Quantum systems are the foundation of quantum technology development. To harness these systems, one must extract information from them and be able to control their dynamics. This thesis presents a body of work, containing both published and unpublished papers, that focuses on two key research areas: quantum continuous measurement and quantum bath sensing. While these topics may seem distinct, they are fundamentally connected through the framework of open quantum systems. As such, this thesis is structured into two parts. The first part of this thesis is dedicated to diffusive continuous quantum measurement, where the system of interest is continuously monitored through a coupled Markovian bath or meter. A key challenge in this context is the numerical errors introduced in quantum trajectory simulations caused by the finite time resolution ( 𝑡) in real experiments. To address this, we propose a systematic framework to assess theoretical tools used in processing measurement records. Focusing on a single Lindblad channel, we analyze the errors of existing measurement (or Kraus) operators in literature, in orders of 𝑡 under conditions that ensure valid average evolution (complete positivity, convex linearity, and trace preservation). We also analyze a stronger condition: finding the order at which these existing measurement operators match the Lindblad equation. Based on these analyzes, we propose a Kraus operator that satisfies the conditions for valid quantum evolution and matches the Lindblad master equation to second order in 𝑡, surpassing all existing approaches. Moreover, to evaluate how well our operator reproduces exact quantum trajectories, we analyze two qubit measurement examples where exact maps can be derived: 𝑧-basis measurement and fluorescence (dissipative) measurement. We show analytically that our proposed operator achieves the smallest average trace distance to the exact quantum trajectories compared to existing methods. Finally, we extend this Kraus operator to multiple Lindblad channels with a driving Hamiltonian. We test our analytical findings numerically using the two qubit examples, considering both single and multiple Lindblad channels with a driving Hamiltonian. The numerical results confirm our theoretical predictions. The second part of this thesis focuses on quantum bath sensing, where we use a quantum system (qubit) to extract information about its surrounding baths. Specifically, we develop protocols to detect nonclassical pure-dephasing noise in a single-qubit system coupled to temporally correlated (non-Markovian) baths. Inspired by the Ramsey protocol, we introduce a coherent intervention (𝜋 2 -pulse) within the protocol, which can reveal the quantum noise - noise correlations affecting the probe qubit that originate from quantum degrees of freedom. Our protocols are simple, experimentally viable, and rigorously derived for general bath models. Using an exactly solvable bosonic bath model, we analyse how key noise parameters respond to fixed control schemes, identifying the optimal strategy for detecting the quantum noise. From the perspective of bath dynamics, we further decompose the qubit-bath state, demonstrating that only Gaussian components of the bath contribute to quantum noise, highlighting the bath's role in system dynamics. Finally, we extend the modified Ramsey protocol by incorporating multi-axis 𝜋 2 pulse and demonstrate that it can emulate the modified Ramsey protocol with any completely positive trace-preserving intervention. This applies to both Gaussian and non-Gaussian baths under the pure-dephasing assumption.
Quantum systems are the foundation of quantum technology development. To harness these systems, one must extract information from them and be able to control their dynamics. This thesis presents a body of work, containing both published and unpublished papers, that focuses on two key research areas: quantum continuous measurement and quantum bath sensing. While these topics may seem distinct, they are fundamentally connected through the framework of open quantum systems. As such, this thesis is structured into two parts. The first part of this thesis is dedicated to diffusive continuous quantum measurement, where the system of interest is continuously monitored through a coupled Markovian bath or meter. A key challenge in this context is the numerical errors introduced in quantum trajectory simulations caused by the finite time resolution ( 𝑡) in real experiments. To address this, we propose a systematic framework to assess theoretical tools used in processing measurement records. Focusing on a single Lindblad channel, we analyze the errors of existing measurement (or Kraus) operators in literature, in orders of 𝑡 under conditions that ensure valid average evolution (complete positivity, convex linearity, and trace preservation). We also analyze a stronger condition: finding the order at which these existing measurement operators match the Lindblad equation. Based on these analyzes, we propose a Kraus operator that satisfies the conditions for valid quantum evolution and matches the Lindblad master equation to second order in 𝑡, surpassing all existing approaches. Moreover, to evaluate how well our operator reproduces exact quantum trajectories, we analyze two qubit measurement examples where exact maps can be derived: 𝑧-basis measurement and fluorescence (dissipative) measurement. We show analytically that our proposed operator achieves the smallest average trace distance to the exact quantum trajectories compared to existing methods. Finally, we extend this Kraus operator to multiple Lindblad channels with a driving Hamiltonian. We test our analytical findings numerically using the two qubit examples, considering both single and multiple Lindblad channels with a driving Hamiltonian. The numerical results confirm our theoretical predictions. The second part of this thesis focuses on quantum bath sensing, where we use a quantum system (qubit) to extract information about its surrounding baths. Specifically, we develop protocols to detect nonclassical pure-dephasing noise in a single-qubit system coupled to temporally correlated (non-Markovian) baths. Inspired by the Ramsey protocol, we introduce a coherent intervention (𝜋 2 -pulse) within the protocol, which can reveal the quantum noise - noise correlations affecting the probe qubit that originate from quantum degrees of freedom. Our protocols are simple, experimentally viable, and rigorously derived for general bath models. Using an exactly solvable bosonic bath model, we analyse how key noise parameters respond to fixed control schemes, identifying the optimal strategy for detecting the quantum noise. From the perspective of bath dynamics, we further decompose the qubit-bath state, demonstrating that only Gaussian components of the bath contribute to quantum noise, highlighting the bath's role in system dynamics. Finally, we extend the modified Ramsey protocol by incorporating multi-axis 𝜋 2 pulse and demonstrate that it can emulate the modified Ramsey protocol with any completely positive trace-preserving intervention. This applies to both Gaussian and non-Gaussian baths under the pure-dephasing assumption.
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.
In the first part of this thesis, we investigate the dynamics of open quantum systems coupled in a purely dephasing way to their environment, which is a paradigmatic example of decoherent dynamics. We focus more specifically on the emergence of non-Markovian effects in the dynamics of such open systems. After reviewing different measures of non-Markovianity, we obtain an analytical expression for the reduced density operator of a finite-dimensional open system coupled with its environment through time-dependent purely dephasing interactions. When the system is initially uncorrelated with its environment, we obtain the time-local master equation that describes its dynamics. In this case, we also derive an exact expression for the witness of non-Markovianity based on the volume of accessible states of the open system. These results are then applied to spin systems coupled to either a spin or a bosonic environment. For spin environments, we study non-Markovianity for different ranges of interaction and in different thermodynamical limits. Moreover, the generation of entanglement between the open system and its environment as well as between spins within the open system is investigated. For bosonic environments, we study the effect of the initial state of the environment on non-Markovianity. We also show that time-dependent modulations of the system-environment coupling can dramatically alter the non-Markovian behavior of the open system. Finally, we consider the case of an open quantum system simultaneously coupled to spin and bosonic baths. In that case, we study how the coupling between the different baths and of the presence of initial correlations in the environment affect the non-Markovianity displayed by the open quantum system. The second part of this thesis is a contribution to the investigation of how quantum systems can be used to process information. More precisely, we focus on the implementation of gate-based quantum computing using neutral atoms trapped in optical or magnetic lattices and interacting through dipole-dipole interactions when excited to Rydberg states. In this context, we present protocols implementing two-qubit quantum gates between atoms far apart in the lattice. To this end, we propose to use a chain of non-coding ancilla atoms to transfer the state of the control qubit to an atom near the target qubit. Before discussing entangling gates between distant qubits, we present two protocols that implement state transfer along a chain of two-level atoms relying respectively on single- and two-atom laser pulses combined with dipole blockade. After reviewing protocols implementing CZ and CNOT gates between nearby qubits using dipole-dipole interactions, we show how the state-transfer protocols previously presented can be used to perform entangling gates between distant qubits. The performance of the state-transfer and gate protocols are assessed using the process fidelity. Moreover, we provide a theoretical explanation for the behavior of the process fidelity with respect to dissipation and imperfect blockade.
Quantum systems are inherently open to their environment and thus they evolve under the influence of dissipation, decoherence and driving from external fields. This poses a significant theoretical challenge: how to track the dynamics of the system of interest while tracing out environmental degrees of freedom. Markovian master equations offer a longstanding solution to this problem, where under a series of assumptions the reduced density matrix of the system can be obtained. These flexible approaches provide a conceptually and numerically simple framework for describing complex many-body systems. However, the assumptions enforced by Markovian master equations create a gap in the availability of generic, simple, and analytical techniques capable of treating open quantum systems beyond the regimes of standard Markovian master equations. In this thesis, we introduce three studies addressing three regimes that are inaccessible to standard Markovian master equations and investigate their consequences in quantum thermodynamics-inspired applications. We begin by developing a Markovian embedding technique to tackle non-Markovian dynamics induced by the long correlation times of a qubit coupled to a structured environment. Subsequently, we propose an "effective" Hamiltonian theory enabling the study of equilibrium properties of strong coupling to a thermal reservoir through a dressed version of the Gibbs state. This framework can also be applied to address problems of equilibration, transport, quantum thermal machines, and quantum dynamics. Lastly, we showcase the importance of including non-secular terms in the quantum master equation, which results in a drastic separation of timescales leading to rich metastable dynamics. We apply this quantum master equation approach to temperature sensing in a nonequilibrium setting offering an alternative to standard equilibrium probes. Overall, this thesis contributes novel theoretical techniques for tackling open quantum systems beyond standard approximations with applications in quantum thermodynamics.
In the last chapter, we dealt with the wide class of physical operations that preserve the Gaussian character of the initial state, treating them as discrete transformations. Here, we describe what could loosely be considered the continuous-time version of such transformations. This chapter is intended to provide the reader with the tools to describe a wide range of notable quantum dynamics, with a very broad applicative scope. After a note on the action of linear and quadratic Hamiltonians, whose description follows directly from the theory of Gaussian states presented in Chapter 3 but was not explicitly clarified so far, we shall address systems linearly coupled to a reservoir of modes that are delta-correlated in time (a situation commonly referred to as ‘white noise’), and thus give rise to Markovian dynamics which we shall refer to as ‘diffusive’ for reasons that will be made clear in due time. Our story will commence with a derivation of the Gaussian dynamics resulting from such an environmental coupling, in the form of dynamical equations for the first and second statistical moments. Besides their interest per se , the latter will be instrumental in obtaining an unconventional derivation of the master equations that govern general, not necessarily Gaussian, quantum states under the same conditions. The corresponding quantum Langevin equations for the canonical operators in the Heisenberg picture will also be derived. Next, we will turn our attention to the study of the system's dynamics that result from the measurement of the environment. This is a topic with a longstanding tradition in quantum mechanics, grounded in the formalism of quantum stochastic calculus that emerged within the mathematical physics community as early as the seventies, and then re-introduced as the quantum trajectories approach in quantum optics almost twenty years later. The ‘weak’ POVMs resulting from observing a weakly coupled environment (as opposed to ‘strong’, projective measurements), carried out continuously in time (a prescription customarily subsumed by the term ‘monitoring’), leads to a stochastic dynamics for the system, where the randomness of the measurement outcomes is compactly and most elegantly represented by infinitesimal stochastic increments, giving rise to continuous but not differentiable quantum dynamics. Existing approaches to this subject tend to be quite impervious to the uninitiated. In the quantum optics literature, this is largely due to the technicalities involved in incorporating the discontinuous update of the quantum state prescribed by the von Neumann postulate. More mathematically oriented treatments have instead typically preferred an algebraic approach where the usual difficulty of describing measurements in the Heisenberg picture is compounded by the adoption of a rather abstract hierarchy of filters, in part inspired by classical control theory, to describe different possible updates of the quantum state. This state of affairs is further complicated by the added difficulties that come with the necessary introduction of some form of quantum stochastic calculus. Our approach to monitoring will therefore take a different route. Like in our derivation of diffusion and master equations, we shall keep restricting to linear couplings with a white noise environment, forfeiting full generality This situation is well modelled by the so called input-output formalism, whose physical origin will be discussed in detail in Chapter 9 , which approximates reliably, among other instances, the interaction between internal resonating modes and electromagnetic radiation leaking in and out of an optical cavity. First, we shall introduce stochastic Wiener increments and the Itô rule, which will arise naturally from the identification of the continuum field's modes subject to monitoring. We shall deliberately keep our arsenal of stochastic methods to these bare essentials, sacrificing to some extent both depth and generality, but still providing the reader with a powerful and seminal demonstration of the formalism. We shall then restrict to Gaussian general-dyne detections and apply the exact formalism developed in the previous chapter to the continuous filtering of the system's state conditioned by such measurements' outcomes. Next, as in our derivation of the unconditional master equations, we shall use the Gaussian dynamics as a key to unlock the full stochastic master equations governing general states. Hence, we will build on the quantum theory of filtering in the Gaussian regime to derive dynamical equations for linear feedback control and also apply our theoretical tools to the enhanced production of squeezing. Finally, we will turn to the closely related paradigm of coherent feedback, where environmental modes do not undergo measurements but are fed back to interact coherently with the system, see in detail how it modifies Gaussian diffusive dynamics and assess its potential for control by reconsidering the production of squeezing assisted by interferometric coherent feedback loops.
In this work, we consider a general feedback protocol based on quantum-jump detections, where the last detected jump channel is stored in a memory and subsequently used to implement a feedback action, such as modifying the system Hamiltonian conditioned on the last jump. We show that the time evolution of this general protocol can be described by a Lindblad master equation defined in a hybrid classical-quantum space, where the classical part encodes the stored measurement record (memory) and the quantum part represents the monitored system. Moreover, we show that this new representation can be used to fully characterize the counting statistics of a system subject to a general jump-based feedback protocol. We apply the formalism to a three-level system coupled to two thermal baths operating as a thermal machine, and we show that jump-based feedback can be used to convert the information obtained from the jump detections into work. Our framework provides analytical tools that enable the characterization of key statistical properties of any counting observable under jump-based feedback, such as the average current, noise, correlation functions, and power spectrum.
This thesis develops a comprehensive framework for the use of continuous variable (CV) Gaussian states under environmental interactions and continuous measurements. Gaussian states provide an experimentally relevant class of quantum states because they are fully described by their first and second statistical moments. This thesis begins by representing Gaussian operations as symplectic transformations on the statistical moments and formulates the evolution of a Gaussian state under both unconditional and conditional open system dynamics. Stochastic methods are introduced in a physicist-accessible manner by sacrificing mathematical rigor over physical intuition. These methods are necessary to model environmental noise and continuous measurements represented by a Wiener process. From stochastic principles, a stochastic version of the Schr\"{o}dinger equation and a master equation are derived that capture the measurement-induced back-action. From these principles a conditional equation of motion for the covariance matrix of a Gaussian state is derived, leading to the Riccati equation. Unconditional evolution always leads to diffusive dynamics when the noise is modeled by a Wiener process. The key difference between unconditional and conditional equations of motion is that monitoring always leads to a reduction of uncertainty because a measurement gains information about the system. At the same time, all correlations to the part of the system being measured are lost, which in many cases can lead to an impure quantum state. At some cases, a sufficient measurement scheme can even be used to stabilize the unconditional equation at all scales. The developed formalism is applied to a system of multiple parametric flux pumps based on spontaneous parametric down-conversion to analyze entanglement generation in a complex network of modes. A simple formula relevant to all symmetric pumping architectures, also relevant for asymmetric cases, is derived with graph theoretical tools. The investigation revealed fundamental challenges in entanglement-generation based on multiple two-mode squeezed modes. Overall, the thesis provides a complete framework of Gaussian state dynamics connecting symplectic geometry, open quantum systems, quantum measurement theory, and stochastic methods. The results highlight the importance of Gaussian states in modern quantum technologies and future improvements in quantum computation and communication.