Related papers: Quantum unsharpness and symplectic rigidity
Invertibility of Toeplitz operators on the Bergman space and the related Douglas problem are long standing open problems. In this paper we study the invertibility problem under the novel geometric condition on the image of the symbols,…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
We establish a relationship between a certain notion of covering complexity of a Riemannian spin manifold and positive lower bounds on its scalar curvature. This makes use of a pairing between quantitative operator $K$-theory and Lipschitz…
By decomposing the regular representation of a particular (Heisenberg-like) Lie supergroup into irreducible subspaces, we show that not all of them can be obtained by applying geometric quantization to coadjoint orbits with an even…
Entanglement is a key ingredient for quantum technologies and a fundamental signature of quantumness in a broad range of phenomena encompassing many-body physics, thermodynamics, cosmology, and life sciences. For arbitrary multiparticle…
We introduce a minimalistic notion of semiclassical quantization and use it to prove that the convex hull of the semiclassical spectrum of a quantum system given by a collection of commuting operators converges to the convex hull of the…
The combination of topology and quantum criticality can give rise to an exotic mix of counterintuitive effects. Here, we show that unexpected topological properties take place in a paradigmatic strongly-correlated Hamiltonian: the 1D…
In this paper, we study quantization on a compact integral symplectic manifold $X$ with transversal real polarizations. In the case of complex polarizations, namely $X$ is K\"ahler equipped with transversal complex polarizations $T^{1, 0}X,…
In both quantum computing and black hole physics, it is natural to regard some deformations, infinitesimal unitaries, as \emph{easy} and others as \emph{hard}. This has lead to a renewed examination of right-invariant metrics on…
The topological charge of a photonic vortex is an essential quantity in singular optics and the critical parameter to characterize the vorticity of twisted light. However, the definition of the photonic topological charge remains elusive.…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance is not broken.…
In this paper, we study the basic properties of Toeplitz Operators with positive measures $\mu$ on harmonic Fock spaces. We prove equivalent conditions for boundedness, compactness and Schatten classes $S_{p}$ of $T_{\mu}$ by using the…
Skew information is a pivotal concept in quantum information, quantum measurement, and quantum metrology. Further studies have lead to the uncertainty relations grounded in metric-adjusted skew information. In this work, we present an…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
The uncertainty principle is deemed as one of cornerstones in quantum mechanics, and exploring its lower limit of uncertainty will be helpful to understand the principle's nature. In this study, we propose a generalized entropic uncertainty…
We construct a canonical quantization of the two dimensional theory of a parametrized scalar field on noncompact spatial slices. The kinematics is built upon generalized charge-network states which are labelled by smooth embedding…
In this paper, we construct a family of Berezin-Toeplitz type quantizations of a compact symplectic manifold. For this, we choose a Riemannian metric on the manifold such that the associated Bochner Laplacian has the same local model at…
A full off-diagonal asymptotic expansion is established for the generalized Bergman kernels of the renormalized Bochner Laplacians associated with high tensor powers of a positive line bundle over a compact symplectic manifold. As an…
We propose a theory of quantum (statistical) measurement which is close, in spirit, to Hepp's theory, which is centered on the concepts of decoherence and macroscopic (classical) observables, and apply it to a model of the Stern-Gerlach…