Related papers: Geometric lower bound for a quantum coherence meas…
It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…
Coherence is the most fundamental quantum resource in quantum information processing. How fast a physical system gets coherence or decoherence is a critical ingredient. We present an attainable quantum speed limit based on the variation of…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
The quantum geometric tensor (QGT) provides nontrivial bounds among physical quantities, as exemplified by the metric-curvature inequality. In this paper, we investigate various bounds for different observables through certain…
Uncertainty relation is a core issue in quantum mechanics and quantum information theory. We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalizedWigner-Yanase-Dyson (MWGWYD) skew…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schr\"odinger framework from this perspective and provide a description of the Weyl-Wigner construction. Finally,…
In this paper, we prove a quantum union bound that is relevant when performing a sequence of binary-outcome quantum measurements on a quantum state. The quantum union bound proved here involves a tunable parameter that can be optimized, and…
We address the nonGaussianity (nG) of states obtained by weakly perturbing a Gaussian state and investigate the relationships with quantum estimation. For classical perturbations, i.e. perturbations to eigenvalues, we found that nG of the…
$\Psi$-epistemic models of quantum mechanics imply that the quantum state does not correspond to physical reality, but instead reflects the observer's knowledge of the underlying quantum system. The epistemic view of the quantum state has…
We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
Quantifying the entanglement and coherence of quantum systems is a topic of significant theoretical and practical interest. In this paper, we propose a method to evaluate lower bounds for several widely used coherence measures and genuine…
We study the average quantum coherence over the pure state decompositions of a mixed quantum state. An upper bound of the average quantum coherence is provided and sufficient conditions for the saturation of the upper bound are shown. These…
The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. Here a generalization of the QGT to mixed quantum states at finite temperatures based on the…
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, already present in a number of settings (see Shimony 1995 and…
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 derive a tight bound between the quality of estimating a quantum state by measurement and the success probability of undoing the measurement in arbitrary dimensional systems, which completely describes the tradeoff relation between the…
The computational power of quantum phases of matter with symmetry can be accessed through local measurements, but what is the most efficient way of doing so? In this work, we show that minimizing operational resources in measurement-based…
The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…