Quantum non-Markovianity: Characterization, quantification and detection

Reports on Progress in Physics

Volumn 77, Issue 9, 2014, Pages

  Rivas, Ángel ^a   Huelga, Susana F ^b,c   Plenio, Martin B ^b,c  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSITY OF ULM   (Germany)

^c Center for Integrated Quantum Science and Technologies   (Germany)

Author keywords

Concepts; Non Markovian; Quantum physics

Indexed keywords

EID: 84907922742     PISSN: 00344885     EISSN: None     Source Type: Journal    
DOI: 10.1088/0034-4885/77/9/094001     Document Type: Review

References (263)

1. Doob J L 1990 Stochastic Processes (New York: Wiley)
2. Gardiner C W 1997 Handbook of Stochastic Methods (Berlin: Springer)
3. Norris J R 1997 Markov Chains (Cambridge: Cambridge University Press)
4. Parzen E 1999 Stochastic Processes (Philadelphia: Society for Industrial and Applied Mathematics)
5. Ethier S N and Kurtz T G 2005 Markov Processes: Characterization and Convergence (New Jersey: Wiley)
6. van Kampen N G 2007 Stochastic Processes in Physics and Chemistry (Amsterdam: Elsevier)
7. Kolmogorov A N 1956 Foundations of the Theory of Probability (New York: Chelsea Publishing)
8. Basharin G P, Langville A N and Naumov V A 2004 Linear Algebra Appl. 386 3
9. Lévy P 1949 C. R. Acad Sci. Paris 228 2004
10. Feller W 1959 Ann. Math. Stat. 30 1252
11. Vacchini B, Smirne A, Laine E-M, Piilo J and Breuer H-P 2011 New J. Phys. 13 093004
12. Vacchini B 2012 J. Phys. B: At. Mol. Opt. Phys. 45 154007
13. Smirne A, Stabile A and Vacchini B 2013 Phys. Scr. T153 014057
14. Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
15. Gähler R, Klein A G and Zeilinger A 1981 Phys. Rev. A 23 1611
16. Weinberg S 1989 Phys. Rev. Lett. 62 485
17. Bollinger J J, Heinzen D J, Itano W M, Gilbert S L and Wineland D J 1989 Phys. Rev. Lett. 63 1031
18. Paulsen V 2002 Completely Bounded Maps and Operator Algebras (Cambridge: Cambridge University Press)
19. Choi M-D 1975 Linear Algebra Appl. 10 285
20. Jamiołkowski A 1972 Rep. Math. Phys. 3 275
21. Kraus K 1971 Ann. Phys., NY 64 311
22. Davies E B 1976 Quantum Theory of Open Systems (London: Academic Press)
23. Kraus K 1983 States, Effects, and Operations Fundamental Notions of Quantum Theory (Berlin: Springer)
24. Breuer H-P and Petruccione F 2002 The Theory of Open Quantum Systems (Oxford: Oxford University Press)
25. Alicki R and Lendi K 2007 Quantum Dynamical Semigroups and Applications (Berlin: Springer)
26. Rivas A and Huelga S F 2011 Open Quantum Systems. An Introduction (Heidelberg: Springer)
27. Wolf M M and Cirac J I 2008 Commun. Math. Phys. 279 147
28. Kossakowski A 1972 Rep. Math. Phys. 3 247
29. Kossakowski A 1972 Bull. Acad. Pol. Sci., Ser. Math. Astron. Phys. 20 1021
30. Gorini V, Kossakowski A and Sudarshan E C G 1976 J. Math. Phys. 17 821
31. Lindblad G 1976 Commun. Math. Phys. 48 119
32. Chrus̈ciński D and Kossakowski A 2012 J. Phys. B: At. Mol. Opt. Phys. 45 154002
33. Breuer H-P, Laine E-M and Piilo J 2009 Phys. Rev. Lett. 103 210401
34. Chrus̈ciński D, Kossakowski A and Rivas A 2011 Phys. Rev. A 83 052128
35. Helstrom C W 1976 Quantum Detection and Estimation Theory (New York: Academic Press)
36. Hayashi M 2006 Quantum Information: An Introduction (Berlin: Springer)
37. Ruskai M B 1994 Rev. Math. Phys. 6 1147
38. Galindo A and Pascual P 1990 Quantum Mechanics (Berlin: Springer)
39. Davies E B 1974 Commun. Math. Phys. 39 91
40. Davies E B 1976 Math. Ann. 219 147
41. Gardiner C W and Zoller P 2004 Quantum Noise (Berlin: Springer)
42. Gorini V, Frigerio A, Verri M, Kossakowski A and Sudarshan E C G 1978 Rep. Math. Phys. 13 149
43. Fain B 2002 Irreversibilities in Quantum Mechanics (New York: Kluwer)
44. Scarani V, Ziman M, Štelmachovič P, Gisin N and Bužek V 2002 Phys. Rev. Lett. 88 097905
45. Ziman M, Štelmachovič P and Bužek V 2005 Open Syst. Inform. Dyn. 12 81
46. Ziman M and Bužek V 2005 Phys. Rev. A 72 022110
47. Stinespring W F 1955 Proc. Am. Math. Soc. 6 211
48. Rivas A, Plato A D K, Huelga S F and Plenio M B 2010 New J. Phys. 12 113032
49. Plenio M B and Virmani S 2007 Phys. Rev. Lett. 99 120504
50. Plenio M B and Virmani S 2008 New J. Phys. 10 043032
51. Rybár T, Filippov S N, Ziman M and Bužek V 2012 J. Phys. B: At. Mol. Opt. Phys. 45 154006
52. Ciccarello F, Palma G M and Giovannetti V 2013 Phys. Rev. A 87 040103(R)
53. Bodor A, Diósi L, Kallus Z and Konrad T 2013 Phys. Rev. A 87 052113
54. Shibata F, Takahashi Y and Hashitsume N 1977 J. Stat. Phys. 17 171
55. Wilkie J 2000 Phys. Rev. E 62 8808
56. Barnett S M and Stenholm S 2001 Phys. Rev. A 64 033808
57. Royer A 2003 Phys. Lett. A 315 335
58. Budini A A 2004 Phys. Rev. A 69 042107
59. Daffer S, Wódkiewicz K, Cresser J D and McIver J K 2004 Phys. Rev. A 70 010304
60. Lee J, Kim I, Ahn D, McAneney H and Kim M S 2004 Phys. Rev. A 70 024301
61. Shabani A and Lidar D A 2005 Phys. Rev. A 71 020101(R)
62. Maniscalco S 2005 Phys. Rev. A 72 024103
63. Maniscalco S and Petruccione F 2006 Phys. Rev. A 73 012111
64. Breuer H-P and Vacchini B 2008 Phys. Rev. Lett. 101 140402
65. Kossakowski A and Rebolledo R 2009 Open Syst. Inform. Dyn. 16 259
66. Chrus̈ciński D, Kossakowski A and Pascazio S 2010 Phys. Rev. A 81 032101
67. Accardi L, Frigerio A and Lewis J T 1982 Publ. Res. Inst. Math. Sci. 18 97
68. Lewis J T 1981 Phys. Rep. 77 339
69. Fagnola F 1999 Proyecciones. J. Math. 18 1
70. Umegaki H 1954 Tohoku Math. J. 6 177
71. Takesaki M 1972 J. Funct. Anal. 9 306
72. Petz D 1988 Conditional expectation in quantum probability Quantum Probability and Applications III ed L Accardi and W von Waldenfels (Berlin: Springer) pp 251-60
73. Sinha K B and Goswami D 2007 Quantum Stochastic Processes and Noncommutative Geometry (New York: Cambridge University Press)
74. Accardi L and Mohari A 1999 Infinite Dimens. Anal. Quantum. Probab. Relat. Top. 2 397
75. Accardi L and Kozyrev S V 2001 Chaos Solitons Fractals 12 2639
76. Hudson R L and Parthasarathy K R 1984 Commun. Math. Phys. 93 301
77. Ji U C, Sahu L and Sinha K B 2010 Commun. Stoch. Anal. 4 593
78. Laine E-M, Piilo J and Breuer H-P 2010 Phys. Rev. A 81 062115
79. Breuer H-P 2012 J. Phys. B: At. Mol. Opt. Phys. 45 154001
80. Haikka P, Cresser J D and Maniscalco S 2011 Phys. Rev. A 83 012112
81. Chrus̈ciński D and Wudarski F A 2013 Phys. Lett. A 377 1425
82. Weiss U 2008 Quantum Dissipative Systems (Singapore: World Scientific)
83. Wiseman H M and Milburn G J 2010 Quantum Measurement and Control (Cambridge: Cambridge University Press)
84. Whitney R S 2008 J. Phys. A: Math. Theor. 41 175304
85. Dümcke R and Spohn H 1979 Z. Phys. B34 419
86. Zhao Y and Chen G H 2002 Phys. Rev. E 65 056120
87. Lindblad G 1979 Commun. Math. Phys. 65 281
88. Alonso D and de Vega I 2005 Phys. Rev. Lett. 94 200403
89. Lo Gullo N, Sinayskiy I, Busch Th and Petruccione F 2014 Non-Markovianity criteria for open system dynamics (arXiv:1401.1126)
90. Chrus̈ciński D and Kossakowski A 2010 Phys. Rev. Lett. 104 070406
91. Chrus̈ciński D and Kossakowski A 2010 General form of quantum evolution (arXiv:1006.2764)
92. Benatti F, Floreanini R and Olivares S 2012 Phys. Lett. A 376 2951
93. Diósi L and Strunz W T 1997 Phys. Lett. A 235 569
94. Diósi L, Gisin N and Strunz W 1998 Phys. Rev. A 58 1699
95. Strunz W T, Diósi L and Gisin N 1999 Phys. Rev. Lett. 82 1801
96. Gaspard P and Nagaoka M 1999 J. Chem. Phys. 111 5676
97. Wolf M M, Eisert J, Cubitt T S and Cirac J I 2008 Phys. Rev. Lett. 101 150402
98. Wolf M M and Perez-Garcia D 2009 Phys. Rev. Lett. 102 190504
99. Cubitt T S, Eisert J and Wolf M M 2012 Commun. Math. Phys. 310 383
100. Cubitt T S, Eisert J and Wolf M M 2012 Phys. Rev. Lett. 108 120503
101. Helm J, Strunz W T, Rietzler S and Würflinger L E 2011 Phys. Rev. A 83 042103
102. Caruso F, Giovannetti V, Lupo C and Mancini S 2012 Quantum channels, memory effects (arXiv:1207.5435)
103. Lo Franco R, Bellomo B, Andersson E and Compagno G 2012 Phys. Rev. A 85 032318
104. Pernice A, Helm J and Strunz W T 2012 J. Phys. B: At. Mol. Opt. Phys. 45 154005
105. Wißmann S, Karlsson A, Laine E-M, Piilo J and Breuer H-P 2012 Phys. Rev. A 86 062108
106. Liu B-H, Wißmann S, Hu X-M, Zhang C, Huang Y-F, Li C-F, Guo G-C, Karlsson A, Piilo J and Breuer H-P 2014 Locality, universality of quantum memory effects (arXiv:1403.4261)
107. Rivas A, Huelga S F and Plenio M B 2010 Phys. Rev. Lett. 105 050403
108. Hou S C, Yi X X, Yu S X and Oh C H 2011 Phys. Rev. A 83 062115
109. Horn R A and Johnson C R 1991 Topics in Matrix Analysis (Cambridge: Cambridge University Press)
110. Magnus J R and Neudecker H 2007 Matrix Differential Calculus with Applications in Statistics and Econometrics (Chichester: Wiley University Press)
111. Andersson E, Cresser J D and Hall M J W 2007 J. Mod. Opt. 54 1695
112. Hou S C, Yi X X, Yu S X and Oh C H 2012 Phys. Rev. A 86 012101
113. Maldonado-Mundo D, Öhberg P, Lovett B W and Andersson E 2012 Phys. Rev. A 86 042107
114. Zeng H-S, Tang N, Zheng Y-P and Wang G-Y 2011 Phys. Rev. A 84 032118
115. Zeng H-S, Tang N, Zheng Y-P and Xu T-T 2012 Eur. Phys. J. D 66 255
116. Addis C, Haikka P, McEndoo S, Macchiavello C and Maniscalco S 2013 Phys. Rev. A 87 052109
117. Xu Z-Y and Zhu S-Q 2014 Chin. Phys. Lett. 31 020301
118. Xu Z-Y, Liu C, Luo S and Zhu S 2013 Anomalous non-Markovian effect in controllable open quantum systems (arXiv:1310.1784)
119. Addis C, Bylicka B, Chrus̈ciński D and Maniscalco S 2014 What we talk about when we talk about non-Markovianity (arXiv:1402.4975)
120. Hao X, Xu X and Wang X 2012 Indivisible quantum evolution of a driven open spin-S system (arXiv:1208.1546)
121. Apollaro T J G, Di Franco C, Plastina F and Paternostro M 2011 Phys. Rev. A 83 032103
122. Žnidarič M, Pineda C and García-Mata I 2011 Phys. Rev. Lett. 107 080404
123. Huelga S F, Rivas A and Plenio M B 2012 Phys. Rev. Lett. 108 160402
124. Apollaro T J G, Lorenzo S, Di Franco C, Plastina F and Paternostro M 2013 Competition between memory-keeping, memory-erasing decoherence channels (arXiv:1311.2045)
125. Brito F and Werlang T 2014 Knob for Markovianity (arXiv:1404.2502)
126. Mannone M, Lo Franco R and Compagno G 2013 Phys. Scr. T153 014047
127. Usha Devi A R, Rajagopal A K, Sudha and Rendell R W 2012 J. Quantum Inform. Sci. 2 47-54
128. Hall M J W, Cresser J D, Li L and Andersson E 2014 Phys. Rev. A 89 042120
129. Yang L-P, Cai C Y, Xu D Z, Zhang W-M and Sun C P 2013 Phys. Rev. A 87 012110
130. Chrus̈ciński D and Maniscalco S 2014 Phys. Rev. Lett. 112 120404
131. Chrus̈ciński D and Kossakowski A 2013 Characterizing non-Markovian dynamics Geometric Methods in Physics ed P Kielanowski et al (Basel: Springer) pp 285-93
132. Chrus̈ciński D and Kossakowski A 2014 Eur. Phys. J. D 68 7
133. Xu Z Y, Yang W L and Feng M 2010 Phys. Rev. A 81 044105
134. Li J-G, Zou J and Shao B 2010 Phys. Rev. A 81 062124
135. Li J-G, Zou J and Shao B 2010 Phys. Rev. A 82 042318
136. He Z, Zou J, Li L and Shao B 2011 Phys. Rev. A 83 012108
137. Haikka P, McEndoo S, De Chiara G, Palma G M and Maniscalco S 2011 Phys. Rev. A 84 031602(R)
138. Xiao X, Fang M-F and Li Y-L 2011 Phys. Scr. 83 015013
139. Laine E-M, Breuer H-P, Piilo J, Li C-F and Guo G-C 2012 Phys. Rev. Lett. 108 210402
140. Zheng Y-P, Tang N, Wang G-Y and Zeng H-S 2011 Chin. Phys. B 20 110301
141. Dijkstra A G and Tanimura Y 2012 Phil. Trans. R. Soc. A 370 3658
142. Zhang Y-J, Han W, Shan C-J and Xia Y-J 2012 J. Opt. Soc. Am. B 29 2060
143. Li J, McKeown G, Semi F L and Paternostro M 2012 Phys. Rev. A 85 022116
144. Uchiyama C 2012 Phys. Rev. A 85 052104
145. Rosario A, Massoni E and De Zela F 2012 J. Phys. B: At. Mol. Opt. Phys. 45 095501
146. Ban M, Kitajima S and Shibata F 2012 Int. J. Theor. Phys. 51 2419
147. Clos G and Breuer H-P 2012 Phys. Rev. A 86 012115
148. Tang N, Wang G, Fan Z and Zeng H 2013 J. Quantum Inform. Sci. 3 27-33
149. Mäkelä H and Möttönen M 2013 Phys. Rev. A 88 052111
150. Haikka P, McEndoo S and Maniscalco S 2013 Phys. Rev. A 87 012127
151. Thilagam A 2013 J. Chem. Phys. 138 175102
152. Wißmann S and Breuer H-P 2013 Nonlocal quantum memory effects in a correlated multimode field (arXiv:1310.7722)
153. Xu Z-Y, Luo S, Yang W L, Liu C and Zhu S 2014 Phys. Rev. A 89 012307
154. Gu W-j and Li G-x 2012 Phys. Rev. A 85 014101
155. Xiao-Li H, Hou S-C, Wang L-C and Yi X-X 2012 Cent. Eur. J. Phys. 10 947
156. Jeske J, Cole J H, Müller C, Marthaler M and Schön G 2012 New J. Phys. 14 023013
157. Lorenzo S, Plastina F and Paternostro M 2013 Phys. Rev. A 87 022317
158. Ma T, Chen Y, Chen T, Hedemann S R and Yu T 2014 Crossover between non-Markovian, Markovian dynamics induced by a hierarchical environment (arXiv:1404.5280)
159. Lemos G B and Toscano F 2011 Phys. Rev. E 84 016220
160. García-Mata I, Pineda C and Wisniacki D 2012 Phys. Rev. A 86 022114
161. García-Mata I, Pineda C and Wisniacki D 2014 J. Phys. A: Math. Theor. 47 115301
162. Mazzola L, Laine E-M, Breuer H-P, Maniscalco S and Piilo J 2010 Phys. Rev. A 81 062120
163. Vacchini B 2013 Phys. Rev. A 87 030101(R)
164. Ban M, Kitajima S and Shibata F 2011 Phys. Rev. A 84 042115
165. Jiang M and Luo S 2013 Phys. Rev. A 88 034101
166. Benedetti C, Paris M G A and Maniscalco S 2014 Phys. Rev. A 89 012114
167. Chancellor N, Petri C and Haas S 2013 Phys. Rev. B 87 184302
168. McCloskey R and Paternostro M 2014 Phys. Rev. A 89 052120
169. Rebentrost P and Aspuru-Guzik A 2011 J. Chem. Phys. 134 101103
170. Kolli A, Nazir A and Olaya-Castro A 2011 J. Chem. Phys. 135 154112
171. Liu B-H, Li L, Huang Y-F, Li C-F, Guo G-C, Laine E-M, Breuer H-P and Piilo J 2011 Nature Phys. 7 931-4
172. Tang J-S, Li C-F, Li Y-L, Zou X-B, Guo G-C, Breuer H-P, Laine E-M and Piilo J 2012 EPL 97 10002
173. Liu B-H, Cao D-Y, Huang Y-F, Li C-F, Guo G-C, Laine E-M, Breuer H-P and Piilo J 2013 Sci. Rep. 3 1781
174. Wu S L, Huang X L, Wang L C and Yi X X 2010 Phys. Rev. A 82 052111
175. Haikka P, Goold J, McEndoo S, Plastina F and Maniscalco S 2012 Phys. Rev. A 85 060101(R)
176. Haikka P and Maniscalco S 2014 Open Syst. Inform. Dyn. 21 1440005
177. Yang H, Miao H and Chen Y 2011 Reveal non-Markovianity of open quantum systems via local operations (arXiv:1111.6079)
178. Smirne A, Mazzola L, Paternostro M and Vacchini B 2013 Phys. Rev. A 87 052129
179. Laine E-M, Piilo J and Breuer H-P 2010 EPL 92 60010
180. Smirne A, Breuer H-P, Piilo J and Vacchini B 2010 Phys. Rev. A 82 062114
181. Li C-F, Tang J-S, Li Y-L and Guo G-C 2011 Phys. Rev. A 83 064102
182. Smirne A, Brivio D, Cialdi S, Vacchini B and Paris M G A 2011 Phys. Rev. A 84 032112
183. Rodríguez-Rosario C A, Modi K, Mazzola L and Aspuru-Guzik A 2012 EPL 99 20010
184. Dajka J and Luczka J 2012 Rep. Math. Phys. 70 193
185. Wissmann S, Leggio B and Breuer H-P 2013 Detecting initial system-environment correlations: performance of various distance measures for quantum states (arXiv:1306.3248)
186. Liu J, Lu X-M and Wang X 2013 Phys. Rev. A 87 042103
187. Mannone M 2013 Characterization of the degree of musical non-Markovianity (arXiv:1306.0229)
188. Uhlmann A 1976 Rep. Math. Phys. 9 273
189. Jozsa R 1994 J. Mod. Opt. 41 2315
190. Molnár L 2001 Rep. Math. Phys. 48 299
191. Vasile R, Maniscalco S, Paris M G A, Breuer H-P and Piilo J 2011 Phys. Rev. A 84 052118
192. Hübner M 1992 Phys. Lett. A 168 239
193. Venkataraman V, Plato A D K, Tufarelli T and Kim M S 2014 J. Phys. B: At. Mol. Opt. Phys. 47 015501
194. Vasile R, Galve F and Zambrini R 2014 Phys. Rev. A 89 022109
195. Hao X, Wu W and Zhu S 2013 Nonunital non-Markovian dynamics induced by a spin bath, interplay of quantum Fisher information (arXiv:1311.5952)
196. Chancellor N, Petri C, Campos Venuti L, Levi A F J and Haas S 2014 Phys. Rev. A 89 052119
197. Rajagopal A K, Usha Devi A R and Rendell R W 2010 Phys. Rev. A 82 042107
198. Lindblad G 1975 Commun. Math. Phys. 40 147
199. Uhlmann A 1977 Commun. Math. Phys. 54 21
200. Lesniewski A and Ruskai M B 1999 J. Math. Phys. 40 5702
201. Mosonyi M and Hiai F 2011 IEEE Trans. Inform. Theory 57 2474
202. Furuichi S, Yanagi K and Kuriyama K 2004 J. Math. Phys. 45 4868
203. Kastoryano M J 2011 Quantum Markov chain mixing and dissipative engineering PhD Thesis University of Copenhagen
204. Usha Devi A R, Rajagopal A K and Sudha 2011 Phys. Rev. A 83 022109
205. Holevo A S 1982 Probabilistic and Statistical Aspects of Quantum Theory (Amsterdam: North-Holland)
206. Braunstein S L and Caves C M 1994 Phys. Rev. Lett. 72 3439
207. Lu X-M, Wang X and Sun C P 2010 Phys. Rev. A 82 042103
208. Hao X, Tong N-H and Zhu S 2013 J. Phys. A: Math. Theor. 46 355302
209. Bylicka B, Chrus̈ciński D and Maniscalco S 2013 Non-Markovianity as a Resource for Quantum Technologies (arXiv:1301.2585)
210. Wilde M M 2013 Quantum Information Theory (Cambridge: Cambridge University Press)
211. Addis C, Brebner G, Haikka P and Maniscalco S 2014 Phys. Rev. A 89 024101
212. Lorenzo S, Plastina F and Paternostro M 2013 Phys. Rev. A 88 020102(R)
213. Plastina F, Sindona A, Goold J, Lo Gullo N and Lorenzo S 2013 Open Syst. Inform. Dyn. 20 1340005
214. Tufarelli T, Kim M S and Ciccarello F Non-Markovianity of a quantum emitter in front of a mirror (arXiv:1312.3920)
215. Plenio M B and Virmani S 2007 Quant. Inform. Comput. 7 1
216. Vedral V, Plenio M B, Rippin M A and Knight P L 1997 Phys. Rev. Lett. 78 2275
217. Vedral V and Plenio M B 1998 Phys. Rev. A 57 1619
218. Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865
219. Lorenzo S, Plastina F and Paternostro M 2011 Phys. Rev. A 84 032124
220. Wu S-T 2012 Chin. J. Phys. 50 118
221. Zhou D and Joynt R 2012 Quantum Inform. Process. 11 571
222. Chiuri A, Greganti C, Mazzola L, Paternostro M and Mataloni P 2012 Sci. Rep. 2 968
223. Henderson L and Vedral V 2001 J. Phys. A: Math. Gen. 34 6899
224. Fanchini F F, Karpat G, Çakmak B, Castelano L K, Aguilar G H, Jiménez Farías O, Walborn S P, Souto Ribeiro P H and de Oliveira M C 2014 Non-Markovianity through accessible information (arXiv:1402.5395)
225. Cialdi S, Brivio D, Tesio E and Paris M G A 2011 Phys. Rev. A 83 042308
226. Luo S, Fu S and Song H 2012 Phys. Rev. A 86 044101
227. Fanchini F F, Karpat G, Castelano L K and Rossatto D Z 2013 Phys. Rev. A 88 012105
228. D'Arrigo A, Benenti G, Lo Franco R, Falci G and Paladino E 2014 Hidden entanglement, system-environment information flow, non-Markovianity (arXiv:1402.1948)
229. Zurek W H 2000 Ann. Phys., Berlin 9 855
230. Ollivier H and Zurek W H 2001 Phys. Rev. Lett. 88 017901
231. Modi K, Brodutch A, Cable H, Paterek T and Vedral V 2012 Rev. Mod. Phys. 84 1655
232. Streltsov A, Kampermann H and Bruß D 2011 Phys. Rev. Lett. 107 170502
233. Ciccarello F and Giovannetti V 2012 Phys. Rev. A 85 010102(R)
234. Girolami D and Adesso G 2012 Phys. Rev. Lett. 108 150403
235. Alipour S, Mani A and Rezakhani A T 2012 Phys. Rev. A 85 052108
236. Haikka P, Johnson T H and Maniscalco S 2013 Phys. Rev. A 87 010103(R)
237. Zhang Y-J, Han W, Shan C-J and Xia Y-J 2011 Quantum correlations dynamics under different non-markovian environmental models (arXiv:1111.2423)
238. Rodríguez-Rosario C A, Modi K, Kuah A, Shaji A and Sudarshan E C G 2008 J. Phys. A: Math. Theor. 41 205301
239. Shabani A and Lidar D A 2009 Phys. Rev. Lett. 102 100402
240. Rodríguez-Rosario C A, Modi K and Aspuru-Guzik A 2010 Phys. Rev. A 81 012313
241. Brodutch A, Datta A, Modi K, Rivas A and Rodríguez-Rosario C A 2013 Phys. Rev. A 87 042301
242. Sabapathy K K, Ivan J S, Ghosh S and Simon R 2013 Quantum discord plays no distinguished role in characterization of complete positivity: Robustness of the traditional scheme (arXiv:1304.4857)
243. Buscemi F 2013 Complete positivity in the presence of initial correlations: necessary, sufficient conditions given in terms of the quantum data-processing inequality (arXiv:1307.0363)
244. Dominy J M, Shabani A and Lidar D A 2013 A general framework for complete positivity (arXiv:1312.0908)
245. Plenio M B 2005 Phys. Rev. Lett. 95 090503
246. Chen Q, Zhang C, Yu S, Yi X X and Oh C H 2011 Phys. Rev. A 84 042313
247. Hall M J W 2008 J. Phys. A: Math. Theor. 41 269801
248. Chrus̈ciński D, Kossakowski A, Aniello P, Marmo G and Ventriglia F 2010 Open Syst. Inform. Dyn. 17 255
249. Audenaert K M R and Plenio M B 2006 New J. Phys. 8 266
250. Brandão F G S L and Plenio M B 2008 Nature Phys. 4 873
251. Gour G and Spekkens R W 2008 New J. Phys. 10 033023
252. Brandão F G S L, Horodecki M, Oppenheim J, Renes J M and Spekkens R W 2013 Phys. Rev. Lett. 111 250404
253. Veitch V, Hamed Mousavian S A, Gottesman D and Emerson J 2014 New J. Phys. 16 013009
254. Gour G, Müller M P, Narasimhachar V, Spekkens R W and Yunger Halpern N 2013 The resource theory of informational nonequilibrium in thermodynamics (arXiv:1309.6586)
255. Baumgratz T, Cramer M and Plenio M B 2013 Quantifying coherence (arXiv:1311.0275)
256. de Vicente J I 2014 On nonlocality as a resource theory, nonlocality measures (arXiv:1401.6941)
257. Sindona A, Goold J, Lo Gullo N, Lorenzo S and Plastina F 2013 Phys. Rev. Lett. 111 165303
258. Borrelli M, Haikka P, De Chiara G and Maniscalco S 2013 Phys. Rev. A 88 010101(R)
259. Borrelli M and Maniscalco S 2014 Effect of temperature on non-Markovian dynamics in Coulomb crystals (arXiv:1404.0149)
260. Chin A W, Huelga S F and Plenio M B 2012 Phys. Rev. Lett. 109 233601
261. Matsuzaki Y, Benjamin S C and Fitzsimons J 2011 Phys. Rev. A 84 012103
262. Laine E-M, Breuer H-P and Piilo J 2014 Sci. Rep. 4 4620
263. Xiang G-Y, Hou Z-B, Li C-F, Guo G-C, Breuer H-P, Laine E-M and Piilo J 2014 Nonlocal memory assisted entanglement distribution in optical fibers (arXiv:1401.5091)