiv:0812.2800. The contents of the present paper have been around in unpublished preprint form since 2008, and have influenced several authors. The new input since then has been our realization that scaling on the Q function is indeed a physical process [28]
    • A Measure of Non-Gaussianity for Quantum States
    • Solomon Ivan, J.1    Kumar, M.S.2    Simon, R.3
  • 26
    • 0000263797 scopus 로고
    • Projection pursuit
    • Huber, P.J.: Projection pursuit. Annal. Stat. 13(2), 435-475 (1985)
    • (1985) Annal. Stat. , vol.13 , Issue.2 , pp. 435-475
    • Huber, P.J.1
  • 27
    • 18344373564 scopus 로고
    • Ordered expansions in boson amplitude operators
    • Cahill, K.E., Glauber, R.J.: Ordered expansions in boson amplitude operators. Phys. Rev. 177, 1857 (1969)
    • (1969) Phys. Rev. , vol.177 , pp. 1857
    • Cahill, K.E.1    Glauber, R.J.2
  • 28
    • 80053616566 scopus 로고    scopus 로고
    • Operator-sum representation for bosonic Gaussian channels
    • Solomon Ivan, J., Sabapathy, K.K., Simon, R.: Operator-sum representation for bosonic Gaussian channels. Phys. Rev. A 84, 042311 (2011)
    • (2011) Phys. Rev. A , vol.84 , pp. 042311
    • Solomon Ivan, J.1    Sabapathy, K.K.2    Simon, R.3
  • 29
    • 77951762081 scopus 로고    scopus 로고
    • Amplification of maximally-path-entangled number states
    • Agarwal, G.S., Chaturvedi, S., Rai, A.: Amplification of maximally-path-entangled number states. Phys. Rev. A 81, 043843 (2010)
    • (2010) Phys. Rev. A , vol.81 , pp. 043843
    • Agarwal, G.S.1    Chaturvedi, S.2    Rai, A.3
  • 30
    • 5444225516 scopus 로고
    • On the relation between classical and quantum-mechanical entropy
    • Wehrl, A.: On the relation between classical and quantum-mechanical entropy. Rep. Math. Phys. 16, 353 (1979)
    • (1979) Rep. Math. Phys. , vol.16 , pp. 353
    • Wehrl, A.1
  • 32
    • 0001253695 scopus 로고
    • Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics
    • Agarwal, G.S., Tara, K.: Nonclassical character of states exhibiting no squeezing or sub-Poissonian statistics. Phys. Rev. A 46, 485 (1992)
    • (1992) Phys. Rev. A , vol.46 , pp. 485
    • Agarwal, G.S.1    Tara, K.2
  • 33
    • 34347357512 scopus 로고    scopus 로고
    • Experimental nonclassicality of single-photon-added thermal light states
    • Zavatta, A., Parigi, V., Bellini, M.: Experimental nonclassicality of single-photon-added thermal light states. Phys. Rev. A 75, 052106 (2007)
    • (2007) Phys. Rev. A , vol.75 , pp. 052106
    • Zavatta, A.1    Parigi, V.2    Bellini, M.3
  • 34
    • 42549120188 scopus 로고    scopus 로고
    • Manipulating thermal light states by the controlled addition and subtraction of single photons
    • Parigi, V., Zavatta, A., Bellini, M.: Manipulating thermal light states by the controlled addition and subtraction of single photons. Laser Phys. Lett. 5, 246 (2008)
    • (2008) Laser Phys. Lett. , vol.5 , pp. 246
    • Parigi, V.1    Zavatta, A.2    Bellini, M.3
  • 35
    • 34848928033 scopus 로고    scopus 로고
    • Probing quantum commutation rules by addition and subtraction of single photons to/from a light field
    • Parigi, V., Zavatta, A., Kim, M.S., Bellini, M.: Probing quantum commutation rules by addition and subtraction of single photons to/from a light field. Science 317, 1890 (2007)
    • (2007) Science , vol.317 , pp. 1890
    • Parigi, V.1    Zavatta, A.2    Kim, M.S.3    Bellini, M.4
  • 36
    • 50249103885 scopus 로고    scopus 로고
    • Experimental determination of a nonclassical Glauber-Sudarshan P function
    • Kiesel, T., Vogel, W., Parigi, V., Zavatta, A., Bellini, M.: Experimental determination of a nonclassical Glauber-Sudarshan P function. Phys. Rev. A 78, 021804 (R) (2008)
    • (2008) Phys. Rev. A , vol.78
    • Kiesel, T.1    Vogel, W.2    Parigi, V.3    Zavatta, A.4    Bellini, M.5
  • 37
    • 21844519694 scopus 로고
    • A recursive formulation of the old problem of obtaining moments from cumulants and vice versa
    • Smith, P.J.: A recursive formulation of the old problem of obtaining moments from cumulants and vice versa. Am. Stat. 49(2), 217-218 (1995)
    • (1995) Am. Stat. , vol.49 , Issue.2 , pp. 217-218
    • Smith, P.J.1
  • 39
    • 34250967320 scopus 로고
    • Sur une propriété de la loi de Gauss
    • Marcinkiewicz, J.: Sur une propriété de la loi de Gauss. Math. Z. 44, 612 (1939)
    • (1939) Math. Z. , vol.44 , pp. 612
    • Marcinkiewicz, J.1
  • 40
    • 0001228874 scopus 로고
    • Some generalizations of the Marcinkiewicz theorem and its implications to certain approximation schemes in many-particle physics
    • Rajagopal, A.K., Sudarshan, E.C.G.: Some generalizations of the Marcinkiewicz theorem and its implications to certain approximation schemes in many-particle physics. Phys. Rev. A 10, 1852 (1974)
    • (1974) Phys. Rev. A , vol.10 , pp. 1852
    • Rajagopal, A.K.1    Sudarshan, E.C.G.2
  • 41
    • 0001218355 scopus 로고
    • When is the wigner quasi-probability density non-negative?
    • Hudson, R.L.: When is the wigner quasi-probability density non-negative?. Rep. Math. Phys. 6, 249 (1974)
    • (1974) Rep. Math. Phys. , vol.6 , pp. 249
    • Hudson, R.L.1
  • 42
    • 5844266551 scopus 로고
    • General properties of entropy
    • Wehrl, A.: General properties of entropy. Rev. Mod. Phys. 50, 221 (1978)
    • (1978) Rev. Mod. Phys. , vol.50 , pp. 221
    • Wehrl, A.1
  • 43
    • 0009242306 scopus 로고
    • Classical entropy of quantum states of light
    • Orłowski, A.: Classical entropy of quantum states of light. Phys. Rev. A 48, 727 (1993)
    • (1993) Phys. Rev. A , vol.48 , pp. 727
    • Orłowski, A.1
  • 44
    • 1942443833 scopus 로고    scopus 로고
    • Wehrl entropy, Lieb conjecture, and entanglement monotones
    • Mintert, F., Zyczkowski, K.: Wehrl entropy, Lieb conjecture, and entanglement monotones. Phys. Rev. A 69, 022317 (2004)
    • (2004) Phys. Rev. A , vol.69 , pp. 022317
    • Mintert, F.1    Zyczkowski, K.2
  • 45
    • 56349150963 scopus 로고    scopus 로고
    • Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals
    • Marchiolli, M.A., Galetti, D.: Generalized squeezing operators, bipartite Wigner functions and entanglement via Wehrl's entropy functionals. Phys. Scr. 78, 045007 (2008)
    • (2008) Phys. Scr. , vol.78 , pp. 045007
    • Marchiolli, M.A.1    Galetti, D.2
  • 46
    • 0002303432 scopus 로고
    • Proof of an entropy conjecture of Wehrl
    • Lieb, E.H.: Proof of an entropy conjecture of Wehrl. Commun. Math. Phys. 62, 35 (1978)
    • (1978) Commun. Math. Phys. , vol.62 , pp. 35
    • Lieb, E.H.1
  • 47
    • 0001679261 scopus 로고
    • Quantum-noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms
    • Simon, R., Mukunda, N., Dutta, B.: Quantum-noise matrix for multimode systems: U(n) invariance, squeezing, and normal forms. Phys. Rev. A 49, 1567 (1994)
    • (1994) Phys. Rev. A , vol.49 , pp. 1567
    • Simon, R.1    Mukunda, N.2    Dutta, B.3
  • 48
    • 78650985566 scopus 로고    scopus 로고
    • Quantifying non-Gaussianity for quantum information
    • Genoni, M.G., Paris, M.G.A.: Quantifying non-Gaussianity for quantum information. Phys. Rev. A 82, 052341 (2010)
    • (2010) Phys. Rev. A , vol.82 , pp. 052341
    • Genoni, M.G.1    Paris, M.G.A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.