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arXiv:2603.13712

Effective Transition from Weak to Essential Non-Markovianity Induced by Coarse-Graining

Gabriel M. Arantes, Barbara Amaral, Nadja K. Bernardes

quant-phSubmitted Mar 14, 2026• Announced Mar 17, 2026• 0 citations• Revised Aug 17, 2026 (v3)
v1 · Mar 14, 2026v2 · May 6, 2026v3 · Aug 17, 2026
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Abstract

Quantum channels generally reduce the distinguishability of quantum states, thereby constraining information transmission and processing in open quantum systems. While it is known that distinguishability can be partially recovered through suitable post-processing protocols, a systematic characterization of the maximal achievable gain has remained elusive. Here, we establish a general framework to determine and optimize the recovery of distinguishability induced by a quantum channel. We introduce an algorithm that identifies the optimal implementation of a multi-copy coarse-graining protocol applicable to arbitrary channels. Within this framework, we derive a general upper bound on the attainable distinguishability gain and quantify the performance of the protocol through its tightness relative to this bound. Our results show that collective coarse-graining can lead to effective dynamics exhibiting the operational signatures of essential non-Markovianity even when the underlying microscopic dynamics remain weakly non-Markovian. A detailed analysis reveals a nontrivial trade-off between mathematical optimality (bound saturation) and operational optimality, together with a strong dependence on both the input ensemble and the number of copies. Taken together, these findings provide a unified and quantitative framework to assess, optimize, and interpret distinguishability recovery in open quantum systems while showing how collective processing can qualitatively modify the operational memory properties of effective dynamical descriptions.

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Quantum channels generally reduce the distinguishability of quantum states, thereby constraining information transmission and processing in open quantum systems. While it is known that distinguishability can be partially recovered through suitable post-processing protocols, a systematic characterization of the maximal achievable gain has remained elusive. Here, we establish a general framework to determine and optimize the recovery of distinguishability induced by a quantum channel. We introduce an algorithm that identifies the optimal implementation of a multi-copy coarse-graining protocol applicable to arbitrary channels. Within this framework, we derive a general upper bound on the attainable distinguishability gain and quantify the performance of the protocol through its tightness relative to this bound. Our results show that collective coarse-graining can lead to effective dynamics exhibiting the operational signatures of essential non-Markovianity even when the underlying microscopic dynamics remain weakly non-Markovian. A detailed analysis reveals a nontrivial trade-off between mathematical optimality (bound saturation) and operational optimality, together with a strong dependence on both the input ensemble and the number of copies. Taken together, these findings provide a unified and quantitative framework to assess, optimize, and interpret distinguishability recovery in open quantum systems while showing how collective processing can qualitatively modify the operational memory properties of effective dynamical descriptions.
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Starting from a coarse-grained map of a quantum many-body system, we construct the inverse map that assigns a microscopic state to a coarse-grained state based on the maximum entropy principle. Assuming unitary evolution in the microscopic system, we examine the resulting dynamics in the coarse-grained system using the assignment map. We investigate both a two-qubit system, with \swap\ and controlled-\textsc{not}\ gates, and nnn-qubit systems, configured either in an Ising spin chain or with all-to-all interactions. We demonstrate that these dynamics exhibit atypical quantum behavior, such as nonlinearity and non-Markovianity. Furthermore, we find that these dynamics depend on the initial coarse-grained state and establish conditions for general microscopic dynamics under which linearity is preserved. As the effective dynamics induced by our coarse-grained description of many-body quantum systems diverge from conventional quantum behavior, we anticipate that this approach could aid in describing the quantum-to-classical transition and provide deeper insights into the effects of coarse graining on quantum systems.
In this work, we investigate the non-Markovian features of the Adapted Caldeira-Leggett model, a computationally efficient framework recently proposed to capture the essential physics of the standard Caldeira-Leggett model. While this effective model has been previously validated for decoherence and einselection, its ability to reproduce memory effects remains to be explored. By exploiting the model's capability to explicitly track both system and environment degrees of freedom, we provide a detailed characterization of non-Markovianity through the lens of information backflow. We evaluate the buildup of system-environment correlations and the corresponding modifications of the environmental state, assessing a quantitative upper bound for the revival of distinguishability in the reduced dynamics. Our results, obtained by comparing different distinguishability quantifiers such as trace distance and the square root of the Jensen-Shannon divergence, show that while correlations are primarily sensitive to coupling strength, environmental state changes are more heavily influenced by temperature. Our analysis substantiates the physical interpretation of the distinguishability-based approach to non-Markovianity, and confirms this variant of the Caldeira-Leggett model as a reliable tool for exploring the microscopic origins of different fundamental phenomena in quantum mechanics.
Entanglement and state distinguishability have long been central topics in quantum foundations. While each has developed into a rich subject in its own right, they can be connected through measurements in complementary bases. This connection provides insights into quantum and classical correlations and underlies many information-processing tasks, most notably quantum error correction (QEC). However, it has remained largely open whether the connection between entanglement and distinguishability extends to general measurements without assuming complementarity. We answer this question in the affirmative: the key is irreducibility induced by measurements, a much more relaxed condition than complementarity. Specifically, for POVMs satisfying an irreducibility condition, we establish a quantitative relation between the infidelity of one-sided local transformation into a maximally entangled state and the failure probability in state discrimination. We then characterize when both errors can vanish simultaneously. Our results have direct applications to entanglement distillation and QEC. Their errors can be certified by estimating classical input-output correlations from experimentally accessible local measurements, without requiring complementarity. The results also extend to quantum measurement theory. We derive novel trade-off relations that bridge two historically distinct approaches: information gain--irreversibility and observable noise--disturbance. Our connection between entanglement and distinguishability via irreducibility thus offers a common framework for entanglement distillation, QEC, and measurement trade-offs.
Understanding whether the features of open quantum dynamics are genuinely quantum remains a central challenge in quantum dynamics. Even though the non-Markovian behavior of quantum dynamics has been widely investigated across different settings, there is still no consensus on which properties of a dynamics reflect genuine quantum features and which arise from classical or non-genuine quantum sources. In this review, we provide detailed information on recent developments in characterizing quantum non-Markovianity based on information backflow and the nature of its origin. We also present a survey on how various approaches separate classical and quantum contributions, as well as how they define operational tasks that reveal genuine quantum non-Markovianity. We analyze several frameworks, including state-distinguishability -based, channel-based (``CP-divisibility''), and process-tensor methods. For each framework, we outline the underlying physical motivation, the criteria proposed to distinguish genuine quantum non-Markovianity from practical or apparent memory effects. We further compare different approaches and their strengths and limitations. The review aims to clarify the conceptual and operational aspects of quantum non-Markovian processes based on their nature and to provide a foundation for future research on quantum non-Markovianity and its role in advancing quantum information science and technology.