相关论文: Classical and quantum geometric information flows …
This work consists an introduction to the classical and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. Basic geometric and physical properties of the canonical nonholonomic…
This paper explores the fundamental relationship between the geometry of entanglement and von Neumann entropy, shedding light on the intricate nature of quantum correlations. We provide a comprehensive overview of entanglement, highlighting…
This article consists of an introduction to the theory of nonassociative geometric classical and quantum information flows defined by star products with R-flux deformations in string gravity. Corresponding nonassociative generalizations of…
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…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxwell and Kaluza-Klein, KK, theories formulated in Lagrange-Hamilton and general covariant variables. There are considered nonholonomic…
We introduce a novel geometric approach to characterize entanglement relations in large quantum systems. Our approach is inspired by Schumacher's singlet state triangle inequality, which used an entropic-based distance to capture the…
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…
Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which…
We analyze the relationship between entanglement (or geometric) entropy with statistical mechanical entropy of horizon degrees of freedom when described in the framework of isolated horizons in loop quantum gravity. We show that, once the…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
Holographic entanglement entropy is a key concept linking quantum information theory and gravity. Since the original conjecture of Ryu and Takayanagi, holographic entanglement entropy has been generalized beyond Einstein--Hilbert gravity to…
The fundamental question of how information spreads in closed quantum many-body systems is often addressed through the lens of the bipartite entanglement entropy, a quantity that describes correlations in a comprehensive (nonlocal) way.…
Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a "geometric entropy", associated with an event…
A framework for a quantum mechanical information theory is introduced that is based entirely on density operators, and gives rise to a unified description of classical correlation and quantum entanglement. Unlike in classical (Shannon)…
I review recent works showing that information geometry is a useful framework to characterize quantum coherence and entanglement. Quantum systems exhibit peculiar properties which cannot be justified by classical physics, e.g. quantum…
Quantum entanglement is a key resource for quantum technologies, including emerging ground-to-satellite quantum communication. In such a scenario, an important challenge to be overcome is to consider entanglement between two or more quantum…
It is shown for classical and quantum ensembles that there is a unique quantity which has the properties of a "volume". This quantity is a function of the ensemble entropy, and hence provides a geometric interpretation for the latter. It…
We summarize recent developments at the interface of quantum gravity and quantum information, and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement,…
Many important quantities in quantum information science, such as entropy and entanglement, are non-linear functions of the density matrix and cannot be expressed as operator observables. Standard open-system approaches evolve only a single…