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PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY

Yıl 2021, , 77 - 92, 30.08.2021

Durgun Duran

https://doi.org/10.20290/estubtdb.863650

Öz

Considering the quantum memory channels, we study the dynamical evolutions of quantum coherence and quantum mutual information as measures of quantum correlations under the actions of different decoherence channels on some bipartite initial states. Under any quantum operation or process occurring in a noisy environment, quantum correlations exhibit behavior that does not increase due to the system interacting with its environment. We state that for such a case the decrement of quantum correlations can be improved by the suitable choice of the initial states and by adjusting the parameters. Thus quantum correlations can be partially preserved against the action of the environment. It can be shown that optimal conditions to prohibit the partial loss in quantum coherence and quantum mutual information for performing any quantum information task may be generated by the memory.

Anahtar Kelimeler

Quantum coherence Quantum mutual information Quantum correlations Quantum channels with memory

Kaynakça

  • [1] Nielsen M, Chuang IL. Quantum Computation and Quantum Information, 10th Anniversary Ed. Cambridge University Press, Cambridge, 2010.
  • [2] DiVincenzo DP. The physical implementation of quantum computation. Fortschr Phys, 2000; 48: 771-783.
  • [3] Plenio MB, Virmani S. An introduction to entanglement measures. Quantum Inf Comput 2007; 7(1): 1-51.
  • [4] Breuer HP, Petruccione F. The Theory of Open Quantum Systems, Oxford University Press, U. K.: Oxford, 2002.
  • [5] Schlosshauer M. Decoherence and the Quantum-to-Classical Transition, Berlin, Germany: Springer, 2008.
  • [6] Xu JS, Xu XY, Li CF, Zhang CJ, Zou XB, Guo GC. Experimental investigation of classical and quantum correlations under Decoherence. Nat Commun 2010; 1:7.
  • [7] Caruso F, Giovannetti V, Lupo C, Mancini S. Quantum channels and memory effects. Rev Mod Phys 2014; 86, 1203.
  • [8] Baumgratz T, Cramer M, Plenio MB. Quantifying coherence. Phys Rev Lett 2014; 113: 140401.
  • [9] Åberg J. Quantifying Superposition. arXiv:0612146v1.
  • [10] Glauber RJ. Coherent and Incoherent states of the radiation field. Phys Rev 1963; 131: 2766.
  • [11] Sudarshan ECG. Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys Rev Lett 1963; 10: 277.
  • [12] Harrow AW, Montanaro A. Quantum computational supremacy. Nature 2017; 549: 203-209.
  • [13] Streltsov A, Adesso G, Plenio MB. Colloquium: Quantum coherence as a resource. Rev Mod Phys 2017; 89: 041003.
  • [14] Rana S, Parashar P, Lewenstein M. Trace-distance measure of coherence. Phys Rev A 2016; 93: 012110.
  • [15] Hu ML, Hu X, Peng Y, Zhang YR, Fan H. Quantum coherence and geometric quantum discord. Physics Reports 2018; 762-764: 1-100.
  • [16] Xi Z, Li Y, Fan H. Quantum coherence and correlations in quantum system. Sci Rep 2015; 5: 10922.
  • [17] Korzekwa K, Lostaglio M, Oppenheim J, Jennings D. The extraction of work from quantum coherence. New J Phys 2016; 18: 023-045.
  • [18] Narasimhachar V, Gour G. Low-temperature thermodynamics with quantum coherence. Nat Commun 2015; 6: 7689.
  • [19] Lostaglio M, Jennings D, Rudolph T. Description of quantum coherence in thermodynamic processes requires constraints beyond free energy. Nat Commun 2015; 6: 63-83.
  • [20] Joo J, Munro WJ, Spiller TP. Quantum metrology with entangled coherent states. Phys Rev Lett 2011; 107: 083601.
  • [21] Giovannetti V, Lloyd S, Maccone L. Advances in quantum metrology. Nature Photon 2011; 5: 222-229.
  • [22] Chuang IL, Vandersypen LMK, Zhou X, Leung DW, Lloyd S. Experimental realization of a quantum algorithm. Nature 1998; 393: 143-146.
  • [23] Gershenfeld NA, Chuang IL. Bulk spin-resonance quantum computation. Science 1997; 275: 350-356.
  • [24] Henao I, Serra RM. Role of quantum coherence in the thermodynamics of energy transfer. Phys. Rev E 2018; 97: 062105.
  • [25] Lloyd S. Quantum coherence in biological systems. J Phys Conf Ser 2011; 302: 012037.
  • [26] Lambert N, Chen YN, Cheng YC, Li CM, Chen GY, Nori F. Quantum biology. Nature Physics 2013; 9: 10-18.
  • [27] Gauger EM, Rieper E, Morton JJL, Benjamin SC, Vedral V. Sustained quantum coherence and entanglement in the avian compass. Phys Rev Lett 2011; 106: 040503.
  • [28] Duran D. Action in Hamiltonian Models Constructed by Yang-Baxter Equation: Entanglement and Measures of Correlation. Chin J Phys 2020; 68: 426-435.
  • [29] Groisman B, Popescu S, Winter A. Quantum, classical, and total amount of correlations in a quantum state. Phys Rev A 2005; 72: 032317.
  • [30] Stinespring WF. Positive functions on C*-algebras. Proc Am Math Soc, 1955; 6: 211-216.
  • [31] Kraus K. Effects and Operations: Fundamental Notions of Quantum Theory, Lecture Notes in Physics, Berlin: Springer, 1983.
  • [32] Macchiavello C, Palma GM. Entanglement-enhanced information transmission over a quantum channel with correlated noise. Phys Rev A, 2002; 65: 050301(R).
  • [33] Yeo Y, Skeen A. Time-correlated quantum amplitude-damping channel. Phys Rev A 2003; 67: 064301.
  • [34] Winter A, Yang D. Operational Resource Theory of Coherence. Phys Rev Lett 2016; 116: 120404.
  • [35] Yu CS. Quantum coherence via skew information and its polygamy. Phys Rev A 2017; 95: 042337.

PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY

Yıl 2021, , 77 - 92, 30.08.2021

Durgun Duran

https://doi.org/10.20290/estubtdb.863650

Öz

Kuantum hafızalı kanallar ele alınarak, bazı iki-parçalı giriş durumlarına farklı dekoherens kanallarının etkileri altında
kuantum korelasyonların ölçüleri olarak kuantum koherens ve kuantum karşılıklı bilişimin dinamik gelişimleri incelenecektir. Gürültülü bir çevrede meyadan gelen herhangi bir kuantum işlem veya süreç altında kuantum korelasyonlar, sistem çevresiyle etkileştiğinden dolayı artamayan bir davranış sergilerler. Böyle bir durumda kuantum korelasyonlardaki bir artışın, parametrelerin ayarlanarak ve uygun giriş durumlarının seçimiyle sağlanabileceğini ifade edeceğiz. Böylece, kuantum korelasyonlar çevrenin etkisine karşın kısmen korunabilirler. Herhangi bir kuantum bilişim yükümlülüğünün gerçekleştirlmesi için kuantum koherens ve kuantum karşılıklı bilişimdeki kısmi kaybı önlemek için en uygun koşulların kuantum hafızayla elde edilebileceği gösterilebilir.

Anahtar Kelimeler

Quantum coherence Quantum mutual information Quantum correlations Quantum channels with memory

Kaynakça

  • [1] Nielsen M, Chuang IL. Quantum Computation and Quantum Information, 10th Anniversary Ed. Cambridge University Press, Cambridge, 2010.
  • [2] DiVincenzo DP. The physical implementation of quantum computation. Fortschr Phys, 2000; 48: 771-783.
  • [3] Plenio MB, Virmani S. An introduction to entanglement measures. Quantum Inf Comput 2007; 7(1): 1-51.
  • [4] Breuer HP, Petruccione F. The Theory of Open Quantum Systems, Oxford University Press, U. K.: Oxford, 2002.
  • [5] Schlosshauer M. Decoherence and the Quantum-to-Classical Transition, Berlin, Germany: Springer, 2008.
  • [6] Xu JS, Xu XY, Li CF, Zhang CJ, Zou XB, Guo GC. Experimental investigation of classical and quantum correlations under Decoherence. Nat Commun 2010; 1:7.
  • [7] Caruso F, Giovannetti V, Lupo C, Mancini S. Quantum channels and memory effects. Rev Mod Phys 2014; 86, 1203.
  • [8] Baumgratz T, Cramer M, Plenio MB. Quantifying coherence. Phys Rev Lett 2014; 113: 140401.
  • [9] Åberg J. Quantifying Superposition. arXiv:0612146v1.
  • [10] Glauber RJ. Coherent and Incoherent states of the radiation field. Phys Rev 1963; 131: 2766.
  • [11] Sudarshan ECG. Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams. Phys Rev Lett 1963; 10: 277.
  • [12] Harrow AW, Montanaro A. Quantum computational supremacy. Nature 2017; 549: 203-209.
  • [13] Streltsov A, Adesso G, Plenio MB. Colloquium: Quantum coherence as a resource. Rev Mod Phys 2017; 89: 041003.
  • [14] Rana S, Parashar P, Lewenstein M. Trace-distance measure of coherence. Phys Rev A 2016; 93: 012110.
  • [15] Hu ML, Hu X, Peng Y, Zhang YR, Fan H. Quantum coherence and geometric quantum discord. Physics Reports 2018; 762-764: 1-100.
  • [16] Xi Z, Li Y, Fan H. Quantum coherence and correlations in quantum system. Sci Rep 2015; 5: 10922.
  • [17] Korzekwa K, Lostaglio M, Oppenheim J, Jennings D. The extraction of work from quantum coherence. New J Phys 2016; 18: 023-045.
  • [18] Narasimhachar V, Gour G. Low-temperature thermodynamics with quantum coherence. Nat Commun 2015; 6: 7689.
  • [19] Lostaglio M, Jennings D, Rudolph T. Description of quantum coherence in thermodynamic processes requires constraints beyond free energy. Nat Commun 2015; 6: 63-83.
  • [20] Joo J, Munro WJ, Spiller TP. Quantum metrology with entangled coherent states. Phys Rev Lett 2011; 107: 083601.
  • [21] Giovannetti V, Lloyd S, Maccone L. Advances in quantum metrology. Nature Photon 2011; 5: 222-229.
  • [22] Chuang IL, Vandersypen LMK, Zhou X, Leung DW, Lloyd S. Experimental realization of a quantum algorithm. Nature 1998; 393: 143-146.
  • [23] Gershenfeld NA, Chuang IL. Bulk spin-resonance quantum computation. Science 1997; 275: 350-356.
  • [24] Henao I, Serra RM. Role of quantum coherence in the thermodynamics of energy transfer. Phys. Rev E 2018; 97: 062105.
  • [25] Lloyd S. Quantum coherence in biological systems. J Phys Conf Ser 2011; 302: 012037.
  • [26] Lambert N, Chen YN, Cheng YC, Li CM, Chen GY, Nori F. Quantum biology. Nature Physics 2013; 9: 10-18.
  • [27] Gauger EM, Rieper E, Morton JJL, Benjamin SC, Vedral V. Sustained quantum coherence and entanglement in the avian compass. Phys Rev Lett 2011; 106: 040503.
  • [28] Duran D. Action in Hamiltonian Models Constructed by Yang-Baxter Equation: Entanglement and Measures of Correlation. Chin J Phys 2020; 68: 426-435.
  • [29] Groisman B, Popescu S, Winter A. Quantum, classical, and total amount of correlations in a quantum state. Phys Rev A 2005; 72: 032317.
  • [30] Stinespring WF. Positive functions on C*-algebras. Proc Am Math Soc, 1955; 6: 211-216.
  • [31] Kraus K. Effects and Operations: Fundamental Notions of Quantum Theory, Lecture Notes in Physics, Berlin: Springer, 1983.
  • [32] Macchiavello C, Palma GM. Entanglement-enhanced information transmission over a quantum channel with correlated noise. Phys Rev A, 2002; 65: 050301(R).
  • [33] Yeo Y, Skeen A. Time-correlated quantum amplitude-damping channel. Phys Rev A 2003; 67: 064301.
  • [34] Winter A, Yang D. Operational Resource Theory of Coherence. Phys Rev Lett 2016; 116: 120404.
  • [35] Yu CS. Quantum coherence via skew information and its polygamy. Phys Rev A 2017; 95: 042337.
Toplam 35 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Durgun Duran 0000-0002-9458-3715

Yayımlanma Tarihi 30 Ağustos 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Duran, D. (2021). PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 9(2), 77-92. https://doi.org/10.20290/estubtdb.863650
AMA Duran D. PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY. Estuscience - Theory. Ağustos 2021;9(2):77-92. doi:10.20290/estubtdb.863650
Chicago Duran, Durgun. “PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 9, sy. 2 (Ağustos 2021): 77-92. https://doi.org/10.20290/estubtdb.863650.
EndNote Duran D (01 Ağustos 2021) PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 9 2 77–92.
IEEE D. Duran, “PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY”, Estuscience - Theory, c. 9, sy. 2, ss. 77–92, 2021, doi: 10.20290/estubtdb.863650.
ISNAD Duran, Durgun. “PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 9/2 (Ağustos 2021), 77-92. https://doi.org/10.20290/estubtdb.863650.
JAMA Duran D. PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY. Estuscience - Theory. 2021;9:77–92.
MLA Duran, Durgun. “PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, c. 9, sy. 2, 2021, ss. 77-92, doi:10.20290/estubtdb.863650.
Vancouver Duran D. PRESERVING QUANTUM CORRELATIONS VIA DECOHERENCE CHANNELS WITH MEMORY. Estuscience - Theory. 2021;9(2):77-92.