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.
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.
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.
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.
This thesis presents a collection of projects spanning different sub-fields of quantum science, undertaken with the goal of understanding and advancing quantum technologies. Broadly, it can be divided into two thematic parts — parameter estimation and open system dynamics. Each project addresses inverse and ill-posed problems in Physics, which lie at the heart of developing robust and scalable quantum devices.A central theme in quantum technology is the challenge of inference of microscopic system parameters from limited, indirect observations. The first part of the thesis investigates this through the problem of Hamiltonian reconstruction via local measurements. Indirect estimation of couplings in quantum systems relies on the measurement of the spectrum and the overlap of eigenvectors with some reference state. For a one-dimensional chain, this data can be obtained by local measurement on one end of the chain, thereby reducing the need for full Hamiltonian tomography. Information about couplings is extracted from the temporal data obtained by measuring the expectation values of the time evolution 𝑒−𝑖𝐻𝑡 for a reference state. In Chapter 3, we analyze the robustness of this estimation scheme under perturbations arising from beyond nearest neighbour interactions. We show that the error scales linearly with the strength of such interactions and on average, the error increases with the distance of interaction between sites.Chapter 4 examines whether coupling information can be extracted from local thermal measurements, using expectation values of the Gibbs state at varying temperatures rather than temporal data. We develop a procedure to obtain the coefficients of the Taylor expansion of these expectation values and relate them to the Hamiltonian parameters. For very small chains, this mapping can be carried out analytically, while for larger systems it reveals the algebraic structure that links local measurements to the underlying couplings and highlights the trade-offs between measurement resources, numerical stability, and identifiability. The analysis also clarifies how additional local fields or self-interaction terms enhance the information content of thermal data, suggesting a role for local thermal probes as practical tools for Hamiltonian verification and parameter estimation.Building on the ideas of controlling and inferring information about a quantum system, we now turn to active intervention through adaptive measurement. In Chapter 5, we develop a process tensor driven procedure for cooling the spin bath that is coupled to a nitrogen vacancy (NV) center in diamond. By modeling the sequence of intermediate quantum instruments acting on a correlated system-environment process, we optimize a pair of completely positive (CP) maps to maximize the population in a lower-energy state. Unlike existing approaches that rely solely on positive operator valued measures (POVMs), our method encompasses a broader class of CP maps, including adaptive feed-forward and mixed operations. We explicitly account for initial correlation between system and environment and distinguish between the controllable and uncontrollable parts of the dynamics. Our framework supports non-Markovian operations and benchmarks them against optimal Markovian strategies. The optimization is performed via Semi-definite Programming (SDP), ensuring global optimality. We also assess robustness to Hamiltonian noise and provide a proposal for implementation using NV center in diamonds.Finally, Chapter 6 explore the relaxation dynamics of topological qubits, focusing on a tetron qubit formed from two uncoupled Kitaev chains coupled to a finite fermionic bath. Using the correlation matrix formalism for purely quadratic couplings, we show that the relaxation is fundamentally independent of temperature when either the bath is large, or the zero-mode energy of the system is close to zero. This challenges a key assumption in the field that cooling enhances coherence. Interestingly, we find that introducing glassy disorder into the system slows down relaxation, offering a potential route to prolong qubit lifetimes.Collectively, these studies form a coherent narrative around extraction, control and utilization of quantum information under fundamental constraints. By tackling such inverse and often ill-posed problems, this thesis contributes new tools and insights essential for the realization of future quantum technologies.
Nuclear Magnetic Resonance (NMR) plays a central role in developing quantum information sciences and technologies. Key features such as its non-invasive nature and the ability to process information on nuclear spins by versatile quantum control designs with electromagnetic fields, have made NMR to become a powerful technique for sensing systems from atomic and molecular scales with spectroscopy to millimeters in imaging. This brief overview provides quantum sensing tools with which we are contributing from Latin America, by combining quantum dynamical control and estimation strategies with NMR methods to probe physical, chemical, and biological processes. It introduces the basic and key concepts on how controlled spin-sensors can monitor the correlation dynamics of their environment, and selectively and optimally infer its relevant parameters. Then these concepts are illustrated with state-of-the-art implementations for characterizing (i) biological tissue microstructure with diffusion weighting imaging, (ii) quantum information dynamics and scrambling in out-of-equilibrium systems with solid-state NMR quantum simulations, and (iii) molecular structures by selective estimation of spin–spin couplings and online learning control designs with experimental proposals. We expect these concepts will motivate the development of quantum dynamical control of spin sensors to monitor systems in a variety of fields, and in particular to exploit the non-invasive strength of NMR, e.g. in biomedical diagnosis. • Quantum control and estimation tools probe physical, chemical, biological processes. • Efficient quantum sensing for maximizing relevant environmental information. • Biological tissue microstructure characterization with diffusion weighting imaging. • Assessing fragility of quantum information dynamics in out-of-equilibrium systems. • Selective estimation of spin–spin couplings and online learning control designs.
Abstract The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcomewhen using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining general precision bounds in the presence of an environment.We adopt a complementary approach,wherewe first analyze the problem within the general framework of describing the quantum systems in terms of quantum dynamical maps and then relate this abstract formalism to a microscopic description of the system’s dissipative time evolution.We will show that although some forms of noise do render quantum systems standard quantum limited, precision beyond classical bounds is still possible in the presence of different forms of local environmental fluctuations.
The dynamics of quantum systems are unavoidably influenced by their environment, but in turn observing a quantum system (probe) can allow one to measure its environment: Measurements and controlled manipulation of the probe such as dynamical decoupling sequences as an extension of the Ramsey interference measurement allow to spectrally resolve a noise field coupled to the probe. Here, we introduce fast and robust estimation strategies for the characterization of the spectral properties of classical and quantum dephasing environments. These strategies are based on filter function orthogonalization, optimal control filters maximizing the relevant Fisher Information and multi-qubit entanglement. We investigate and quantify the robustness of the schemes under different types of noise such as finite-precision measurements, dephasing of the probe, spectral leakage and slow temporal fluctuations of the spectrum.