In the quantum world, memory isn’t a simple feature you store and recall. It’s a property of how a tiny system—think a single qubit or a pair of them—talks with its surroundings. When a quantum object sits in an environment, information leaks away. But sometimes that same environment can push information back, like a shy echo returning after a quiet moment. This back-and-forth is the heartbeat of non-Markovian dynamics, a term that sounds technical but translates to a very human idea: memory matters, especially when you want quantum devices to perform reliably. For technologies ranging from precision sensors to secure quantum communication, understanding and harnessing memory effects could be the difference between fragile proofs of concept and robust real-world tools. Memory backflow isn’t just a curiosity; it’s a lever researchers want to turn.
The study behind this shift comes from Mohammed V University in Rabat, Morocco, where Yassine Dakir, Abdallah Slaoui, and Rachid Ahl Laamara lead a team spanning the LPHE-Modeling and Simulation and the Centre of Physics and Mathematics, with collaborators at the Center of Excellence in Quantum and Intelligent Computing at Prince Sultan University. Their aim is to detect and quantify non-Markovianity—the fingerprint of memory—in a way that feels natural to experimentalists: through quantum coherence. They hook coherence to the Kirkwood-Dirac quasiprobability, a two-basis representation of a quantum state, and show that the imaginary part of this distribution, tracked over time, can reveal whether information is flowing back from the environment. It’s a conceptual bridge between abstract math and something a lab can actually measure.
What Kirkwood-Dirac coherence is
At its heart, the Kirkwood-Dirac (KD) quasiprobability is a way of describing a quantum state using two different reference views. Imagine watching a dancer with two different pair of glasses: one emphasizes a fixed, incoherent basis, while the other lets you see how the state looks when you reframe the measurement. The KD quasiprobability PKD(µ, ν|ρ) encodes the overlaps between these bases and the state ρ, and because quantum mechanics is inherently noncommutative, PKD can take on complex values. That might sound abstract, but it’s precisely what makes the imaginary part of PKD so revealing: it ties directly to the coherence of the state with respect to the incoherent reference basis. In the paper, the authors formalize a quantity CKD[ρ; {Xµ}] that captures this coherence—maximized over all choices of the second basis {|ν⟩}—and then relate it to how the state evolves under open-system dynamics. Two-basis lens is a good shorthand here: KD coherence is not a property tied to a single basis but to how the state looks when you allow a second, freely chosen viewpoint.
That KD-based coherence is designed to behave like a resource: it should be zero if the state is incoherent in the chosen basis, it should be convex under probabilistic mixtures, and it should not explode under simple, noise-free (unitary) transformations. Crucially for this story, the authors show it monotonically decreases under incoherent, memoryless maps. In plain terms: if the environment isn’t feeding memory back into the system, CKD should slide downward over time. If CKD ever climbs, that climb is a whisper that memory is back in play. The paper grounds these ideas with a set of properties that make CKD a sensible, physically meaningful beacon for non-Markovianity without injecting undue mathematical baggage into the experimental dialogue.
Seeing memory in motion through KD coherence
The authors’ core move is to define a time-dependent CKD, CKD[ρ(t); {Xµ}], and then look at how it changes. Because CKD cannot increase under purely incoherent, memoryless dynamics, any positive derivative with respect to time signals information reshaping the environment-to-system flow. They formalize a measure NCKD(Φt) by integrating the positive parts of this time derivative across the evolution. In other words, they quantify how much “breathing back” the system experiences by watching how the KD coherence responds as time unfolds. The effect is not forced into a single, fixed experiment; it is a property of the dynamics that can be observed across different setups, from simple single-qubit channels to more complex two-qubit arrangements.
The paper walks through concrete examples to anchor the idea. In a single-qubit dephasing channel—the archetype of a system losing phase information to its environment—the authors derive explicit expressions showing how a time-dependent function R(t) and a decay rate γ(t) govern CKD(t). When the effective decay rate γ(t) dips negative, the system briefly regains coherence, and CKD(t) rises. The environment’s memory, encoded in how γ(t) fluctuates, is then mapped onto a memoryiness parameter s that describes the reservoir’s spectral structure. For certain regimes—roughly when s climbs above a threshold around 2.2—the back-and-forth becomes pronounced, and CKD tracks it with a clear, measurable tail. In parallel, the familiar ℓ1-norm coherence sometimes mirrors this behavior, but CKD can reveal non-Markovian footprints that the older metric might miss. The upshot: CKD coherence is not just another flavor of coherence; it’s a specific, physically interpretable signal of memory in quantum dynamics.
The study also climbs into the realm of two-qubit systems, where the math gets richer and the patterns more nuanced. In a dephasing channel with a shared reservoir, the authors tune the two-qubit basis and compute the KD quasiprobability for particular initial states and couplings. They find that CKD can surface non-Markovianity in an intermediate regime of environment parameters and can show oscillations or partial revivals of coherence when memory returns. In the amplitude-damping scenario—an energy-loss channel common in quantum optics—the CKD measure similarly exhibits nonmonotonic behavior in non-Markovian regimes, with the imaginary part of the KD distribution acting as a diagnostic flare when information flows back. Across these cases, CKD’s behavior aligns with intuitive signs of memory—revivals, echoes, and backflow of information—while also linking to the broader concept of nonclassicality that physicists track in quantum states.
From theory to tech: implications for experiments and devices
One of the paper’s practical anchors is that CKD coherence can be evaluated without resorting to auxiliary quantum systems. In a field where many memory-detection schemes rely on entanglement with an extra qubit or a carefully prepared ancilla, the KD approach promises a more accessible path. The authors argue that CKD offers an experimentally friendly, physically transparent route to flag non-Markovian dynamics, which could accelerate the debugging and optimization of quantum devices operating in imperfect environments. That isn’t a theoretical nicety; it’s a potential plug-and-play advantage for laboratories building sensors, communication links, and computational hardware that must contend with real-world noise.
Beyond the immediacy of measurement practicality, the work points to a broader set of implications for quantum technologies. Non-Markovian environments aren’t universally bad: the memory backflow can, in some regimes, help preserve or even recover quantum resources that decohere away in a memoryless setting. If researchers can precisely map when and how memory reenters the dynamics, they can design environments or control strategies that exploit backflow to boost metrological precision, prolong entanglement in small quantum processors, or improve the robustness of quantum key distribution against noise. The KD-based framework gives a language and a toolkit for thinking about these trade-offs in concrete, testable terms.
Looking ahead, the authors emphasize that their measure—while powerful—does not replace all other non-Markovianity indicators. Instead, it adds a complementary perspective: a coherence-centric view tied to a physically meaningful quasiprobability distribution. In systems with richer correlations or more complicated dynamics, CKD and traditional measures may disagree, but that tension itself becomes a diagnostic feature, sharpening our understanding of when memory helps and when it hinders. The researchers explicitly hope their framework spurs further experiments and cross-disciplinary exploration, extending the reach of KD coherence from abstract quantum optics to biological-ish systems or even social-physics analogies where memory and information flow matter.
In short, this work reframes non-Markovianity as something you can read in the language of coherence, through a two-basis quasiprobability. It offers a practically accessible, conceptually sharp way to quantify memory effects in open quantum systems, demonstrated in clear, concrete qubit models. The study is a reminder that memory isn’t merely a nuisance to be avoided; in the quantum realm, it can be harnessed, steered, and read as a resource to make tomorrow’s quantum devices more reliable and capable.
Institutional note: The research is led by Yassine Dakir, Abdallah Slaoui, and Rachid Ahl Laamara, affiliated with Mohammed V University in Rabat (LPHE-Modeling and Simulation and CPM) and its partner institutions, with collaboration from the Center of Excellence in Quantum and Intelligent Computing at Prince Sultan University. The work showcases how a university in Rabat and its regional partners are contributing to a global conversation about quantum memory, coherence, and the practical paths from theory to experiment.
