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Erschienen in: Optical and Quantum Electronics 11/2022

01.11.2022

Temporal evolution of quantum correlations under non-Hermitian operation

verfasst von: J. Ramya Parkavi, R. Muthuganesan, V. K. Chandrasekar

Erschienen in: Optical and Quantum Electronics | Ausgabe 11/2022

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Abstract

In this article, we investigate the non-unitary dynamics of a two-qubit system under the action of local non-Hermitian operation from the perspectives of quantum correlations. The correlations are quantified by entanglement, maximal Bell function and different versions of measurement-induced nonlocality (MIN). The analysis is carried out for different initial conditions. We show the advantages of MIN in capturing the nonlocal aspects of the mixed quantum states over the entanglement and Bell function. Interestingly, by proper tuning of the system’s parameter, one can observe the stationary quantum correlations under this non-Hermitian circumstance which have potential applications in quantum information processing and quantum computation.

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Literatur
Zurück zum Zitat Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)ADS Baumgratz, T., Cramer, M., Plenio, M.B.: Quantifying coherence. Phys. Rev. Lett. 113, 140401 (2014)ADS
Zurück zum Zitat Bender, C.M.: Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947 (2007)ADSMathSciNet Bender, C.M.: Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947 (2007)ADSMathSciNet
Zurück zum Zitat Bender, C.M., Boettcher, S.: Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243 (1998)ADSMathSciNetMATH Bender, C.M., Boettcher, S.: Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243 (1998)ADSMathSciNetMATH
Zurück zum Zitat Bender, C.M., Boettcher, S., Meisinger, S.: PT-symmetric quantum mechanics. J. Math. Phys. 40, 2201 (1999)ADSMathSciNetMATH Bender, C.M., Boettcher, S., Meisinger, S.: PT-symmetric quantum mechanics. J. Math. Phys. 40, 2201 (1999)ADSMathSciNetMATH
Zurück zum Zitat Bender, C.M., Brody, D.C., Jones, H.F.: Complex extension of quantum mechanics. Phys. Rev. Lett. 89, 270401 (2002)MathSciNetMATH Bender, C.M., Brody, D.C., Jones, H.F.: Complex extension of quantum mechanics. Phys. Rev. Lett. 89, 270401 (2002)MathSciNetMATH
Zurück zum Zitat Bhuvaneswari, S., Muthuganesan, R., Radha, R.: Spotlighting quantum phase transition in spin-1/2 Ising-Heisenberg diamond chain employing Measurement-Induced Nonlocality. Physica A 573, 125932 (2021)MathSciNetMATH Bhuvaneswari, S., Muthuganesan, R., Radha, R.: Spotlighting quantum phase transition in spin-1/2 Ising-Heisenberg diamond chain employing Measurement-Induced Nonlocality. Physica A 573, 125932 (2021)MathSciNetMATH
Zurück zum Zitat Bian, Z., Xiao, L., Wang, K., Onanga, F.A., Ruzicka, F., Yi, W., Joglekar, Y.N., Xue, P.: Quantum information dynamics in a high-dimensional parity-time-symmetric system. Phys. Rev. A 102, 030201(R) (2020)ADS Bian, Z., Xiao, L., Wang, K., Onanga, F.A., Ruzicka, F., Yi, W., Joglekar, Y.N., Xue, P.: Quantum information dynamics in a high-dimensional parity-time-symmetric system. Phys. Rev. A 102, 030201(R) (2020)ADS
Zurück zum Zitat Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)ADS Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V., Wehner, S.: Bell nonlocality. Rev. Mod. Phys. 86, 419 (2014)ADS
Zurück zum Zitat Dakić, B.V., Brukner, V.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSMATH Dakić, B.V., Brukner, V.: Necessary and sufficient condition for nonzero quantum discord. Phys. Rev. Lett. 105, 190502 (2010)ADSMATH
Zurück zum Zitat Dakic, B., Lipp, Y.O., Ma, X., Ringbauer, M., Kropatschek, S., Barz, S., Paterek, T., Vedral, V., Zeilinger, A., Brukner, C., Walther, P.: Quantum discord as resource for remote state preparation. Nat. Phys. 8, 666 (2012) Dakic, B., Lipp, Y.O., Ma, X., Ringbauer, M., Kropatschek, S., Barz, S., Paterek, T., Vedral, V., Zeilinger, A., Brukner, C., Walther, P.: Quantum discord as resource for remote state preparation. Nat. Phys. 8, 666 (2012)
Zurück zum Zitat Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSMATH Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)ADSMATH
Zurück zum Zitat El-Hadidy, E.G., Farouk, A., Abdel-Aty, M., Ghose, S.: Controlling steady-state entanglement and quantum discord through squeezing angle. Chaos Solitons Fractals 128, 382 (2019)ADSMathSciNetMATH El-Hadidy, E.G., Farouk, A., Abdel-Aty, M., Ghose, S.: Controlling steady-state entanglement and quantum discord through squeezing angle. Chaos Solitons Fractals 128, 382 (2019)ADSMathSciNetMATH
Zurück zum Zitat Feshbach, H., Porter, C.E., Weisskopf, V.F.: Model for nuclear reactions with neutrons. Phys. Rev. 96, 448 (1954)ADSMATH Feshbach, H., Porter, C.E., Weisskopf, V.F.: Model for nuclear reactions with neutrons. Phys. Rev. 96, 448 (1954)ADSMATH
Zurück zum Zitat Girolami, D., Adesso, G.: Observable measure of bipartite quantum correlations. Phys. Rev. Lett. 108, 150403 (2012)ADS Girolami, D., Adesso, G.: Observable measure of bipartite quantum correlations. Phys. Rev. Lett. 108, 150403 (2012)ADS
Zurück zum Zitat Girolami, D., Souza, A.M., Giovannetti, V., Tufarelli, T., Filgueiras, J.G., Sarthour, R.S., Soares-Pinto, D.O., Oliveira, I.S., Adesso, G.: Quantum discord determines the interferometric power of quantum states. Phys. Rev. Lett. 112, 210401 (2014)ADS Girolami, D., Souza, A.M., Giovannetti, V., Tufarelli, T., Filgueiras, J.G., Sarthour, R.S., Soares-Pinto, D.O., Oliveira, I.S., Adesso, G.: Quantum discord determines the interferometric power of quantum states. Phys. Rev. Lett. 112, 210401 (2014)ADS
Zurück zum Zitat Gu, M., Chrzanowski, H.M., Assad, S.M., Symul, T., Modi, K., Ralph, T.C., Vedral, V., Lam, P.K.: Observing the operational significance of discord consumption. Nat. Phys. 8, 671 (2012) Gu, M., Chrzanowski, H.M., Assad, S.M., Symul, T., Modi, K., Ralph, T.C., Vedral, V., Lam, P.K.: Observing the operational significance of discord consumption. Nat. Phys. 8, 671 (2012)
Zurück zum Zitat Hill, S.A., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)ADS Hill, S.A., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022 (1997)ADS
Zurück zum Zitat Horodecki, R., Horodecki, P., Horodecki, M.: Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition. Phys. Lett. A 200, 340 (1995)ADSMathSciNetMATH Horodecki, R., Horodecki, P., Horodecki, M.: Violating Bell inequality by mixed spin-12 states: necessary and sufficient condition. Phys. Lett. A 200, 340 (1995)ADSMathSciNetMATH
Zurück zum Zitat Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sende, A., Sen, U., Synak-Radtke, B.: Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A 71, 62307 (2005)ADS Horodecki, M., Horodecki, P., Horodecki, R., Oppenheim, J., Sende, A., Sen, U., Synak-Radtke, B.: Local versus nonlocal information in quantum-information theory: formalism and phenomena. Phys. Rev. A 71, 62307 (2005)ADS
Zurück zum Zitat Indrajith, V.S., Muthuganesan, R., Sankaranarayanan, R.: Entanglement and Measurement-induced quantum correlation in Heisenberg spin models. Physica A 527, 121325 (2019)MathSciNetMATH Indrajith, V.S., Muthuganesan, R., Sankaranarayanan, R.: Entanglement and Measurement-induced quantum correlation in Heisenberg spin models. Physica A 527, 121325 (2019)MathSciNetMATH
Zurück zum Zitat Indrajith, V.S., Muthuganesan, R., Sankaranarayanan, R.: Measurement induced nonlocality quantified by hellinger distance and weak measurements. Physica A 566, 125615 (2021)MathSciNetMATH Indrajith, V.S., Muthuganesan, R., Sankaranarayanan, R.: Measurement induced nonlocality quantified by hellinger distance and weak measurements. Physica A 566, 125615 (2021)MathSciNetMATH
Zurück zum Zitat Jia-Sen, J., Feng-Yang, Z., Chang-Shui, Y., He-Shan, S.: Journal of physics a: direct scheme for measuring the geometric quantum discord. Math. Theor. 45, 115308 (2012)MATH Jia-Sen, J., Feng-Yang, Z., Chang-Shui, Y., He-Shan, S.: Journal of physics a: direct scheme for measuring the geometric quantum discord. Math. Theor. 45, 115308 (2012)MATH
Zurück zum Zitat Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2011)ADS Luo, S.: Using measurement-induced disturbance to characterize correlations as classical or quantum. Phys. Rev. A 77, 022301 (2011)ADS
Zurück zum Zitat Luo, S., Fu, S.: Measurement-induced nonlocality. Phys. Rev. Lett. 106, 120401 (2011)ADSMATH Luo, S., Fu, S.: Measurement-induced nonlocality. Phys. Rev. Lett. 106, 120401 (2011)ADSMATH
Zurück zum Zitat Ming-Liang, H., Fan, H.: Dynamics of entropic measurement-induced nonlocality in structured reservoirs. Ann. Phys. 327, 2343 (2012)ADSMATH Ming-Liang, H., Fan, H.: Dynamics of entropic measurement-induced nonlocality in structured reservoirs. Ann. Phys. 327, 2343 (2012)ADSMATH
Zurück zum Zitat Ming-Liang, H., Fan, H.: Measurement-induced nonlocality based on the trace norm. New J. Phys. 17, 33004 (2015)MATH Ming-Liang, H., Fan, H.: Measurement-induced nonlocality based on the trace norm. New J. Phys. 17, 33004 (2015)MATH
Zurück zum Zitat Mohamed, A.-B.A., Hessian, H.A., Eleuch, H.: Quantum correlations of two qubits beyond entanglement in two lossy cavities linked by a waveguide. Chaos, Solitons and Fractals 135, 109773 (2020)MathSciNetMATH Mohamed, A.-B.A., Hessian, H.A., Eleuch, H.: Quantum correlations of two qubits beyond entanglement in two lossy cavities linked by a waveguide. Chaos, Solitons and Fractals 135, 109773 (2020)MathSciNetMATH
Zurück zum Zitat Mohamed, A.-B.A., Abdel-Aty, A.-H., Eleuch, H.: Dynamics of trace distance and Bures correlations in a three-qubit XY chain: Intrinsic noise model. Physica E 128, 114529 (2020) Mohamed, A.-B.A., Abdel-Aty, A.-H., Eleuch, H.: Dynamics of trace distance and Bures correlations in a three-qubit XY chain: Intrinsic noise model. Physica E 128, 114529 (2020)
Zurück zum Zitat Muthuganesan, R., Chandrasekar, V.K.: Measurement-induced nonlocality based on affinity. Commun. Theor. Phys. 72, 075103 (2020)ADSMathSciNetMATH Muthuganesan, R., Chandrasekar, V.K.: Measurement-induced nonlocality based on affinity. Commun. Theor. Phys. 72, 075103 (2020)ADSMathSciNetMATH
Zurück zum Zitat Muthuganesan, R., Chandrasekar, V.K.: Intrinsic decoherence effects on measurement-induced nonlocality. Quantum Inf. Process 20, 46 (2021)ADSMathSciNet Muthuganesan, R., Chandrasekar, V.K.: Intrinsic decoherence effects on measurement-induced nonlocality. Quantum Inf. Process 20, 46 (2021)ADSMathSciNet
Zurück zum Zitat Muthuganesan, R., Sankaranarayanan, R.: Fidelity based measurement induced nonlocality. Phys. Lett. A 381, 3028 (2017)ADSMATH Muthuganesan, R., Sankaranarayanan, R.: Fidelity based measurement induced nonlocality. Phys. Lett. A 381, 3028 (2017)ADSMATH
Zurück zum Zitat Nielsen, M., Chuang, I.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2010)MATH Nielsen, M., Chuang, I.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2010)MATH
Zurück zum Zitat Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSMATH Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88, 017901 (2001)ADSMATH
Zurück zum Zitat Passante, G., Moussa, O., Laflamme, R.: Measuring geometric quantum discord using one bit of quantum information. Phys. Rev. A 85, 032325 (2012)ADS Passante, G., Moussa, O., Laflamme, R.: Measuring geometric quantum discord using one bit of quantum information. Phys. Rev. A 85, 032325 (2012)ADS
Zurück zum Zitat Piani, M.: Problem with geometric discord. Phys. Rev. A 86, 034101 (2012)ADS Piani, M.: Problem with geometric discord. Phys. Rev. A 86, 034101 (2012)ADS
Zurück zum Zitat Qing-Wen, W., Shu-Qian, S., Li, M., Li, L.: Measurement-induced nonlocality based on Wigner-Yanase skew information. Europhys. Lett. 114, 10007 (2016) Qing-Wen, W., Shu-Qian, S., Li, M., Li, L.: Measurement-induced nonlocality based on Wigner-Yanase skew information. Europhys. Lett. 114, 10007 (2016)
Zurück zum Zitat Roccati, F., Lorenzo, S., Palma, G.M., Landi, G.T., Brunelli, M., Ciccarello, F.: Quantum correlations in PT-symmetric systems. Quantum Sci. Technol. 6, 025005 (2021)ADS Roccati, F., Lorenzo, S., Palma, G.M., Landi, G.T., Brunelli, M., Ciccarello, F.: Quantum correlations in PT-symmetric systems. Quantum Sci. Technol. 6, 025005 (2021)ADS
Zurück zum Zitat Schneeloch, J., Broadbent, C.J., Walborn, S.P., Cavalcanti, E.G., Howell, J.C.: Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations. Phys. Rev. A 87, 062103 (2013)ADS Schneeloch, J., Broadbent, C.J., Walborn, S.P., Cavalcanti, E.G., Howell, J.C.: Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations. Phys. Rev. A 87, 062103 (2013)ADS
Zurück zum Zitat Schrodinger, E.: Discussion of probability relations between separated systems. Proc. Cambridge Philos. Soc. 31, 555 (1935)ADSMATH Schrodinger, E.: Discussion of probability relations between separated systems. Proc. Cambridge Philos. Soc. 31, 555 (1935)ADSMATH
Zurück zum Zitat Sergi, A., Zloshchastiev, K.G.: Non-Hermitian quantum dynamics of a two-level system and models of dssipative environments. Int. J. Mod. Phys. B 27, 1350163 (2013)ADSMATH Sergi, A., Zloshchastiev, K.G.: Non-Hermitian quantum dynamics of a two-level system and models of dssipative environments. Int. J. Mod. Phys. B 27, 1350163 (2013)ADSMATH
Zurück zum Zitat Sergi, A., Zloshchastiev, K.G.: Time correlation functions for non-Hermitian quantum systems. Phys. Rev. A 91, 062108 (2015)ADS Sergi, A., Zloshchastiev, K.G.: Time correlation functions for non-Hermitian quantum systems. Phys. Rev. A 91, 062108 (2015)ADS
Zurück zum Zitat Shin-Liang, C., Chen, G.Y., Yueh-Nan, C.: Increase of entanglement by local PT-symmetric operations. Phys. Rev. A 90, 54301 (2014) Shin-Liang, C., Chen, G.Y., Yueh-Nan, C.: Increase of entanglement by local PT-symmetric operations. Phys. Rev. A 90, 54301 (2014)
Zurück zum Zitat Shi-Yang, Z., Mao-Fa, F., Xu, L.: Quantum entropy of non-Hermitian entangled systems. Quantum Inf. Process 16, 234 (2017)ADSMathSciNetMATH Shi-Yang, Z., Mao-Fa, F., Xu, L.: Quantum entropy of non-Hermitian entangled systems. Quantum Inf. Process 16, 234 (2017)ADSMathSciNetMATH
Zurück zum Zitat W, Shao-Xiong., Zhang, J., Y Chang-Shui., S He-Shan,: Uncertainty-induced quantum nonlocality. Phys. Lett. A 378, 344 (2014)ADS W, Shao-Xiong., Zhang, J., Y Chang-Shui., S He-Shan,: Uncertainty-induced quantum nonlocality. Phys. Lett. A 378, 344 (2014)ADS
Zurück zum Zitat Wan-Yue, L., Liu, Y.: Impact of PT-symmetric operation on concurrence and the first-order coherence. Int. J. Theor. Phys. 60, 2878 (2021)MathSciNetMATH Wan-Yue, L., Liu, Y.: Impact of PT-symmetric operation on concurrence and the first-order coherence. Int. J. Theor. Phys. 60, 2878 (2021)MathSciNetMATH
Zurück zum Zitat Werner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)ADSMATH Werner, R.F.: Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277 (1989)ADSMATH
Zurück zum Zitat Xi, Z., Wang, X., Li, Y.: Measurement-induced nonlocality based on the relative entropy. Phys. Rev. A 85, 042325 (2012)ADS Xi, Z., Wang, X., Li, Y.: Measurement-induced nonlocality based on the relative entropy. Phys. Rev. A 85, 042325 (2012)ADS
Zurück zum Zitat Xiao, L., Wang, K., Zhan, X., Bian, Z., Kawabata, K., Ueda, M., Yi, W., Xue, P.: Observation of critical phenomena in parity-time-symmetric quantum dynamics. Phys. Rev. Lett. 123, 230401 (2019)ADS Xiao, L., Wang, K., Zhan, X., Bian, Z., Kawabata, K., Ueda, M., Yi, W., Xue, P.: Observation of critical phenomena in parity-time-symmetric quantum dynamics. Phys. Rev. Lett. 123, 230401 (2019)ADS
Zurück zum Zitat Yan, X.Q., Yue, Z.L.: Dynamics of quantum and classical correlations of a two-atom system in thermal reserviors. Chaos, Solitons and Fractals 57, 117 (2013)ADSMATH Yan, X.Q., Yue, Z.L.: Dynamics of quantum and classical correlations of a two-atom system in thermal reserviors. Chaos, Solitons and Fractals 57, 117 (2013)ADSMATH
Zurück zum Zitat Yan-Yi, W., Mao-Fa, F.: Enhancing and protecting quantum correlations of a two-qubit entangled system via non-Hermitian operation. Quantum Inf. Process 17, 208 (2018)ADSMathSciNetMATH Yan-Yi, W., Mao-Fa, F.: Enhancing and protecting quantum correlations of a two-qubit entangled system via non-Hermitian operation. Quantum Inf. Process 17, 208 (2018)ADSMathSciNetMATH
Zurück zum Zitat Yi-Chan, L., Min-Hsiu, H., Flammia, S.T., Lee, R.-K.: Local PT symmetry violates the no-signaling principle. Phys. Rev. Lett. 112, 130404 (2014) Yi-Chan, L., Min-Hsiu, H., Flammia, S.T., Lee, R.-K.: Local PT symmetry violates the no-signaling principle. Phys. Rev. Lett. 112, 130404 (2014)
Metadaten
Titel
Temporal evolution of quantum correlations under non-Hermitian operation
verfasst von
J. Ramya Parkavi
R. Muthuganesan
V. K. Chandrasekar
Publikationsdatum
01.11.2022
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 11/2022
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-022-04152-2

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