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

Recently, an explicit relation between a measure of entanglement and a geometric entity has been reported in Quantum Inf. Process. (2016) 15:1629-1638. It has been shown that if a qubit gets entangled with another ancillary qubit then…

A complete geometric unification of gravity and electromagnetism is proposed by considering two aspects of torsion: its relation to spin established in Einstein--Cartan theory and the possible interpretation of the torsion trace as the…

Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…

The notion of {\em entanglement entropy} in quantum mechanical systems is an important quantity, which measures how much a physical state is entangled in a composite system. Mathematically, it measures how much the state vector is not…

Entanglement properties of purified quantum states are of key interest for two reasons. First, in quantum information theory, minimally entangled purified states define the Entanglement of Purification as a fundamental measure for the…

After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose…

The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric…

Choosing the Fisher information as the metric tensor for a Riemannian manifold provides a powerful yet fundamental way to understand statistical distribution families. Distances along this manifold become a compelling measure of statistical…

It is a specific type of quantum correlated state that achieves optimal precision in parameterestimation under unitary encoding. We consider the potential experimental limitation on probe entanglement, and find a relation between achievable…

We investigate the global-symmetry projections applied to the tensor network states from the view point of the entanglement entropy and the mutual information. The projections to the translational invariant space and to the total-$S^z$-zero…

This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement…

We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin…

Despite their elegance and widespread use, the current Geometric Measures (GMs) of entanglement exhibit a significant limitation: they fail to effectively distinguish Local Unitary (LU) inequivalent states due to the inherent nature of…

We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields…

A deep neural network is a hierarchical nonlinear model transforming input signals to output signals. Its input-output relation is considered to be stochastic, being described for a given input by a parameterized conditional probability…

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…

Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By…

One of the most important questions in quantum information theory is the so-called separability problem. It involves characterizing the set of separable (or, equivalently entangled) states among mixed states of a multipartite quantum…

We have introduced a measure of Gaussian quantum correlations based on quantum Fisher information. For bipartite Gaussian states the minimum quantum Fisher information due to local unitary evolution on one of the parties reliably quantifies…

Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is…