Related papers: From Classical to Quantum Information Geometry: A …
The manifold of coupling constants parametrizing a quantum Hamiltonian is equipped with a natural Riemannian metric with an operational distinguishability content. We argue that the singularities of this metric are in correspondence with…
Integrated Information Theory (IIT) has emerged as one of the leading research lines in computational neuroscience to provide a mechanistic and mathematically well-defined description of the neural correlates of consciousness. Integrated…
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…
Quantum Fisher information (QFI) has potential applications in quantum metrology tasks. We investigate QFI when the consecutive actions of a quantum channel on the sequence of qubits have partial classical correlations. Our results showed…
Studies about Quantum Information Theory continue actively in many research institutions. Very recently, pratical setups of large scale quantum computers are widely studied e.g. quantum repeaters, memories and processors. Entanglement…
It is shown that the geometry of quantum theory can be derived from geometrical structure that may be considered more fundamental. The basic elements of this reconstruction of quantum theory are the natural metric on the space of…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
Geometrical phases, such as the Berry phase, have proven to be powerful concepts to understand numerous physical phenomena, from the precession of the Foucault pendulum to the quantum Hall effect and the existence of topological insulators.…
For pure states, the quantum Berry curvature was well studied. However, the quantum curvature for mixed states has received less attention. From the concept of symmetric logarithmic derivative, we introduce a mixed-state quantum curvature…
We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher…
A series of geometric concepts are formulated for $\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a…
Berry curvature that describes local geometrical properties of energy bands can elucidate many fascinating phenomena in solid-state, photonic, and phononic systems, given its connection to global topological invariants such as the Chern…
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which…
There have been suggestions within the Information Retrieval (IR) community that quantum mechanics (QM) can be used to help formalise the foundations of IR. The invoked connection to QM is mathematical rather than physical. The proposed…
We present a framework for the detection and estimation of deformations applied to a grid of sources. Our formalism uses the Hamiltonian formulation of the quantum Fisher information matrix (\textsc{qfim}) as the figure of merit to quantify…
We investigate two special classes of two-mode Gaussian states of light that are important from both the experimental and theoretical points of view: the mode-mixed thermal states and the squeezed thermal ones. Aiming to a parallel study,…
In this letter, we elaborate on the identification and construction of the differential geometric elements underlying Berry's phase. Berry bundles are built generally from the physical data of the quantum system under study. We apply this…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
The importance of simple geometrical invariants, such as the Berry curvature and quantum metric, constructed from the Bloch states of a crystal has become well-established over four decades of research. More complex aspects of geometry…
Despite the widespread use and success of machine-learning techniques for detecting phase transitions from data, their working principle and fundamental limits remain elusive. Here, we explain the inner workings and identify potential…