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Divisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps

Publicated to:Physical Review Letters. 121 (8): 080407- - 2018-08-24 121(8), DOI: 10.1103/PhysRevLett.121.080407

Authors: Chru?ci?ski D; Rivas A; Størmer E

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Abstract

© 2018 American Physical Society. We analyze the relation between completely positive (CP) divisibility and the lack of information backflow for an arbitrary - not necessarily invertible - dynamical map. It is well known that CP divisibility always implies a lack of information backflow. Moreover, these two notions are equivalent for invertible maps. In this Letter, it is shown that for a map which is not invertible the lack of information backflow always implies the existence of a completely positive propagator which, however, needs not be trace preserving. Interestingly, for a wide class of image nonincreasing dynamical maps, this propagator becomes trace preserving as well, and hence, the lack of information backflow implies CP divisibility. This result sheds new light into the structure of the time-local generators giving rise to CP-divisible evolutions. We show that if the map is not invertible then positivity of dissipation/decoherence rates is no longer necessary for CP divisibility.

Keywords

Reduced inequalities

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Physical Review Letters due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2018, it was in position 6/81, thus managing to position itself as a Q1 (Primer Cuartil), in the category Physics, Multidisciplinary. Notably, the journal is positioned above the 90th percentile.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.39. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Weighted Average of Normalized Impact by the Scopus agency: 2.97 (source consulted: FECYT Feb 2024)
  • Field Citation Ratio (FCR) from Dimensions: 44.6 (source consulted: Dimensions May 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-05-31, the following number of citations:

  • WoS: 32
  • Scopus: 57
  • Open Alex: 66
  • OpenCitations: 55

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-05-31:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 27.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 27 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 1.25.
  • The number of mentions on the social network X (formerly Twitter): 2 (Altmetric).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.
Continuing with the social impact of the work, it is important to emphasize that, due to its content, it can be assigned to the area of interest of ODS 10 - Reduce inequality within and among countries, with a probability of 53% according to the mBERT algorithm developed by Aurora University.

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: Norway; Poland.