Related papers: The differential information-geometry of quantum p…
Riemannian metric on real 2n-dimensional space associated with the equation governing complex diffusion of pure states of an open quantum system is introduced and studied. Examples of a qubit under the influence of dephasing and thermal…
Information geometry promotes an investigation of the geometric structure of statistical manifolds, providing a series of elucidations in various areas of scientific knowledge. In the physical sciences, especially in quantum theory, this…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Kitaev honeycomb model with topological phase transition at zero temperature is studied using quantum information method. Based on the exact solution of the ground state, the mutual information between two nearest sites and between two…
We summarize basic features of quantum gravity states and processes, common to a number of related quantum gravity formalisms, and sharing a purely combinatorial and algebraic language, and a discrete geometric interpretation. We emphasize…
The notion of quantum information related to the two different perspectives of the global and local states is examined. There is circularity in the definition of quantum information because we can speak only of the information of systems…
Noncommutative or `quantum' differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics) but also differential forms, bundles and…
In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of…
Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry.…
Identifying quantum phases and phase transitions is key to understand complex phenomena in statistical physics. In this work, we propose an unconventional strategy to access quantum phases and phase transitions by visualization based on the…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
We explore the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory. For this, we work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
We construct information geometry for hydrodynamics with global gauge and gravitational anomalies in $1+1$ and $3+1$ dimensions. We introduce the metric on a parameter space and show that turning on non-zero rotations leads to a curvature…
We define geometric critical exponents for systems that undergo continuous second order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near…
Decoherence of a quantum system (which then starts to display classical features) results from the interaction of the system with the environment, and is well described in the framework of the theory of continuous quantum measurements…
We present detailed analytical calculations for an 1D Ising ring of arbitrary number of spin-1/2 particles, in order to reveal entanglement properties of the stationary states. We show that the ground state and specific eigenstates of the…
Basic quantum information measures involved in the information analysis of quantum systems are considered. It is shown that the main quantum information measurement methods depend on whether the corresponding quantum events are compatible…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…