تحول زمانی همبستگی کوانتمی و رابطه آنتروپی عدم قطعیت در حضور حافظه کوانتمی تحت واهمدوسی و هامیلتونی پیچش تک-محوری

نوع مقاله: مقاله پژوهشی کامل

نویسنده

گروه فیزیک، دانشگاه سلمان فارسی، کازرون، کازرون، ایران

چکیده

در این مقاله یک سیستم متقارن N ذره‌ای با اسپین 2/1 که تحت هامیلتونی پیچش تک-محوری قرار دارد را در نظر می‌گیریم. سپس با اعمال کانال‌های مختلف نویز دار، همچون کانال میرایی دامنه، کانال فاز-گردان و کانال میرایی فاز، تحول زمانی همبستگی کوانتمی و رابطه آنتروپی عدم قطعیت در حضور حافظه کوانتمی را بدست می‌آوریم. مقایسه رفتار آنتروپی عدم قطعیت و همبستگی کوانتمی نشان می‌دهد که در لحظه شروع، با افزایش تعداد ذرات، مقدار اولیه این کمیت‌ها افزایش می‌یابد. اما در طی زمان رفتار آنها عکس یکدیگر خواهد بود. بطور کلی با کاهش همبستگی کوانتمی، عدم قطعیت در اندازه گیری مشاهده‌پذیرهای ناسازگار افزایش می‌یابد.

کلیدواژه‌ها


عنوان مقاله [English]

Time evolution of quantum correlation and entropic uncertainty relation in the presence of quantum memory under noisy channels and one-axis twisting Hamiltonian

نویسنده [English]

  • Mohammad Reza Pourkarimi
Department of Physics, Salman Farsi University of Kazerun, Kazerun, Iran
چکیده [English]

Assuming, a symmetric system with N qubits under Hamiltonian one-axis twisting and different kinds of noisy channels, such as amplitude damping, phase-flip and phase-damping channel, it is studied the time evolution of quantum correlation and entropic uncertainty relation in the presence of quantum memory. By comparing the behaviors of the dynamics of entropic uncertainty and quantum correlation, it is shown that they increase with increasing of the number of qubits in the beginning of the time. But, they behave in contrary to each other, during the time. As a result, the uncertainty of incompatible observables increases, when quantum correlation decreases.

کلیدواژه‌ها [English]

  • Quantum correlation
  • Entropic uncertainty relation
  • Quantum discord
[1] W. Heisenberg, Mehrkörperproblem und Resonanz in der Quantenmechanik, Zeitschrift für Physik 43 (1927) 172. https://doi.org/10.1007/BF01397160

[2] H.P. Robertson, The uncertainty principle, Physical Review 34 (1929) 163. https://doi.org/10.1103/PhysRev.34.163

[3] K. Kraus, Complementary observables and uncertainty relations, Physical Review D 35 (1987) 3070. https://doi.org/10.1103/physrevd.35.3070

[4] H. Maassen, J.B.M. Uffink, Generalized entropic uncertainty relations, Physical Review Letters 60 (1988) 1103. https://doi.org/10.1103/physrevlett.60.1103

[5] M. Berta, M. Christandl, R. Colbeck, M.J. Renes, R. Renner, The uncertainty principle in the presence of quantum memory, Nature Physics 6 (2010) 659. https://doi.org/10.1038/nphys1734

[6] R. Prevedel, D.R. Hamel, R.Colbeck, K. Fisher, K.J. Resch, Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnes singent anglement, Nature Physics7(2011) 757. https://doi.org/10.1038/nphys2048

[7] C.F. Li, J.S.Xu, X.Y. Xu, K. Li, G.C. Guo, Experimental investigation of the entanglement assisted entropic uncertainty principle, Nature Physics7 (2011) 752. https://doi.org/10.1038/nphys2047

[8] K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, The classical-quantum boundary for correlations: Discord and related measures, Reviews of Modern Physics 84, (2012) 1655. https://doi.org/10.1103/RevModPhys.84.1655

[9] L. Henderson, V. Vedral, Classical, quantum and total correlations, Journal of Physics A: Mathematical and General 34 (2001)6899. https://doi.org/10.1088/0305-4470/34/35/315

[10] H. Ollivier, W.H. Zurek, Quantum discord: a measure of the quantumness of correlations, Physical Review Letters 88 (2001) 017901. https://doi.org/10.1103/PhysRevLett.88.017901

[11] W.K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Physical Review Letters 80 (1998) 2245. https://doi.org/10.1103/PhysRevLett.80.2245

[12] M.R. Pourkarimi, M. Rahnama, H. Rooholamini, Decoherence effect on quantum correlation and entanglement in a two-qubit spin chain, International Journal of Theoretical Physics 54 (2015) 1085. https://doi.org/10.1007/s10773-014-2302-7

[13] M.R. Pourkarimi, M.Rahnama, Quantum teleportation under the effect of dissipative environment and Hamiltonian XY model, International Journal of Theoretical Physics 53 (2014) 1415. https://doi.org/10.1007/s10773-013-1938-z

[14] M.R. Pourkarimi, The dynamics of quantum correlations in multi-qubit spin chainsunder the effect of Dzyaloshinskii-Moriya interaction, International Journal of Theoretical Physics 57 (2018) 1158. https://doi.org/10.1007/s10773-017-3646-6

[15] M. Jafarpour, M.R. Pourkarimi, A. Akhound, Entanglement sudden death and itssuppression inmulti-qubit channels, using a magnetic field, IL Nuovo Cimento B 124 (2009) 269. https://doi.org/10.1393/ncb/i2009-10762-2

[16] S. Bose, Quantum communication through an unmodulated spin chain, Physical Review Letters 91 (2003)207901.

[17] A. Akhound, S. Haddadi, M.A. Chaman Motlagh, Bipartite and multipartite entanglement in entangled graphs, Journal of research on Many-body systems, 8 (19), 1-10 https://dx.doi.org/10.22055/jrmbs.2018.13972

[18] S. Ghanavati, M. Jafarpour, Calculating the ground state entanglement of a two-dimensional spin star lattice, Journal of research on Many-body systems, 8 (17), 135-143 https://dx.doi.org/10.22055/jrmbs.2018.13894

[19] H. Varghese, M. Ravendranadhan, Quantum entanglement and generalized uncertaintyrelations, arXiv: 1706.09377v1 [quant-ph] (2017). https://arxiv.org/abs/1706.09377

[20] D. Wang, A. Huang, F. Ming, W. Sun, H. Lu, C. Liu, L. Ye, Quantum-memory-assisted entropic uncertainty relation in a Heisenberg XYZ chain with an inhomogeneous magnetic field, Laser Physics Letters 14 (2017) 065203. https://doi.org/10.1088/1612-202X/aa6f85

[21] AJ. Huang, D. Wang, J.M. Wang, et al, Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field, Quantum information Processing 16 (2017) 204. https://doi.org/10.1007/s11128-017-1657-0

[22] M.R. Pourkarimi, Quantum correlations and entropic uncertainty relation in a three-qubit spin chain under the effect of magnetic field and DM interaction, International Journal of Quantum Information 16 (2018) 1850057. https://doi.org/10.1142/S0219749918500570

[23] S. Haddadi, M.R. Pourkarimi, A. Akhound, M. Ghominejad, Quantum correlations and quantum-memory-assisted entropicuncertainty relation in two kinds of spin squeezing models, Laser Physics Letters 16 (2019) 095202. https://doi.org/10.1088/1612-202X/ab2cc7

[24] M. Jafarpour, A. Akhound, Entanglement and squeezing of multi-qubit systems using a two-axis countertwisting Hamiltonian with an external field, Physics Letters A 372 (2008) 2374. https://doi.org/10.1016/j.physleta.2007.12.021

[25] M. Kitagawa, M. Ueda, Sgueezed spin states, Physical Review A 47(1993) 5138. https://doi.org/10.1103/PhysRevA.47.5138

[26] M.F. Riedel, P. Böhi, Y. Li, T.W. Hänsch, A.Sinatra, P. Treutlein, Atom-chip-based generation of entanglement for quantum metrology, Nature 464 (2010) 1170. https://doi.org/10.1038/nature08988

 

[27] X.G. Wang, K. Mølmer, Pairwise entanglement in symmetric multi-qubit systems, The European Physical Journal D 18 (2002) 385. https://doi.org/10.1140/epjd/e20020045

 

[28] YN. Guo, K. Zeng, GY. Wang, Pairwise quantum discord for a symmetric multi-qubit system in different types of noisy channels, International Journal of Theoretical Physics 55 (2016) 2894. https://doi.org/10.1007/s10773-016-2920-3

 

[29] G.X. Wang, B.C. Sander, Spin squeezing and pairwise entanglement for symmetric multiqubit states, Physical Review A 68 (2003) 012101. https://doi.org/10.1103/PhysRevA.68.012101