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Von Neumann entropy rate for open quantum systems is, in general, written in terms of entropy production and entropy flow rates, encompassing the second law of thermodynamics. When the open-quantum-system evolution corresponds to a quantum…
We establish a comprehensive theoretical framework for coherent quantum speed limits (QSLs), deriving fundamental bounds on the rate of quantum evolution that explicitly isolate the contribution of quantum coherence. By applying H\"older's…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…
Based on the stabilizer formalism underlying Quantum Error Correction (QEC), the design of an original Lindblad master equation for the density operator of a quantum harmonic oscillator is proposed. This Lindblad dynamics stabilizes exactly…
These notes introduce quantum computation and quantum error correction, emphasising the importance of stabilisers and the mathematical foundations in basic Lie theory. We begin by using the double cover map $\mathrm{SU}_2 \rightarrow…
The quantum systems with finite-dimensional Hilbert space have several applications and are intensively explored theoretically and experimentally. The mathematical description of these systems follows the analogy with the usual…
The quantum speed limit provides fundamental bound on how fast a quantum system can evolve between the initial and the final states. For the unitary evolution, the celebrated Mandelstam-Tamm (MT) bound has been widely studied for various…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable entanglement for a system consisting of two noninteracting modes embedded in a…
We review some recent advances in the field of element-based algebraic stabilization for continuous finite element discretizations of nonlinear hyperbolic problems. The main focus is on multidimensional convex limiting techniques designed…
We establish a central limit theorem (CLT) for families of products of $\epsilon$-independent random variables. We utilize graphon limits to encode the evolution of independence and characterize the limiting distribution. Our framework…
We establish a mapping between a continuous variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a…
Entanglement distillation, the process of converting weakly entangled states into maximally entangled ones using Local Operations and Classical Communication (LOCC), is pivotal for robust entanglement-assisted quantum information processing…
We outline an exact approach to decoherence and entanglement problems for continuous variable systems. The method is based on a construction of quantum distribution functions introduced by Ford and Lewis \cite{ford86} in which a system in…
We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it…
Characterizing the most efficient evolution, the quantum speed limit (QSL) plays a significant role in quantum technology. How to generalize the well-established QSL from closed systems to open systems has attracted much attention. In…
Quantum phase transitions occur at zero temperature and involve the appearance of long-range correlations. These correlations are not due to thermal fluctuations but to the intricate structure of a strongly entangled ground state of the…
Finding ways to quantify magic is an important problem in quantum information theory. Recently Leone, Oliviero and Hamma introduced a class of magic measures for qubits, the stabilizer entropies of order $\alpha$, to aid in studying…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
This paper provides a stabilizing preparation method for quantum Gaussian states by utilizing continuous measurement. The stochastic evolution of the open quantum system is described in terms of the quantum stochastic master equation. We…