相关论文: Duality in quantum information manifolds
We introduce two notions of hyperbolicity for not necessarily K\"ahler $n$-dimensional compact complex manifolds $X$. The first, called {\it balanced hyperbolicity}, generalises Gromov's K\"ahler hyperbolicity by means of Gauduchon's…
Looking for a quantum-mechanical implementation of duality, we formulate a relation between coherent states and complex-differentiable structures on classical phase space ${\cal C}$. A necessary and sufficient condition for the existence of…
The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of…
We introduce a dual Zariski topology on the spectrum of fully coprime $R$-submodules of a given duo module $M$ over an associative (not necessarily commutative) ring $R$. This topology is defined in a way dual to that of defining the…
We formulate a general theory of wave-particle duality for many-body quantum states, which quantifies how wave- and particle-like properties balance each other. Much as in the well-understood single-particle case, which-way information --…
We explore the relationship between complexity and duality in quantum systems, focusing on how local and non-local operators evolve under time evolution. We find that non-local operators, which are dual to local operators under specific…
The ``holography of information'' (HoI) principle argues that gravity can encode information redundantly in asymptotic observables. Although HoI is ultimately a nonperturbative claim, its standard motivation uses semiclassical gravitational…
Given a dynamical twist for a finite dimensional Hopf algebra we construct two weak Hopf algebras, using methods of Xu and Etingof-Varchenko, and show that they are dual to each other. We generalize the theory of dynamical quantum groups to…
Topology is a fundamental aspect of quantum physics, and it has led to key breakthroughs and results in various fields of quantum materials. In condensed matters, this has culminated in the recent discovery of symmetry-protected topological…
The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a…
A class of two-qubit states called X-states are increasingly being used to discuss entanglement and other quantum correlations in the field of quantum information. Maximally entangled Bell states and "Werner" states are subsets of them.…
In holographic duality, if a boundary state has a geometric description that realizes the Ryu-Takayanagi proposal then its entanglement entropies must obey certain inequalities that together define the so-called holographic entropy cone. A…
We demonstrate that multipartite entanglement is able to characterize one-dimensional symmetry-protected topological order, which is witnessed by the scaling behavior of the quantum Fisher information of the ground state with respect to the…
The holographic duality allows to construct and study models of strongly coupled quantum matter via dual gravitational theories. In general such models are characterized by the absence of quasiparticles, hydrodynamic behavior and Planckian…
We develop an operator-algebraic framework for modular self-duality, symmetrized relative entropy, and Bogoliubov--Kubo--Mori susceptibility of local states in quantum field theory. In finite dimensions, modular self-duality singles out…
The mutual information of disconnected regions in large $N$ gauge theories with holographic gravity duals can undergo phase transitions. These occur when connected and disconnected bulk Ryu-Takayanagi surfaces exchange dominance. That is,…
Quantum discord (QD) measures the fraction of the pairwise mutual information that is locally inaccessible, in a multipartite system. Fundamental aspects related to two important measures in quantum information theory the Entanglement of…
We describe the doubled space of Double Field Theory as a group manifold $G$ with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so $G$ only captures the topology of the doubled…
Macaulay Duality, between quotients of a polynomial ring over a field, annihilated by powers of the variables, and finitely generated submodules of the ring's graded dual, is generalized over any Noetherian ring, and used to provide…
We will show that for a polynomially contractible manifold of bounded geometry and of polynomial volume growth every coarse and rough cohomology class pairs continuously with the K-theory of the uniform Roe algebra. As an application we…