Related papers: Is Quantization Geometry?

In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…

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),…

Measurement is a fundamental operation in quantum computing and has many important use cases in quantum algorithms. This article provides a comprehensive overview of the basic measurement operations in quantum computing and represents a…

We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical…

A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical…

Probabilistic Spacetime is a simple generalization of the classical model of spacetime in General Relativity, such that it allows to consider multiple metric field realizations endowed with probabilities. The motivation for such a…

Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

We discuss and implement experimentally a method for characterizing quantum gates operating on superpositions of coherent states. The peculiarity of this encoding of qubits is to work with a non-orthogonal basis, and therefore some…

A reliable method for characterizing quantum operations that is suitable for improving and validating their accuracies is indispensable for realizing a practical quantum computer. Known methods are still not sufficient because they lack…

One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus…

Classical mechanics, in the operatorial formulation of Koopman and von Neumann, can be written also in a functional form. In this form two Grassmann partners of time make their natural appearance extending in this manner time to a three…

Measurement is integral to quantum information processing and communication; it is how information encoded in the state of a system is transformed into classical signals for further use. In quantum optics, measurements are typically…

This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.

One of the biggest problems in the theory of quantum information is the quantification of amount of entanglement in an arbitrary multipartite mixed state. Different axiomatic and operational measures were proposed so far. In this work we…

Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…

We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…

The geometric phases for standard coherent states which are widely used in quantum optics have attracted a large amount of attention. Nevertheless, few physicists consider about the counterparts of non-linear coherent states, which are…

We derive the quantization map in geometric quantization of symplectic manifolds via the Poisson sigma model. This gives a polarization-free (path integral) definition of quantization which pieces together most known quantization schemes.…

Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…