Related papers: Geometric classical and total correlations via tra…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
It is shown that for any ensemble, whether classical or quantum, continuous or discrete, there is only one measure of the "volume" of the ensemble that is compatible with several basic geometric postulates. This volume measure is thus a…
We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and…
Einstein Equivalence Principle (EEP) requires all matter components to universally couple to gravity via a single common geometry: that of spacetime. This relates quantum theory with geometry as soon as interactions with gravity are…
Classical integral geometry takes place in Euclidean space, but one can attempt to imitate it in any other metric space. In particular, one can attempt this in R^n equipped with the metric derived from the p-norm. This has, in effect, been…
We quantify the total, quantum, and classical correlations with entropic measures, and quantitatively compare these correlations in a quantum system, as exemplified by a Heisenberg dimer which is subjected to the change of environmental…
We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of…
We present a classical analog of the quantum metric tensor, which is defined for classical integrable systems that undergo an adiabatic evolution governed by slowly varying parameters. This classical metric measures the distance, on the…
This paper investigates the interplay between the geometric and topological properties of spherically symmetric black hole metrics within Einstein gravity, emphasizing implications for Bose-Einstein Condensation (BEC). By analyzing metric…
In this work, we show how Euclidean 3-space uniquely emerges from the structure of quantum temporal correlations associated with sequential measurements of Pauli observables on a single qubit. Quite remarkably, the quantum temporal…
We show that trace distance measure of coherence is a strong monotone for all qubit and, so called, $X$ states. An expression for the trace distance coherence for all pure states and a semi definite program for arbitrary states is provided.…
Physical systems with non-trivial topological order find direct applications in metrology[1] and promise future applications in quantum computing[2,3]. The quantum Hall effect derives from transverse conductance, quantized to unprecedented…
Quantum correlations are subject to certain distribution rules represented by so-called monogamy relations. Derivation of monogamy relations for multipartite systems is a non-trivial problem, as the multipartite correlations reveal their…
We introduce a constructive procedure that maps all spatial correlations of a broad class of states into temporal correlations between general quantum measurements. This allows us to present temporal phenomena analogous to genuinely…
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Quantum mechanics can produce correlations that are stronger than classically allowed. This stronger-than-classical correlation is the "fuel" for quantum computing. In 1991 Schumacher forwarded a beautiful geometric approach, analogous to…
We derive fundamental bounds for general quantum metrological models involving both temporal or spatial correlations (mathematically described by quantum combs), which may be effectively computed in the limit of a large number of probes or…
We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence…
For systems of an arbitrary dimension, a theory of geometric chained Bell inequalities is presented. The approach is based on chained inequalities derived by Pykacz and Santos. For maximally entangled states the inequalities lead to a…