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Causal and Noncausal Revivals of Information: A New Regime of Non-Markovianity in Quantum Stochastic Processes

Francesco Buscemi1,*, Rajeev Gangwar2, Kaumudibikash Goswami3,†, Himanshu Badhani4,5,6, Tanmoy Pandit7, Brij Mohan2, Siddhartha Das6,‡, and Manabendra Nath Bera2,§

  • *Contact author: buscemi@nagoya-u.jp
  • †Contact author: goswami.kaumudibikash@gmail.com
  • ‡Contact author: das.seed@iiit.ac.in
  • §Contact author: mnbera@gmail.com
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PRX Quantum 6, 020316 – Published 23 April, 2025

DOI: https://doi.org/10.1103/PRXQuantum.6.020316

Abstract

The study of information revivals, witnessing the violation of certain data-processing inequalities, has provided an important paradigm in the study of non-Markovian quantum stochastic processes. Although often used interchangeably, we argue here that the notions of “revivals” and “backflows,” i.e., flows of information from the environment back into the system, are distinct: an information revival can occur without any backflow ever taking place. In this paper, we examine in detail the phenomenon of noncausal revivals and relate them to the theory of short Markov chains and squashed non-Markovianity. We also provide an operational condition, in terms of system-only degrees of freedom, to witness the presence of genuine backflow that cannot be explained by noncausal revivals. As a byproduct, we demonstrate that focusing on processes with genuine backflows, while excluding those with only noncausal revivals, resolves the issue of nonconvexity of Markovianity, thus enabling the construction of a convex resource theory of genuine quantum non-Markovianity.

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Popular Summary

The concept of information revivals plays a pivotal role in the study of non-Markovian quantum stochastic processes. In this paper, we present compelling evidence that distinguishes between genuine backflows and noncausal revivals.

We demonstrate that quantum non-Markovianity can manifest in the absence of an actual backflow of information, which we argue is an artifact of the dynamics. We provide the operational conditions for genuine backflow leading to genuine non-Markovianity. We resolve several conceptual issues associated with non-Markovianity, in particular its lack of convexity and the resulting inability to describe it in a straightforward manner from a resource-theoretic perspective, thus paving the way for the formulation of a convex resource theory of genuine quantum non-Markovianity and its usefulness as a quantum resource in quantum information theory, including quantum thermodynamics, quantum communication, quantum dynamics, and causality.

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PRX Quantum 6, 020316– Published 23 April, 2025
  • Received 22 May 2024
  • Revised 25 February 2025
  • Accepted 5 March 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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