A universal approach to decoherence control combined with quantum estimation theory reveals a critical behavior, akin to a phase transition, of the information obtainable by a qubit probe concerning the memory time of environmental fluctuations of generalized Ornstein-Uhlenbeck processes. The criticality is intrinsic to the environmental fluctuations but emerges only when the probe is subject to suitable dynamical control aimed at inferring the memory time. A sharp transition is anticipated between two dynamical phases characterized by either a short or long memory time compared to the probing time. This phase transition of the environmental information is a fundamental feature that characterizes open quantum-system dynamics and is important for attaining the highest estimation precision of the environment memory time under experimental limitations.
A universal approach to decoherence control combined with quantum estimation theory reveals a critical behavior, akin to a phase transition, of the information obtainable by a qubit probe concerning the memory time of environmental fluctuations of generalized Ornstein-Uhlenbeck processes. The criticality is intrinsic to the environmental fluctuations but emerges only when the probe is subject to suitable dynamical control aimed at inferring the memory time. A sharp transition is anticipated between two dynamical phases characterized by either a short or long memory time compared to the probing time. This phase transition of the environmental information is a fundamental feature that characterizes open quantum-system dynamics and is important for attaining the highest estimation precision of the environment memory time under experimental limitations.
Quantum probes offer a powerful platform for exploring environmental dynamics, particularly through their sensitivity to decoherence processes. In this work, we investigate the emergence of critical behavior in the estimation of the environmental memory time , modeled as an Ornstein–Uhlenbeck process characterized by a Lorentzian spectral density. Using dynamically controlled qubit-based sensors—realized experimentally via solid-state Nuclear Magnetic Resonance (NMR) and supported by numerical simulations—we implement tailored filter functions to interrogate the environmental noise spectrum and extract from its spectral width. Our results reveal a sharp transition in estimation performance between short-memory (SM) and long-memory (LM) regimes, reflected in a non-monotonic estimation error that resembles a phase transition. This behavior is accompanied by an avoided-crossing-like structure in the estimated parameter space, indicative of two competing solutions near the critical point. These features underscore the interplay between control, decoherence, and inference in open quantum systems. Beyond their fundamental significance, these critical phenomena offer a practical diagnostic tool for identifying dynamical regimes and optimizing quantum sensing protocols. By exploiting this criticality, our findings pave the way for adaptive control strategies aimed at enhancing precision in quantum parameter estimation—particularly in complex or structured environments such as spin networks, diffusive media, and quantum materials.
Environmental noise is a major source of decoherence and errors in quantum systems. In a non-Markovian environment, the noise has a finite correlation time, and the system can retain information about its previous interactions with the environment. Here, we investigate how such environmental memory can be observed through a finite-duration coherent quantum operation. Coherent control dynamically reshapes the stochastic coupling operator and thereby changes how two-time noise correlations affect the quantum process. For Ornstein-Uhlenbeck noise, we show analytically that two different limits reduce the information on the correlation time. In the short-memory limit, the leading dynamics depend on the integrated-noise combination σ/τc, where σ is the noise variance and τc is the correlation time, making these parameters locally degenerate. In the long-memory limit, the stochastic field becomes quasi-static during the operation, and sensitivity to the correlation time is suppressed. Exact stochastic simulations for a driven single-qubit Xπ rotation and a two-qubit exchange gate show that independent correlation-time information becomes largest between these limits, when the environmental and control timescales are comparable. Noncommuting controls enhance this information, whereas commuting controls do not. Simulations at different gate durations tg further show that the information window approximately follows the dimensionless correlation ratio τc/tg. These results provide a timescale-matching principle for probing finite-correlation non-Markovian noise with coherent quantum control.
We explore the ability of a qubit probe to characterize unknown parameters of its environment. By resorting to the quantum estimation theory, we analytically find the ultimate bound on the precision of estimating key parameters of a broad class of ubiquitous environmental noises ("baths") which the qubit may probe. These include the probe-bath coupling strength, the correlation time of generic types of bath spectra, and the power laws governing these spectra, as well as their dephasing times T2. Our central result is that by optimizing the dynamical control on the probe under realistic constraints one may attain the maximal accuracy bound on the estimation of these parameters by the least number of measurements possible. Applications of this protocol that combines dynamical control and estimation theory tools to quantum sensing are illustrated for a nitrogen-vacancy center in diamond used as a probe.
Quantum mechanics has both deepened our understanding of the physical reality and allowed development of quantum technologies beating their classical counterparts in efficiency, security, and sensitivity. As a major downside, the quantum properties behind these technologies are very sensitive to the effects the system’s interaction with its environment. The theory of open quantum systems describes how such interaction influences the system, and as a consequence, how the quantum features are lost, controlled, and possibly returned by manipulating the environment. This thesis begins with a short description of the most relevant features and results of the open quantum system theory. We continue by presenting some commonly used measures to quantify the information encoded in quantum systems and the correlations between spatially or temporally separated parties. The literature review ends with discussion of non-Markovianity and memory effects which combine the fields of open quantum systems and quantum information in a natural way. The rest of the thesis presents the main results of Publications I – VII. We study the memory effects and physicality conditions of open system dynamics described by the vast family of phase-covariant master equations. We show how the open quantum system picture can be exploited to design probing protocols to extract information without knowing how the probe and system interact. Such protocols are considered also from the point-of view of efficiently obtaining the information required in the probing, both in theory and by experimental implementation. The experiment serves also as evidence for applicability of recently developed geometric tools to design informationally incomplete measurements for solving so-called membership problems. We present and experimentally realize a protocol where control over intial correlations between polarization and frequency gives full freedom to implement any dephasing dynamics in the open system polarization, thus dictating how its information content changes in time. We study the two-qubit memory effects of dephasing dynamics and compare them to the effect of such noise in the transmission efficiency in superdense coding. Optimal noise configurations in different situations are found. Finally, we characterize the families of initial states for which the decay of quantum correlations depends or does not depend on the noise location.
This paper presents a formal framework framing quantum decoherence as an information-theoretic phase transition at the quantum-to-classical boundary. We demonstrate that environment-induced superselection (einselection) can be characterized as a true dynamical phase transition where the system-environment coupling strength acts as a thermodynamic control parameter, and the suppression of off-diagonal density matrix elements functions as an order parameter analogous to magnetization in the Ising model. Using quantum mutual information, von Neumann entropy, and entanglement entropy, we track the operational flow of information from a quantum system into environmental degrees of freedom, demonstrating how a singular classical reality emerges via the redundant copying of pointer states into environmental fragments—a process governed by Quantum Darwinism. We analyze a simulated spin-boson model and random unitary circuits with tunable dissipation, extracting clear signatures of criticality including power-law scaling and diverging correlation times at a critical threshold . Crucially, we connect this behavior to recent advancements (2023–2025) in mixed-state topological order, establishing that decoherence-induced transitions map onto anyon condensation transitions within an errorfield double formulation. Finally, we explore the foundational implications of this framework: it sharpens the measurement problem via informational symmetry breaking, reframes observation as a high-decoherence thermodynamic limit, and introduces a Gödelian perspective by demonstrating that determining the critical threshold for arbitrary many-body environments is formally undecidable due to the non-computability of the spectral gap in the thermodynamic limit.
From computers to medicine, miniaturization approaches the atomic scale, where device operation can be dominated by quantum effects that are strongly coupled to the local environment. These influences may be seen not as a nuisance, but rather a nearly untapped source of information about physical or biochemical processes playing out nearby. How can one extract maximum information from such fluctuations with an atomic probe, under typical experimental constraints? The authors use quantum estimation theory to outline a general strategy for dynamical measurement of a broad class of environmental processes.