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In recent years, the great progress of studying the quantum entanglement has been made. In the field of optics, the great success has been achieved in quantum entanglement theory and technology. Then researchers concentrate on the microwave frequency band whose frequency is lower than that of optical frequency band. The signal in the microwave frequency band has a longer wavelength, and it has the diffraction capability that the optical signal does not possess. Furthermore, it can spread further in complex environments. Now it is possible to experimentally produce squeezed state of microwave signals and spatially separated path-entangled microwave signals. It is an important issue to judge whether the microwave signals received through dual paths are in entanglement state. In this paper, we firstly introduce the method of using squeezed state of microwave and microwave beam splitter to prepare path-entangled microwave signals. Then we use entanglement witness method to detect entanglement. Through constructing the entanglement witness operator in path-entangled microwave signals, the entanglement of path-entangled microwave signals can be effectively detected. We decompose the expression of the continuous variables path-entangled microwave signals into a large number of 2 2 entangled superposition states, deduce an entangled witness operator of path-entangled microwave signals based on the principle of partial transpose criterion and entanglement witnessing, and prove that the entangled witness can be used to detect the path-entangled microwave signals. Finally, we propose a physical verification of path-entangled microwave signal entanglement. The verification can be realized as follows:firstly, we reverse the phase of a received quantum-state microwave signal by utilizing continuous variable controlled phase gate in a range of 0-, then we send two microwave signals into the two input ports of the microwave beam splitter, and we operate coincidence counting of microwave photons on the two output ports after entanglement microwave signals have passed through the microwave splitter. By analyzing the results of the whole process, we have the following conclusions:if the coincidence rate of two input signals is higher than that of non-entangled microwave signals under the same power, signals can be counted as entanglement. The proposed method can detect the entangled microwave signals more efficiently than the conventional methods, such as quantum state reconstruction, and thus reduce the detection and computational complexity. The entanglement of the two microwave quantum state signals can be observed directly by using this method. This paper provides a new idea for detecting the path-entangled microwave signals.
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Keywords:
- path-entangled microwave signals /
- entanglement witness /
- detection of path-entangled microwave signals
[1] Johansson 2012 Physics 5 103120
[2] Herrmann L G, Portier F, Roche P, Levy Yeyati A, Kontos T, Strunk C 2010 Phys. Rev. Lett. 104 026801
[3] Recher P, Sukhorakov E V, Loss D 2001 Phys. Rev. B 63 165314
[4] Ou Z Y, Pereira S F, Kimble H J, Peng K C 1992 Phys. Rev. Lett. 68 3663
[5] Gisin N, Thew R 2007 Nat. Photon. 1 165
[6] Zhou C H, Qian W P 2015 Radar Sci. Tech. 13 457 (in Chinese)[周城宏, 钱卫平 2015 雷达科学与技术 13 457]
[7] Zagoskin A M, Il'ichev E, McMutcheon M W, Young J F, Nori F 2008 Phys. Rev. Lett. 101 253602
[8] Eichler C, Bozyigit D, Lang C, Baur M, Steffen L, Fink J M, Filipp S, Wallraff A 2011 Phys. Rev. Lett. 107 113601
[9] Johansson R, Johansson G, Wilson C M, Delsing P, Nori F 2013 Phys. Rev. A 87 043804
[10] Menzel E P 2013 Ph. D. Dissertation (Munich:Technic University of Munich)
[11] Eder P 2012 Ph. D. Dissertation (Munich:Technic University of Munich)
[12] Roy A, Jiang L, Stone A D, Devoret M 2015 Phys. Rev. Lett. 115 150503
[13] Fedorov K G, Zhong L, Pogorzalek S, Eder P, Fischer M, Goetz J, Xie E, Wulschner F, Inomata K, Yamamoto T, Nakamura Y, Di Candia R, Las Heras U, Sanz M, Solano E, Menzel E P, Deppe F, Marx A, Gross R 2016 Phys. Rev. Lett. 117 020502
[14] Cavalcanti D, Brandao F G S L, Cunha M O T 2005 Phys. Rev. A 72 040303
[15] Horodecki M, Horodecki P, Horodecki R 1996 Phys. Lett. A 223 1
[16] Hyllus P, Ghne O, Bruss D, Lewenstein M 2005 Phys. Rev. A 72 012321
[17] Mariantoni M, Menzel E P, Deppe F, Araque-Caballero M A, Baust A, Niemczyk T, Hoffmann E, Solano E, Marx A, Gross R 2010 Phys. Rev. Lett. 105 133601
[18] Premaratne S P, Wellstood F C, Palmer B S 2017 Nat. Commun. 8 14148
[19] Li X, Wu D W, Wang X, Miao Q, Chen K, Yang C Y 2016 Acta Phys. Sin. 65 114204 (in Chinese)[李响, 吴德伟, 王希, 苗强, 陈坤, 杨春燕 2016 65 114204]
[20] Kim M S, Son W, Buzek V, Knight P L 2002 Phys. Rev. A 65 032323
[21] Hoffmann E, Deppe F, Niemczyk T, Wirth T, Menzel E P 2010 Appl. Phys. Lett. 97 222508
[22] Peres A 1996 Phys. Rev. Lett. 77 1413
[23] Barenco A, Bennett C H, Cleve R, DiVincenzo D P, Margolus N, Shor P, Sleator T, Smolin J, Weinfurter H 1995 Phys. Rev. A 52 3457
[24] Wang Z W, Li J, Huang Y F, Zhang Y S, Ren X F, Zhang P, Guo G C 2006 Phys. Lett. A 372 106
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[1] Johansson 2012 Physics 5 103120
[2] Herrmann L G, Portier F, Roche P, Levy Yeyati A, Kontos T, Strunk C 2010 Phys. Rev. Lett. 104 026801
[3] Recher P, Sukhorakov E V, Loss D 2001 Phys. Rev. B 63 165314
[4] Ou Z Y, Pereira S F, Kimble H J, Peng K C 1992 Phys. Rev. Lett. 68 3663
[5] Gisin N, Thew R 2007 Nat. Photon. 1 165
[6] Zhou C H, Qian W P 2015 Radar Sci. Tech. 13 457 (in Chinese)[周城宏, 钱卫平 2015 雷达科学与技术 13 457]
[7] Zagoskin A M, Il'ichev E, McMutcheon M W, Young J F, Nori F 2008 Phys. Rev. Lett. 101 253602
[8] Eichler C, Bozyigit D, Lang C, Baur M, Steffen L, Fink J M, Filipp S, Wallraff A 2011 Phys. Rev. Lett. 107 113601
[9] Johansson R, Johansson G, Wilson C M, Delsing P, Nori F 2013 Phys. Rev. A 87 043804
[10] Menzel E P 2013 Ph. D. Dissertation (Munich:Technic University of Munich)
[11] Eder P 2012 Ph. D. Dissertation (Munich:Technic University of Munich)
[12] Roy A, Jiang L, Stone A D, Devoret M 2015 Phys. Rev. Lett. 115 150503
[13] Fedorov K G, Zhong L, Pogorzalek S, Eder P, Fischer M, Goetz J, Xie E, Wulschner F, Inomata K, Yamamoto T, Nakamura Y, Di Candia R, Las Heras U, Sanz M, Solano E, Menzel E P, Deppe F, Marx A, Gross R 2016 Phys. Rev. Lett. 117 020502
[14] Cavalcanti D, Brandao F G S L, Cunha M O T 2005 Phys. Rev. A 72 040303
[15] Horodecki M, Horodecki P, Horodecki R 1996 Phys. Lett. A 223 1
[16] Hyllus P, Ghne O, Bruss D, Lewenstein M 2005 Phys. Rev. A 72 012321
[17] Mariantoni M, Menzel E P, Deppe F, Araque-Caballero M A, Baust A, Niemczyk T, Hoffmann E, Solano E, Marx A, Gross R 2010 Phys. Rev. Lett. 105 133601
[18] Premaratne S P, Wellstood F C, Palmer B S 2017 Nat. Commun. 8 14148
[19] Li X, Wu D W, Wang X, Miao Q, Chen K, Yang C Y 2016 Acta Phys. Sin. 65 114204 (in Chinese)[李响, 吴德伟, 王希, 苗强, 陈坤, 杨春燕 2016 65 114204]
[20] Kim M S, Son W, Buzek V, Knight P L 2002 Phys. Rev. A 65 032323
[21] Hoffmann E, Deppe F, Niemczyk T, Wirth T, Menzel E P 2010 Appl. Phys. Lett. 97 222508
[22] Peres A 1996 Phys. Rev. Lett. 77 1413
[23] Barenco A, Bennett C H, Cleve R, DiVincenzo D P, Margolus N, Shor P, Sleator T, Smolin J, Weinfurter H 1995 Phys. Rev. A 52 3457
[24] Wang Z W, Li J, Huang Y F, Zhang Y S, Ren X F, Zhang P, Guo G C 2006 Phys. Lett. A 372 106
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