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针对目前没有合适的方法从产生方来表征纠缠量子微波信号的质量好坏, 提出了一种基于von Neumann熵的双路径纠缠量子微波信号生成质量评估方法. 利用双模压缩真空态描述了纠缠量子微波的信号格式, 给出了光子数与压缩参量之间的函数关系, 以熵评估纠缠态信号所占比例, 分析了熵与压缩参量和光子数之间的关系. 仿真结果表明, 纠缠量子微波信号中的光子数是由压缩参量决定的, 它们之间呈指数平方的规律性变化; 熵随着压缩参量的增大而减小, 但是减小的趋势越来越平缓, 近似呈负指数关系, 熵的极限值约为65%. 研究结果表明, 通过选择合适的压缩参量可以提高纠缠微波信号生成质量以满足实际需要, 因此, 本研究对于生成双路径纠缠量子微波电路参数选择、提高系统可用性提供了方法和依据.
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关键词:
- 纠缠量子微波 /
- von Neumann熵 /
- 压缩参量 /
- 光子数
The entangled state of continuous variables of microwave frequency is an important resource in the field of quantum. In order to apply it to quantum communication protocol and quantum radar, the entanglement between two spatially separated subsystems, namely dual-path entangled quantum microwave is needed. However, for the circuit that generates the entangled quantum microwave, there is no suitable method to indicate whether the quality of the entangled microwave signal is good or not. Aiming at this problem, we put forward a method of evaluating the quality of dual-path entangled quantum microwave signals generated based on von Neumann entropy. The origin of the entangled quantum microwave is that vacuum state signals are transformed into squeezed state signals in driven pump, so in this paper we use a two-mode squeezed vacuum state to describe the formation of dual-path entangled quantum microwave signal, thus providing the function relation between the photon number and the squeezed parameter. In a communication system, the signal-noise ratio is usually used to express the reliability of system. Entropy is a measure of disorder degree in information. If both of them can be made the analogy, the entropy is used to evaluate the proportion of entangled state signals, the quality of original signals will be evaluated and the relationship among the entropy and squeezed parameter and the photon number will be analyzed. The simulation results show that the photon number in the entangled quantum microwave signal is determined by the squeezed parameter, and there is an index change with the square rule between them. Entropy decreases with the increase of squeezed parameter: its minimum value is 0, and its maximum value can be found from 0.9 to 1. The slope of curve is steep near the maximum, which reflects that the influence of squeezed parameter on the degree of entanglement is obvious, and that the range of optimal value choices in squeezed parameter is very narrow. The optimal value of squeezed parameter is dependent on photon number; it increases with the increase of the photon number. Entropy tends to decrease smoothly with the increase of squeezed parameter and it approximately has a negative exponent relation. The photon number in an actual signal is limited, so the limit value of entropy is estimated to be about 65%. The research shows that the quality of the entangled microwave signal can be improved by choosing appropriate squeezed parameter in different circuits that generate dual-path entangled quantum microwave signals for meeting the actual needs. Therefore, the research can provide the method of choosing the parameters of dual-path entangled quantum microwave circuit and improve the availability of system.[1] Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865
[2] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev 47 777
[3] Raimond J, Brune M, Haroche S 2001 Rev. Mod. Phys 73 565
[4] Braunstein S L, Loock P 2005 Rev. Mod. Phys 77 513
[5] Clarke J, Wilhelm F K 2008 Nature. 453 1031
[6] Wu Y L, Deng H, Yu H F, Xue G M, Tian Y, Li J, Chen Y F, Zhao S P, Zheng D N 2013 Chin. Phys. B 22 060309
[7] Nakamura Y, Yamamoto T {2012 IEEE Photon. 5 0701406
[8] Pechal M, Huthmacher L, Eichler C, Zeytinolu S, Abdumalikov A A, Berger J S, Wallraff A, Filipp S {2014 Phys. Rev. X 4 041010
[9] Ware M E 2015 Ph. D. Dissertation (Tuscaloosa: University of Alabama)
[10] Andersen U L, Neergaard-Nielsen J S, van Loock P, Furusawa A 2015 Nature Phys. 11 713
[11] Wallra A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M, Schoelkopf R J 2004 Nature 431 162
[12] Niemczyk T, Deppe F, Huebl H, Menzel E P, Hocke F, Schwarz M J, Garcia-Ripoll J J, Zueco D, Hummer T, Solano E, Marx A, Gross R 2010 Nature Phys 6 772
[13] Lucero E, Barends R, Chen Y, Kelly J, Mariantoni M, Megrant A, Malley P O, Sank D, Vainsencher A, Wenner J, White T, Yin Y, Cleland A N, Martinis J M 2012 Nature Phys. 8 719
[14] Lin Z R, Inomata K, Oliver W D, Koshino K, Nakamura Y, Tsai J S, Yamamoto T 2013 Appl. Phys. Lett. 103 132602
[15] Liu X, Liao Q H, Fang G Y, Wang Y Y, Liu S T 2014 Chin. Phys. B 23 020311
[16] 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
[17] Eichler C, Bozyigit D, Lang C, Baur M, Steffen L, Fink J M, Filipp S, Wallraff A 2011 Phys. Rev. Lett. 107 113601
[18] Pillet J D, Flurin E, Mallet F, Huard B 2015 Appl. Phys. Lett. 106 222603
[19] Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015 Phys. Rev. Lett. 114 090503
[20] Trif M, Simon P {2015 Phys. Rev. B 92 014503
[21] Menzel E P, Candia R D, Deppe F, Eder P, 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
[22] Menzel E P 2013 Ph. D. Dissertation (Munchen: Technische Universitat Munchen)
[23] Flurin E, Roch N, Mallet F, Devoret M H, Huard B 2012 Phys. Rev. Lett. 109 183901
[24] Eder P 2012 Ph. D. Dissertation (Munchen: Technische Universitat Munchen)
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[1] Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865
[2] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev 47 777
[3] Raimond J, Brune M, Haroche S 2001 Rev. Mod. Phys 73 565
[4] Braunstein S L, Loock P 2005 Rev. Mod. Phys 77 513
[5] Clarke J, Wilhelm F K 2008 Nature. 453 1031
[6] Wu Y L, Deng H, Yu H F, Xue G M, Tian Y, Li J, Chen Y F, Zhao S P, Zheng D N 2013 Chin. Phys. B 22 060309
[7] Nakamura Y, Yamamoto T {2012 IEEE Photon. 5 0701406
[8] Pechal M, Huthmacher L, Eichler C, Zeytinolu S, Abdumalikov A A, Berger J S, Wallraff A, Filipp S {2014 Phys. Rev. X 4 041010
[9] Ware M E 2015 Ph. D. Dissertation (Tuscaloosa: University of Alabama)
[10] Andersen U L, Neergaard-Nielsen J S, van Loock P, Furusawa A 2015 Nature Phys. 11 713
[11] Wallra A, Schuster D I, Blais A, Frunzio L, Huang R S, Majer J, Kumar S, Girvin S M, Schoelkopf R J 2004 Nature 431 162
[12] Niemczyk T, Deppe F, Huebl H, Menzel E P, Hocke F, Schwarz M J, Garcia-Ripoll J J, Zueco D, Hummer T, Solano E, Marx A, Gross R 2010 Nature Phys 6 772
[13] Lucero E, Barends R, Chen Y, Kelly J, Mariantoni M, Megrant A, Malley P O, Sank D, Vainsencher A, Wenner J, White T, Yin Y, Cleland A N, Martinis J M 2012 Nature Phys. 8 719
[14] Lin Z R, Inomata K, Oliver W D, Koshino K, Nakamura Y, Tsai J S, Yamamoto T 2013 Appl. Phys. Lett. 103 132602
[15] Liu X, Liao Q H, Fang G Y, Wang Y Y, Liu S T 2014 Chin. Phys. B 23 020311
[16] 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
[17] Eichler C, Bozyigit D, Lang C, Baur M, Steffen L, Fink J M, Filipp S, Wallraff A 2011 Phys. Rev. Lett. 107 113601
[18] Pillet J D, Flurin E, Mallet F, Huard B 2015 Appl. Phys. Lett. 106 222603
[19] Flurin E, Roch N, Pillet J D, Mallet F, Huard B 2015 Phys. Rev. Lett. 114 090503
[20] Trif M, Simon P {2015 Phys. Rev. B 92 014503
[21] Menzel E P, Candia R D, Deppe F, Eder P, 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
[22] Menzel E P 2013 Ph. D. Dissertation (Munchen: Technische Universitat Munchen)
[23] Flurin E, Roch N, Mallet F, Devoret M H, Huard B 2012 Phys. Rev. Lett. 109 183901
[24] Eder P 2012 Ph. D. Dissertation (Munchen: Technische Universitat Munchen)
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