Related papers: Quantum coherence generating power, maximally abel…
Given a preferred orthonormal basis $B$ in the Hilbert space of a quantum system we define a measure of the coherence generating power of a unitary operation with respect to $B$. This measure is the average coherence generated by the…
Given an orthonormal basis in a $d$-dimensional Hilbert space and a unital quantum operation $\cal E$ acting on it one can define a non-linear mapping that associates to $\cal E$ a $d\times d$ real-valued matrix that we call the Coherence…
The maximal minors of a p by (m + p) matrix of univariate polynomials of degree n with indeterminate coefficients are themselves polynomials of degree np. The subalgebra generated by their coefficients is the coordinate ring of the quantum…
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system with a complex projective Hilbert space as its phase space, thus equipped with a Riemannian metric in addition to a symplectic structure.…
Metrics in Grassmannians, or distances between subspaces of same dimension, have many uses, and extending them to the Total Grassmannian of subspaces of different dimensions is an important problem, as usual extensions lack good properties…
Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a…
We study the ability of a quantum channel to generate quantum coherence when it applies to incoherent states. Based on probabilistic averages, we define a measure of such coherence generating power (CGP) for a generic quantum channel, based…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
We elaborate that $s$-wave and $d$-wave superconductors described by mean field theories possess a nontrivial quantum geometry. From the overlap of two quasihole states at slightly different momenta, one can define a quantum metric that…
The complete quantum metric of a parametrized quantum system has a real part (usually known as the Provost-Vallee metric) and a symplectic imaginary part (known as the Berry curvature). In this paper, we first investigate the relation…
The operational meaning of coherence measure lies at very heart of the coherence theory. In this paper, we provide an operational interpretation for geometric coherence, by proving that the geometric coherence of a quantum state is equal to…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \delta_{ij} + g(P^2) P_i P_j $ for any…
Much of our understanding of gapless quantum matter stems from low-energy descriptions using conformal field theory. This is especially true in 1+1 dimensions, where such theories have an infinite-dimensional parameter space induced by…
Quantum geometry has emerged as a central and ubiquitous concept in quantum sciences, with direct consequences on quantum metrology and many-body quantum physics. In this context, two fundamental geometric quantities are known to play…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
Attention is focused on antisymmetrized versions of quantum spaces that are of particular importance in physics, i.e. two-dimensional quantum plane, q-deformed Euclidean space in three or four dimensions as well as q-deformed Minkowski…
We study the PI degree of various quantum algebras at roots of unity, including quantum Grassmannians, quantum Schubert varieties, partition subalgebras, and their associated quantum affine spaces. By a theorem of De Concini and Procesi,…
It is well--known that if one is given a principal $G$--bundle with a principal connection, then for every unitary finite--dimensional linear representation of $G$ one can induce a linear connection and a Hermitian structure on the…
Reduction of a state of a quantum system to a subsystem gives partial quantum information about the true state of the total system. Two subalgebras A1 and A2 of B(H) are called complementary if the traceless subspaces of A1 and A2 are…