相关论文: Fisher Metric, Geometric Entanglement and Spin Net…

We present a description of entanglement in composite quantum systems in terms of symplectic geometry. We provide a symplectic characterization of sets of equally entangled states as orbits of group actions in the space of states. In…

The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated…

We describe an efficient theoretical criterion, suitable for indistinguishable particles to quantify the quantum correlations of any pure two-fermion state, based on the Slater rank concept. It represents the natural generalization of the…

This work aims to understand the monogamy of quantum entanglement from a geometrical point of view. By regarding quantum entanglement as a geometrical structure on the state space of quantum systems and attributing all entanglement related…

A new framework is formulated to study entanglement dynamics in many-body quantum systems along with an associated geometric description. In this formulation, called the Quantum Correlation Transfer Function (QCTF), the system's wave…

The Fisher information metric or the Fisher-Rao metric corresponds to a natural Riemannian metric defined on a parameterized family of probability density functions. As in the case of Riemannian geometry, we can define a distance in terms…

Recent developments on holography and quantum information physics suggest that quantum information theory come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing…

Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of…

An efficient scheme to compute the geometric entanglement per lattice site for quantum many-body systems on a periodic finite-size chain is proposed in the context of a tensor network algorithm based on the matrix product state…

Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of…

The thesis includes the original results of our articles [30, 37, 40, 42, 51, 53, 75]. A method is developed to compute analytically entanglement measures of three-qubit pure states. Owing to it closed-form expressions are presented for the…

We investigate the entanglement properties of multi-mode Gaussian states, which have some symmetry with respect to the ordering of the modes. We show how the symmetry constraints the entanglement between two modes of the system. In…

This thesis is dedicated to the study of open spin networks. We formulate quasi-local descriptions of loop quantum gravity. We investigate the coarse-graining procedure via tracing over bulk degrees of freedom, which encodes all that we can…

Imaging systems are represented as linear operators, and their singular value spectra describe the structure recoverable at the operator level. Building on an operator-based information-theoretic framework, this paper introduces a minimal…

Several inequivalent definitions of the geometric measure of entanglement (GM) have been introduced and studied in the past. Here we review several known and new definitions, with the qualifying criterion being that for pure states the…

We summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with…

We develop a geometric approach to spin networks with Heisenberg or XX coupling. Geometry is acquired by defining a distance on the discrete set of spins. The key feature of the geometry of such networks is their Gauss curvature $\kappa$,…

In this note we present preliminary study on the relation between the quantum entanglement of boundary states and the quantum geometry in the bulk in the framework of spin networks. We conjecture that the emergence of space with non-zero…

The geometric measure of entanglement is the distance or angle between an entangled target state and the nearest unentangled state. Often one considers the geometric measure of entanglement for highly symmetric entangled states because it…

We consider graph states generated by the action of controlled phase shift operators on a separable state of a multi-qubit system. The case when all the qubits are initially prepared in arbitrary states is investigated. We obtain the…