相关论文: Duality in quantum information manifolds

Quantum theory of the free Maxwell field in Minkowski space is constructed using a representation in which the self dual connection is diagonal. Quantum states are now holomorphic functionals of self dual connections and a decomposition of…

This article presents a concrete mathematical framework for the generation of entangled quantum states from classical stochastic processes. We demonstrate that any density operator $\rho_{AB}$ of a composite system can be derived from the…

We investigate the dynamics of quantum information flow in one and two impurity qubits trapped in a double-well potential and interacting with a one-dimensional ultracold Bose-Bose mixture reservoir. For a single qubit immersed in a binary…

Given a cohesive sheaf $\Cal S$ over a complex Banach manifold $M$, we endow the cohomology groups $H^q(M,\Cal S)$ of $M$ and $H^q(\frak U,\Cal S)$ of open covers $\frak U$ of $M$ with a locally convex topology. Under certain assumptions we…

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are…

Quantum Fisher Information (QFI) is a measure quantifying the sensitivity of a quantum state with respect to changes in tuning parameters in quantum metrology, and defining quantum speed limits. We show that even if the quantum state is…

We define the double quantum affinization $\ddot{\mathrm{U}}_q(\mathfrak a_1)$ of type $\mathfrak{a}_1$ as a topological Hopf algebra. We prove that it admits a subalgebra $\ddot{\mathrm{U}}_q'(\mathfrak a_1)$ whose completion is…

Topology identification comprises reconstructing the interaction Hamiltonian of a quantum network by properly processing measurements of its density operator within a fixed time interval. It finds application in several quantum technology…

Among the many important geometric properties of quantum state space are: transitivity of the group of symmetries of the cone of unnormalized states on its interior (homogeneity), identification of this cone with its dual cone of effects…

We introduce a quantum integrated-information measure $\Phi$ for multipartite states within the Relational Quantum Dynamics (RQD) framework. $\Phi(\rho)$ is defined as the minimum quantum Jensen-Shannon distance between an n-partite density…

We consider some formulations of the entropy bounds at the semiclassical level. The entropy S(V) localized in a region V is divergent in quantum field theory (QFT). Instead of it we focus on the mutual information I(V,W)=S(V)+S(W)-S(V\cup…

We introduce a binary relation on the finite discrete probability distributions which generalizes notions of majorization that have been studied in quantum information theory. Motivated by questions in thermodynamics, our relation describes…

This note will introduce some notation and definitions for information theoretic quantities in the context of quantum systems, such as (conditional) entropy and (conditional) mutual information. We will employ the natural C*-algebra…

Consider the infinite dimensional flag manifold $LK/T$ corresponding to the simple Lie group $K$ of rank $l$ and with maximal torus $T$. We show that, for $K$ of type $A$, $B$ or $C$, if we endow the space $H^*(LK/T)\otimes…

A uniform matrix product state defined on a tripartite system of spins, denoted by $ABC,$ is shown to be an approximate quantum Markov chain when the size of subsystem $B,$ denoted $|B|,$ is large enough. The quantum conditional mutual…

Entangling properties of a mixed 2-qubit system can be described by the local homogeneous unitary invariant polynomials in elements of the density matrix. The structure of the corresponding invariant polynomial ring for the special subclass…

In relation of observable and quantum state, the entity $I_C$ from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this article its application to quantum correlations in bipartite states is studied.…

The axioms of topological electromagnetism are refined by the introduction of the de Rham homology of k-vector fields on orientable manifolds and the use of Poincare duality in place of Hodge duality. The central problem of defining the…

A symmetry extending the $T^2$-symmetry of the noncommutative torus $T^2_q$ is studied in the category of quantum groups. This extended symmetry is given by the quantum double-torus defined as a compact matrix quantum group consisting of…

The manifold structure of subsets of classical probability distributions and quantum density operators in infinite dimensions is investigated in the context of $C^{*}$-algebras and actions of Banach-Lie groups. Specificaly, classical…