Related papers: Information-Geometric Quantum Process Tomography o…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the…
This paper deals with the problem of identifying and estimating dynamical parameters of continuous-time quantum open systems, in the input-output formalism. First, we characterise the space of identifiable parameters for ergodic dynamics,…
The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional matrix algebra satisfies a modified log-Sobolev inequality. In the discrete time setting, we prove that every finite dimensional GNS-symmetric quantum…
The application of the eigenstate thermalization hypothesis to non-Hermitian quantum systems has become one of the most important topics in dissipative quantum chaos, recently giving rise to intense debates. The process of thermalization is…
Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…
Both quantum information features and irreversible quantum evolution of the models arising in physical systems in one-particle approximation are discussed. It is shown that the calculation of the reduced density matrix and entanglement…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…
Quantum state tomography faces exponential scaling with system size, while recent neural network approaches achieve polynomial scaling at the cost of losing the geometric structure of quantum state space. We introduce geometric latent space…
In a quantum (inhomogeneous) Markov process $\rho_1:=\Gamma_1(\rho)$, $\rho_2:=\Gamma_1(\rho_1)$, ..., where $\Gamma_i$ are CPTP maps and $\rho$ is the initial state, the the state of the system is either oscillatory or convergent to a…
Intrinsic noise in pre-fault-tolerant quantum devices poses a major challenge to the reliable realization of unitary dynamics in quantum algorithms and simulations. To address this, we present a method for simulating open quantum system…
Recently, there is a growing interest in study quantum mechanics from the information geometry perspective, where a quantum state is depicted with a point in the projective Hilbert space. By taking quantum Fisher information (QFI) as the…
Standard quantum metrology relies on ensemble-averaged quantities, such as the Quantum Fisher Information (QFI), which often mask the fluctuations inherent to single-shot realizations. In this work, we bridge the gap between quantum…
We present an information geometric analysis of entropic speeds and entropy production rates in geodesic evolution on manifolds of parametrized quantum states. These pure states emerge as outputs of suitable su(2; C) time-dependent…
We find equivalent hypergeometric- and difference-equation-based formulas, $Q(k,\alpha)= G_1^k(\alpha) G_2^k(\alpha)$, for $k = -1, 0, 1,\ldots,9$, for that (rational-valued) portion of the total separability probability for generalized…
Several approximation procedures, such as the full or partial rotating-wave, time-averaging, and geometric-arithmetic approximations, have been proposed to derive Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generators from the Born-Markov…
A statistically feasible data post-processing method for the conventional qubit state tomography is studied from an information geometrical point of view. It is shown that the space $(-1,1)^3$ of the Stokes parameters $(\xi_1, \xi_2,\xi_3)$…