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

Using extensive numerical analysis of 20,000 randomly generated two-qubit states, we provide a quantitative analysis of the connection between entanglement measures and Maximized Quantum Fisher Information (MQFI). Our systematic study shows…

We investigate the geometric characterization of pure state bipartite entanglement of $(2\times{D})$- and $(3\times{D})$-dimensional composite quantum systems. To this aim, we analyze the relationship between states and their images under…

Can a secret be hidden not in which quantum state is prepared, but in the way that state \emph{moves} through its space of possibilities? Motivated by this question, we propose an essential geometric perspective on quantum cryptography in…

Multi-qubit graph states generated by the action of controlled phase shift operators on a separable quantum state of a system, in which all the qubits are in arbitrary identical states, are examined. The geometric measure of entanglement of…

In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two…

Using inelastic X-ray scattering (IXS), we experimentally investigate the quantum geometry and quantum information in the large-gap insulator, LiF. Using sum rules for the density-density response function measured in IXS, we compute the…

In the context of loop quantum gravity, quantum states of geometry are mathematically defined as spin networks living on graphs embedded in the canonical space-like hypersurface. In the effort to study the renormalisation flow of loop…

A measure for the maximum quantum information transfer capacity (ITC) between nodes of a spin network is defined, and shown to induce a metric on a space of equivalence classes of nodes for homogeneous chains with XX and Heisenberg…

Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the…

We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…

A quantum measurement is Fisher symmetric if it provides uniform and maximal information on all parameters that characterize the quantum state of interest. Using (complex projective) 2-designs, we construct measurements on a pair of…

Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product…

Natural gradient is an advanced optimization method based on information geometry, where the Fisher metric plays a crucial role. Its quantum counterpart, known as quantum natural gradient (QNG), employs the symmetric logarithmic derivative…

We present a geometric approach to the characterization of separability and entanglement in pure Gaussian states of an arbitrary number of modes. The analysis is performed adapting to continuous variables a formalism based on single…

A general geometrical structure of the entanglement entropy for spatial partition of a relativistic QFT system is established by using methods of the effective gravity action and the spectral geometry. A special attention is payed to the…

Grid states form a discrete set of mixed quantum states that can be described by graphs. We characterize the entanglement properties of these states and provide methods to evaluate entanglement criteria for grid states in a graphical way.…

Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…

In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…

We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-1/2 fermions distributed over 2L modes (single particle states). The measure…

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is…