Related papers: Generalized quantum geometric tensor for excited s…
The rise of quantum information science has opened up a new venue for applications of the geometric phase (GP), as well as triggered new insights into its physical, mathematical, and conceptual nature. Here, we review this development by…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
For decades, ``geometry" in band theory has largely meant Berry phase and Berry curvature-quantities that reshape semiclassical dynamics and underpin modern topological matter. Yet the full geometric content of a Bloch band is richer and…
This work introduces a geometrical object that generalizes the quantum geometric tensor; we call it $N$-bein. Analogous to the vielbein (orthonormal frame) used in the Cartan formalism, the $N$-bein behaves like a ``square root'' of the…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
Entangled resources enable quantum sensing that achieves Heisenberg scaling, a quadratic improvement on the standard quantum limit, but preparing large scale entangled states is challenging in the presence of decoherence. We present a…
The relation between quantum phase transitions, entanglement, and geometric phases is investigated with a system of two qubits with XY type interaction. A seam of level crossings of the system is a circle in parameter space of the…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
We generalize the Quantum Geometric Tensor by replacing a Hamiltonian with a modular Hamiltonian. The symmetric part of the Quantum Geometric Tensor provides a Fubini-Study metric, and its anti-symmetric sector gives a Berry curvature. Now…
We introduce a general approach to realize quantum states with holographic entanglement structure via monitored dynamics. Starting from random unitary circuits in $1+1$ dimensions, we introduce measurements with a spatiotemporally-modulated…
We study the quantum entanglement structure of integer quantum Hall states via the reduced density matrix of spatial subregions. In particular, we examine the eigenstates, spectrum and entanglement entropy (EE) of the density matrix for…
We discuss two measures of entanglement in quantum field theory and their holographic realizations. For field theories admitting a global symmetry, we introduce a global symmetry entanglement entropy, associated with the partitioning of the…
The quantum geometric tensor (QGT) characterizes the local geometry of quantum states, and its components directly account for the dynamical effects observed, e.g., in condensed matter systems. In this work, we address the problem of…
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric…
We study the holographic properties of a class of quantum geometry states characterized by a superposition of discrete geometric data, in the form of generalised tensor networks. This class specifically includes spin networks, the kinematic…
We construct a generalized controlled phased gate entangler for a multi-qubit state based on the geometrical structure of quantum systems. We also investigate relation between the generalized controlled phase construction of a quantum gate…