Study of Entangled K-meson and Its Decoherence
Main Article Content
Abstract
In this paper, entangled K-meson model and decoherence phenomenon in the
system is studied. Using Lindblad equation, dynamical equation of entangled K-meson system
that interacts with the environment is obtained. We find that non-Hermitian Hamiltonian of
the system makes completely positive and trace-preserving map (CPT-map) on the space of
density matrix does not satisfy trace preserving properties. We also find that purity of density
matrix can be less than 1=d which does not satisfy the property of purity. From the dynamical
equation, parameters related to the decoherence of the system, decoherence parameter (λ) and
effective decoherence parameter (ζ), are determined. Using Standard Least-Squares method,
we obtain ζ = 0; 13±0; 865. This result is in accordance with references result that use effective
variance method, ζ = 0; 13±+0 -0;;16 15. We show that ζ = 0; 13±+0 -0;;16 15 corresponds with references
result, λ = (1; 84±+2 -2;;50 17) × 10-12 MeV. The value of both parameters are close to zero relative
to ζ = 1 or λ ! 1. It means that the interaction between system and environment does
not affect the system significantly. Therefore, quantum properties in the system related to the
entanglement of the strangeness is preserved.
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Syahbana, A., Zen, F., & Dwiputra, D. (2022). Study of Entangled K-meson and Its Decoherence. Indonesian Journal of Physics, 33(1), 39 - 44. https://doi.org/10.5614/itb.ijp.2022.33.1.4
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References
[1] E. Schrödinger, Discussion of Probability Relations between Separated Systems, Mathematical Proceedings of the Cambridge Philosophical Society, 31, 555, 1935.
[2] D. V. Schroeder, Entanglement isn't just for spin, American Journal of Physics, 85, 812, 2017.
[3] D. Bouwmeester et al., Experimental quantum teleportation, Nature, 390, 575, 1997.
[4] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 10th Anniversary Edition, Cambridge University Press, New York, 2010.
[5] S. Akama, Elements of Quantum Computing: History, Theories and Engineering Applications, Springer International Publishing, Cham, 2015.
[6] S. Pirandola et al., Advances in Quantum Teleportation, Nature Photonics, 9, 641, 2015.
[7] E. B. Manoukian, 100 Years of Fundamental Theoretical Physics in the Palm of Your Hand: Integrated Technical Treatment, Springer International Publishing, Cham, 2020.
[8] S. Kurgalin, Concise Guide to Quantum Computing: Algorithms, Exercises, and Implementations, Springer International Publishing, Cham, 2021.
[9] B. P. Williams, R. J. Sadlier, and T. S. Travis, Superdense Coding over Optical Fiber Links with Complete Bell-State Measurements, Phys. Rev. Lett., 118, 050501, 2017.
[10] X. M. Hu et al., Beating the channel capacity limit for superdense coding with entangled ququarts, 4, 2018.
[11] A. K. Ekert, Quantum cryptography based on Bell's theorem, Phys. Rev. Lett., 67, 661, 1991.
[12] R. Arnon-Friedman et al., Practical device-independent quantum cryptography via entropy accumulation, Nature Communications, 9, 2018.
[13] M. Brune et al., Observing the Progressive Decoherence of the “Meter'” in a Quantum Measurement, Phys. Rev. Lett., 77, 4887, 1996.
[14] R. A. Bertlmann, W. Grimus, and B. C. Hiesmayr, Quantum mechanics, Furry's hypothesis, and a measure of decoherence in the system, Phys. Rev. D, 60, 114032, 1999.
[15] R. A. Bertlmann, K. Durstberger, and B. C. Hiesmayr, Decoherence of entangled kaons and its connection to entanglement measures, Phys. Rev. A, 68, 012111, 2003.
[16] R. A. Bertlmann, Entanglement, Bell Inequalities and Decoherence in Particle Physics, Springer Berlin Heidelberg, Berlin, 2006.
[17] F. Ambrosino et al., First observation of quantum interference in the process ϕ→KSKL→π+π−π+π−: A test of quantum mechanics and CPT symmetry, Physics Letters B, 642, 315, 2006.
[18] T. Traxler, Decoherence and Entanglement of two qubit systems, Master’s thesis, University of Vienna, Vienna, 2011.
[19] D. Samitz, Particle Oscillations, Entanglement and Decoherence, Bachelor's thesis, University of Vienna, Vienna, 2012.
[20] R. Bertlmann and A. Zeilinger, Quantum [Un]Speakables II: Half a Century of Bell's Theorem, Springer International Publishing, Cham, 2017.
[21] W. Krzemien and E. P. del Rio, The KLOE-2 experiment: Overview of recent results, International Journal of Modern Physics A, 34, 1930012, 2019.
[22] C. F. Li, G. C. Guo, and J. Piilo, Non-Markovian quantum dynamics: What is it good for?, EPL, 128, 30001, 2020.
[23] D. Dwiputra et al., Driving the Dephasing Assisted Quantum Transport, Journal of Physics: Conference Series, 1245, 012075, 2019.
[24] D. Dwiputra et al., Driving-assisted open quantum transport in qubit networks, Phys. Rev. A, 101, 012113, 2020.
[25] D. Dwiputra and F. P. Zen, Environment-assisted quantum transport and mobility edges, Phys. Rev. A, 104, 022205, 2021.
[26] H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, New York, 2002.
[27] A. Strathearn et al., Efficient non-Markovian quantum dynamics using time-evolving matrix product operators, Nature Communications, 9, 2018.
[28] D. Manzano, A short introduction to the Lindblad master equation, AIP Advances, 10, 025106, 2020.
[29] A. D. Domenico, Quantum mechanics, CPT violation, and neutral kaons, AIP Conference Proceedings, 1424, 414, 2012.
[30] P. A. Zyla et al. (Particle Data Group), Review of Particle Physics, Progress of Theoretical and Experimental Physics, 2020, 2020.
[31] M. M. Wilde, Quantum Information Theory, 2, Cambridge University Press, Cambridge, 2017.
[32] S. L. Braunstein, A. Mann, and M. Revzen, Maximal violation of Bell inequalities for mixed states, Phys. Rev. Lett., 68, 3259, 1992.
[33] D. Sych and G. Leuchs, A complete basis of generalized Bell states, New Journal of Physics, 11, 013006, 2009.
[34] P. Meystre and M. Sargent, Elements of Quantum Optics, Springer Berlin Heidelberg, Berlin, 2007.
[35] V. V. Albert and L. Jiang, Symmetries and conserved quantities in Lindblad master equations, Phys. Rev. A, 89, 022118, 2014.
[36] F. Zaman, Y. Jeong, and H. Shin, Counterfactual Bell-State Analysis, Scientific Reports, 8, 2018.
[37] A. Apostolakis et al., An EPR experiment testing the non-separability of the K0K0 wave function, Physics Letters B, 422, 339, 1998.
[38] G. Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics, 48, 119, 1976.
[39] V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N‐level systems, Journal of Mathematical Physics, 17, 821, 1976.
[40] C. Brasil, F. Fanchini, and R. Napolitano, A simple derivation of the Lindblad equation, Revista Brasileira de Ensino de Física, 35, 2011.
[41] S. Weinberg, Quantum mechanics without state vectors, Phys. Rev. A, 90, 042102, 2014.
[42] D. Aharonov, A. Kitaev, and N. Nisan, Quantum Circuits with Mixed States, Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing (May 24-26, 1998, Dallas, Texas, USA), (New York: Association for Computing Machinery), 20, 1998.
[43] C. M. Caves, Quantum Error Correction and Reversible Operations, Journal of Superconductivity, 12, 707, 1999.
[44] P. Pearle, Simple derivation of the Lindblad equation, European Journal of Physics, 33, 805, 2012.
[45] P. Caban et al., Unstable particles as open quantum systems, Phys. Rev. A, 72, 032106, 2005.
[46] R. A. Bertlmann, W. Grimus, and B. C. Hiesmayr, Open-quantum-system formulation of particle decay, Phys. Rev. A, 73, 054101, 2006.
[47] R. J. Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences, Wiley, Chichester, 1993.
[48] A. Bevan, Statistical Data Analysis for the Physical Sciences, Cambridge University Press, Cambridge, 2013.
[49] J. Orear, Least squares when both variables have uncertainties, American Journal of Physics, 50, 912, 1982.
[50] E. Tiesinga et al., CODATA recommended values of the fundamental physical constants: 2018, Rev. Mod. Phys., 93, 025010, 202
[2] D. V. Schroeder, Entanglement isn't just for spin, American Journal of Physics, 85, 812, 2017.
[3] D. Bouwmeester et al., Experimental quantum teleportation, Nature, 390, 575, 1997.
[4] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, 10th Anniversary Edition, Cambridge University Press, New York, 2010.
[5] S. Akama, Elements of Quantum Computing: History, Theories and Engineering Applications, Springer International Publishing, Cham, 2015.
[6] S. Pirandola et al., Advances in Quantum Teleportation, Nature Photonics, 9, 641, 2015.
[7] E. B. Manoukian, 100 Years of Fundamental Theoretical Physics in the Palm of Your Hand: Integrated Technical Treatment, Springer International Publishing, Cham, 2020.
[8] S. Kurgalin, Concise Guide to Quantum Computing: Algorithms, Exercises, and Implementations, Springer International Publishing, Cham, 2021.
[9] B. P. Williams, R. J. Sadlier, and T. S. Travis, Superdense Coding over Optical Fiber Links with Complete Bell-State Measurements, Phys. Rev. Lett., 118, 050501, 2017.
[10] X. M. Hu et al., Beating the channel capacity limit for superdense coding with entangled ququarts, 4, 2018.
[11] A. K. Ekert, Quantum cryptography based on Bell's theorem, Phys. Rev. Lett., 67, 661, 1991.
[12] R. Arnon-Friedman et al., Practical device-independent quantum cryptography via entropy accumulation, Nature Communications, 9, 2018.
[13] M. Brune et al., Observing the Progressive Decoherence of the “Meter'” in a Quantum Measurement, Phys. Rev. Lett., 77, 4887, 1996.
[14] R. A. Bertlmann, W. Grimus, and B. C. Hiesmayr, Quantum mechanics, Furry's hypothesis, and a measure of decoherence in the system, Phys. Rev. D, 60, 114032, 1999.
[15] R. A. Bertlmann, K. Durstberger, and B. C. Hiesmayr, Decoherence of entangled kaons and its connection to entanglement measures, Phys. Rev. A, 68, 012111, 2003.
[16] R. A. Bertlmann, Entanglement, Bell Inequalities and Decoherence in Particle Physics, Springer Berlin Heidelberg, Berlin, 2006.
[17] F. Ambrosino et al., First observation of quantum interference in the process ϕ→KSKL→π+π−π+π−: A test of quantum mechanics and CPT symmetry, Physics Letters B, 642, 315, 2006.
[18] T. Traxler, Decoherence and Entanglement of two qubit systems, Master’s thesis, University of Vienna, Vienna, 2011.
[19] D. Samitz, Particle Oscillations, Entanglement and Decoherence, Bachelor's thesis, University of Vienna, Vienna, 2012.
[20] R. Bertlmann and A. Zeilinger, Quantum [Un]Speakables II: Half a Century of Bell's Theorem, Springer International Publishing, Cham, 2017.
[21] W. Krzemien and E. P. del Rio, The KLOE-2 experiment: Overview of recent results, International Journal of Modern Physics A, 34, 1930012, 2019.
[22] C. F. Li, G. C. Guo, and J. Piilo, Non-Markovian quantum dynamics: What is it good for?, EPL, 128, 30001, 2020.
[23] D. Dwiputra et al., Driving the Dephasing Assisted Quantum Transport, Journal of Physics: Conference Series, 1245, 012075, 2019.
[24] D. Dwiputra et al., Driving-assisted open quantum transport in qubit networks, Phys. Rev. A, 101, 012113, 2020.
[25] D. Dwiputra and F. P. Zen, Environment-assisted quantum transport and mobility edges, Phys. Rev. A, 104, 022205, 2021.
[26] H. P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford University Press, New York, 2002.
[27] A. Strathearn et al., Efficient non-Markovian quantum dynamics using time-evolving matrix product operators, Nature Communications, 9, 2018.
[28] D. Manzano, A short introduction to the Lindblad master equation, AIP Advances, 10, 025106, 2020.
[29] A. D. Domenico, Quantum mechanics, CPT violation, and neutral kaons, AIP Conference Proceedings, 1424, 414, 2012.
[30] P. A. Zyla et al. (Particle Data Group), Review of Particle Physics, Progress of Theoretical and Experimental Physics, 2020, 2020.
[31] M. M. Wilde, Quantum Information Theory, 2, Cambridge University Press, Cambridge, 2017.
[32] S. L. Braunstein, A. Mann, and M. Revzen, Maximal violation of Bell inequalities for mixed states, Phys. Rev. Lett., 68, 3259, 1992.
[33] D. Sych and G. Leuchs, A complete basis of generalized Bell states, New Journal of Physics, 11, 013006, 2009.
[34] P. Meystre and M. Sargent, Elements of Quantum Optics, Springer Berlin Heidelberg, Berlin, 2007.
[35] V. V. Albert and L. Jiang, Symmetries and conserved quantities in Lindblad master equations, Phys. Rev. A, 89, 022118, 2014.
[36] F. Zaman, Y. Jeong, and H. Shin, Counterfactual Bell-State Analysis, Scientific Reports, 8, 2018.
[37] A. Apostolakis et al., An EPR experiment testing the non-separability of the K0K0 wave function, Physics Letters B, 422, 339, 1998.
[38] G. Lindblad, On the generators of quantum dynamical semigroups, Communications in Mathematical Physics, 48, 119, 1976.
[39] V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of N‐level systems, Journal of Mathematical Physics, 17, 821, 1976.
[40] C. Brasil, F. Fanchini, and R. Napolitano, A simple derivation of the Lindblad equation, Revista Brasileira de Ensino de Física, 35, 2011.
[41] S. Weinberg, Quantum mechanics without state vectors, Phys. Rev. A, 90, 042102, 2014.
[42] D. Aharonov, A. Kitaev, and N. Nisan, Quantum Circuits with Mixed States, Proceedings of the Thirtieth Annual ACM Symposium on Theory of Computing (May 24-26, 1998, Dallas, Texas, USA), (New York: Association for Computing Machinery), 20, 1998.
[43] C. M. Caves, Quantum Error Correction and Reversible Operations, Journal of Superconductivity, 12, 707, 1999.
[44] P. Pearle, Simple derivation of the Lindblad equation, European Journal of Physics, 33, 805, 2012.
[45] P. Caban et al., Unstable particles as open quantum systems, Phys. Rev. A, 72, 032106, 2005.
[46] R. A. Bertlmann, W. Grimus, and B. C. Hiesmayr, Open-quantum-system formulation of particle decay, Phys. Rev. A, 73, 054101, 2006.
[47] R. J. Barlow, Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences, Wiley, Chichester, 1993.
[48] A. Bevan, Statistical Data Analysis for the Physical Sciences, Cambridge University Press, Cambridge, 2013.
[49] J. Orear, Least squares when both variables have uncertainties, American Journal of Physics, 50, 912, 1982.
[50] E. Tiesinga et al., CODATA recommended values of the fundamental physical constants: 2018, Rev. Mod. Phys., 93, 025010, 202