Related papers: The differential information-geometry of quantum p…
Given its well known spectral decomposition profile, the $1$-dim harmonic oscillator potential modified by an inverse square ($1$-dim angular momentum-like) contribution works as an efficient platform for probing classical and quantum…
Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…
We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the…
We study a random matrix model for the statistical properties of the purity of a bipartite quantum system at a finite (fictitious) temperature. This enables us to write the generating function for the cumulants, for both balanced and…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
While the quantum mutual information is a fundamental measure of quantum information, it is only defined for spacelike-separated quantum systems. Such a limitation is not present in the theory of classical information, where the mutual…
Critical quantum metrology relies on the extreme sensitivity of a system's eigenstates near the critical point of a quantum phase transition to Hamiltonian perturbations. This means that these eigenstates are extremely sensitive to all the…
The quantum phase diagram for a finite $3$-level system in the $\Lambda$ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility…
(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…
This study targets quantum phases which are characterized by topological properties and no associated with the symmetry breaking. We concern ourselves primarily with the transitions among these quantum phases. This type of quantum phase…
Critical metrology relies on the precise preparation of a system in its ground state near a quantum phase transition point where quantum correlations get very strong. Typically this increases the quantum Fisher information with respect to…
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a…
Recent advancements in the discipline of quantum algorithms have displayed the importance of the geometry of quantum operators. Given this thrust, this paper develops a rigorous geometric framework to analyze how the Riemannian structure of…
We review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
We study information geometry of the Dicke model, in the thermodynamic limit. The scalar curvature $R$ of the Riemannian metric tensor induced on the parameter space of the model is calculated. We analyze this both with and without the…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…