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Entangled microwave signal is the reflection of the quantum characteristics of electromagnetic field in a GHz frequency range. Its generation is mainly dependent on superconducting circuits. Owing to the fact that there is no canonical expression to describe the format of entangled microwave signals, two expressional methods are presented on the basis of analyzing the characteristics of entangled microwave signals. One is in quantum frame, and the other is in classical frame. In quantum frame, we express entangled microwave signals in two-mode squeezed vacuum state. According to input-output relationship and parametric amplifier property in the generating process of entangled microwave signals, we describe the characteristics by two-mode squeezing operator and quantum Langevin equation. In the representation of photon number and Wigner function, we analyze the photon number distribution and the quadrature components' distribution of two-mode squeezed vacuum state, which shows the entangled two-photon correlation and the non-localized positive (negative) correlation of quadrature components. These are consistent with the characteristics of entangled microwave signals. Therefore, the results demonstrate that the entangled microwave signals can be expressed by two-mode squeezed vacuum state. In classical frame, we express entangled microwave signals in correlated random signals approximately. According to the relationship between quadrature components and the quantization of electromagnetic field, we construct the relation among electric-field intensity, input angular frequency, and squeezed parameter. The random number with Gaussian distribution is used as an input state to implement the simulation analysis. We illustrate the waveforms of entangled microwave signals after measurement and the extracted quadrature component waveform varying with time. The simulation results are consistent with the measurement results. These results show that the classical expression can reflect the one-path randomicity and two-path correlativity, which are the intrinsic characteristics of entangled microwave signals. Therefore, it is rational to express entangled microwave signals in correlated random signals. These two expressions properly reflect the continuous variable entanglement characteristics of entangled microwave signals. The expression of two-mode squeezed vacuum state is complete. Plenty of parameters that represent quantum information can be calculated by two-mode squeezed vacuum state, such as entanglement degree or the power of noise fluctuation. The merit of the expression of correlated random signals is intuitive, which makes it easier to understand the nonclassical characteristics of entangled microwave signals.
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Keywords:
- entangled microwave signals /
- positive and negative correlation /
- two-mode squeezed vacuum state /
- correlated random signals
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[12] Dambach S, Kubala B, Ankerhold J 2017 New J. Phys. 19 023027
[13] Mallet F, Castellanos-Beltran M A, Ku H S, Glancy S, Knill E, Irwin K D, Hilton G C, Vale L R, Lehnert K W 2011 Phys. Rev. Lett. 106 220502
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[18] Pillet J D, Flurin E, Mallet F, Huard B 2015 Appl. Phys. Lett. 106 083509
[19] Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015 Phys. Rev. Lett. 114 090503
[20] Zhao Y J, Wang C Q, Zhu X B, Liu Y X 2016 Sci. Rep. 6 23646
[21] Khrennikov A, Ohya M, Watanab N 2010 J. Russ. Laser Res. 31 462
[22] Bharath H M, Ravishankar V 2014 Phys. Rev. A 89 062110
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[1] Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865
[2] Raimond J, Brune M, Haroche S 2001 Rev. Mod. Phys. 73 565
[3] Braunstein S L, Loock P 2005 Rev. Mod. Phys. 77 513
[4] Gisin N, Thew R T 2010 Electron. Lett. 46 965
[5] Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (New York: Cambridge University Press)
[6] Benjamin H 2016 C. R. Phys. 17 679
[7] Yamamoto T, Inomata K, Watanabe M, Matsuba K, Miyazaki T, Oliver W D, Nakamura Y, Tsai J S 2008 Appl. Phys. Lett. 93 042510
[8] Zhong L, Menzel E P, Candia R D, Eder P, Ihmig M, Baust A, Haeberlein M, Hoffmann E, Inomata K, Yamamoto T, Nakamura Y, Solano E, Deppe F, Marx A, Gross R 2013 New J. Phys. 15 125013
[9] Eichler C, Bozyigit D, Lang C, Baur M, Steffen L, Fink J M, Filipp S, Wallraff A 2011 Phys. Rev. Lett. 107 113601
[10] Menzel E P, Candia R D, Deppe F, Zhong L, Ihmig M, Haeberlein M, Baust A, Hoffmann E, Ballester D, Inomata K, Yamamoto T, Nakamura Y, Solano E, Marx A, Gross R 2012 Phys. Rev. Lett. 109 250502
[11] Flurin E, Roch N, Mallet F, Devoret M H, Huard B 2012 Phys. Rev. Lett. 109 183901
[12] Dambach S, Kubala B, Ankerhold J 2017 New J. Phys. 19 023027
[13] Mallet F, Castellanos-Beltran M A, Ku H S, Glancy S, Knill E, Irwin K D, Hilton G C, Vale L R, Lehnert K W 2011 Phys. Rev. Lett. 106 220502
[14] Bergeal N, Schackert F, Metcalfe M, Vijay R, Manucharyan V E, Frunzio L, Prober D E, Schoelkopf R J, Girvin S M, Devoret M H 2010 Nature 465 64
[15] Abdo B, Kamal A, Devoret M H 2013 Phys. Rev. B 87 014508
[16] Zhou X, Schmitt V, Bertet P, Vion D, Wustmann W, Shumeiko V, Esteve D 2014 Phys. Rev. B 89 214517
[17] Mutus J Y, White T C, Barends R, Chen Y, Chen Z, Chiaro B, Dunsworth A, Jeffrey E, Kelly J, Megrant A, Neill C, O'Malley P J J, Roushan P, Sank D, Vainsencher A, Wenner J, Sundqvist K M, Cleland A N, Martinis John M 2014 Appl. Phys. Lett. 104 263513
[18] Pillet J D, Flurin E, Mallet F, Huard B 2015 Appl. Phys. Lett. 106 083509
[19] Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015 Phys. Rev. Lett. 114 090503
[20] Zhao Y J, Wang C Q, Zhu X B, Liu Y X 2016 Sci. Rep. 6 23646
[21] Khrennikov A, Ohya M, Watanab N 2010 J. Russ. Laser Res. 31 462
[22] Bharath H M, Ravishankar V 2014 Phys. Rev. A 89 062110
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