In this work, we analyze the so-called Superactivation of Backflow of Information, namely the activation of memory effects for a bipartite system that are not detectable when only one party is considered. In particular, we study this phenomenon from the point of view of entropy revivals. We prove that such an effect is never manifested as revivals of the 2-Renyi entropy or, equivalently, of the purity of the state. Conversely, we show that the von Neumann entropy is able to expose SBFI for a class of non-Markovian evolutions.
BenattiF.ChruścińskiD.FilippovS. (2017). Tensor power of dynamical maps and positive versus completely positive divisibility. Physical Review A, 95(1), Article 012112. https://doi.org/10.1103/PhysRevA.95.012112
BenattiF.NarnhoferH. (1988). Entropy behaviour under completely positive maps. Letters in Mathematical Physics, 15(4), 325–334. https://doi.org/10.1007/BF00419590
6.
BhatiaR. (2009). Positive definite matrices. Princeton University Press.
7.
BreuerH. P.LaineE. M.PiiloJ. (2009). Measure for the degree of non-Markovian behavior of quantum processes in Open Systems. Physical Review Letters, 103(21), Article 210401. https://doi.org/10.1103/PhysRevLett.103.210401
8.
BuscemiF.DattaN. (2016). Equivalence between divisibility and monotonic decrease of information in classical and quantum stochastic processes. Physical Review A, 93(1), Article 012101. https://doi.org/10.1103/PhysRevA.93.012101
9.
BuscemiF.GangwarR.GoswamiK.BadhaniH.PanditT.MohanB.DasS.BeraM. N. (2025). Causal and noncausal revivals of information: A new regime of non-markovianity in quantum stochastic processes. PRX Quantum, 6(2), Article 020316. https://doi.org/10.1103/PRXQuantum.6.020316
ChruścińskiD.KossakowskiA.RivasÁ. (2011). Measures of non-Markovianity: Divisibility versus backflow of information. Physical Review A, 83(5), Article 052128. https://doi.org/10.1103/PhysRevA.83.052128
12.
ChruścińskiD.MacchiavelloC.ManiscalcoS. (2017). Detecting non-markovianity of quantum evolution via spectra of dynamical maps. Physical Review Letters, 118(8), Article 080404. https://doi.org/10.1103/PhysRevLett.118.080404
DasS.KhatriS.SiopsisG.WildeM. M. (2018). Fundamental limits on quantum dynamics based on entropy change. Journal of Mathematical Physics, 59(1), 4997044. https://doi.org/10.1063/1.4997044
16.
DaviesE. B. (1974). Markovian master equations. Communications in Mathematical Physics, 39(2), 91–110. https://doi.org/10.1007/BF01608389
17.
DümckeR. (1985). The low density limit for an n-level system interacting with a free bose or fermi gas. Communications in Mathematical Physics, 97, 331–359. https://doi.org/10.1007/BF01213401
18.
FilippovS. N.GlinovA.LeppäjärviL. (2020). Phase covariant qubit dynamics and divisibility. Lobachevskii Journal of Mathematics, 41(4), 617–630. https://doi.org/10.1134/S1995080220040095
19.
GoriniV.KossakowskiA. (1976). N-level system in contact with a singular reservoir. Journal of Mathematical Physics, 17(7), 1298–1305. https://doi.org/10.1063/1.523057
20.
GoriniV.KossakowskiA.SudarshanE. C. G. (1976). Completely positive dynamical semigroups of N-level systems. Journal of Mathematical Physics, 17(5), 821–825. https://doi.org/10.1063/1.522979
KossakowskiA. (1972). On necessary and sufficient conditions for a generator of a quantum dynamical semi-group. Bull. Acad. Pol. Sci. Ser. Math. Astr. Phys, 20, 1021.
23.
LindbladG. (1976). On the generators of quantum dynamical semigroups. Communications in Mathematical Physics, 48(2), 119–130. https://doi.org/10.1007/BF01608499
Muratore-GinanneschiP.KimuraG.ChruścińskiD. (2025). Universal bound on the relaxation rates for quantum markovian dynamics. Journal of Physics A: Mathematical and Theoretical, 58(4), Article 045306. https://doi.org/10.1088/1751-8121/adaa3f
Pérez-GarcíaD.WolfM. M.PetzD.RuskaiM. B. (2006). Contractivity of positive and trace-preserving maps under Lp norms. Journal of Mathematical Physics, 47(8), 2218675. https://doi.org/10.1063/1.2218675
29.
RajagopalA.Usha DeviA.RendellR. (2010). Kraus representation of quantum evolution and fidelity as manifestations of markovian and non-markovian forms. Physical Review A, 82(4), Article 042107. https://doi.org/10.1103/PhysRevA.82.042107
30.
ReedM.SimonB. (1975). Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness. Academic Press.
31.
RivasÁ. (2022). Unidirectional information flow and positive divisibility are nonequivalent notions of quantum markovianity for noninvertible dynamics. Open Systems & Information Dynamics, 29(03), Article 2250012. https://doi.org/10.1142/S1230161222500123
32.
RivasÁ.HuelgaS. F. (2012). Open quantum systems: An introduction. SpringerBriefs in physics: Springer.
33.
RivasÁ.HuelgaS. F.PlenioM. B. (2014). Quantum non-markovianity: Characterization, quantification and detection. Reports on progress in physics. Physical Society (Great Britain), 77(9), Article 094001. https://doi.org/10.1088/0034-4885/77/9/094001
34.
SettimoF.BreuerH. P.VacchiniB. (2022). Entropic and trace-distance-based measures of non-Markovianity. Physical Review A, 106(4), Article 042212. https://doi.org/10.1103/PhysRevA.106.042212
35.
SmirneA.MegierN.VacchiniB. (2022). Holevo skew divergence for the characterization of information backflow. Physical Review A, 106(1), Article 012205. https://doi.org/10.1103/PhysRevA.106.012205
36.
VacchiniB. (2024). Comparison of distances and entropic distinguishability quantifiers for the detection of memory effects. International Journal of Quantum Information, 22(06), 17419. https://doi.org/10.1142/S0219749924500072
37.
WatrousJ. (2018). The theory of quantum information. Cambridge University Press.
38.
WißmannS.BreuerH. P.VacchiniB. (2015). Generalized trace-distance measure connecting quantum and classical non-Markovianity. Phys. Rev. A, 92(4), Article 042108. https://doi.org/10.1103/PhysRevA.92.042108
