Related papers: Wigner-Yanase information on quantum state space:t…
This work is a simple extension of \cite{NNjpa}. We apply the concepts of information geometry to study the mean-field approximation for a general class of quantum statistical models namely the higher-order quantum Boltzmann machines…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
The unitary dynamics of quantum systems can be modeled as a trajectory on a Riemannian manifold. This theoretical framework naturally yields a purely geometric interpretation of computational complexity for quantum algorithms, a notion…
It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called…
Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a "geometric entropy", associated with an event…
Information geometry is an emergent branch of probability theory that consists of assigning a Riemannian differential geometry structure to the space of probability distributions. We present an information geometric investigation of gases…
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We…
We demonstrate --- using the case of the two-dimensional quantum systems --- that the "natural measure on the space of density matrices describing N-dimensional quantum systems" proposed by Zyczkowski et al (quant-ph/9804024) does not…
We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: i. classical part associated to the Fisher information of the…
The dynamics of relative entropy and $l_{1}$-norm of coherence, as well as, the Wigner-Yanase-skew and quantum Fisher information are studied for a time-dependent coupled XY spin chain in presence of a time-dependent transverse magnetic…
Random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), found applications in literature in study of following quantum…
Classical and quantum statistical mechanics are cast here in the language of projective geometry to provide a unified geometrical framework for statistical physics. After reviewing the Hilbert space formulation of classical statistical…
We show that the Hilbert space spanned by a continuously parametrized wavefunction family---i.e., a quantum state manifold---is dominated by a subspace, onto which all member states have close to unity projection weight. Its characteristic…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in…
We define a mixed topology on the fiber space $\cup_\mu \oplus^n L^n(\mu)$ over the space $\mathcal{M}(\Omega)$ of all finite non-negative measures $\mu$ on a separable metric space $\Omega$ provided with Borel $\sigma$-algebra. We define a…
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…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…
Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically…