**Symplectic Geometry of Quantum Noise**

by Leonid Polterovich

**Publisher**: arXiv 2012**Number of pages**: 57

**Description**:

We discuss a quantum counterpart, in the sense of the Berezin-Toeplitz quantization, of certain constraints on Poisson brackets coming from 'hard' symplectic geometry. It turns out that they can be interpreted in terms of the quantum noise of observables and their joint measurements in operational quantum mechanics. Our findings include various geometric mechanisms of quantum noise production and a noise-localization uncertainty relation.

Download or read it online for free here:

**Download link**

(470KB, PDF)

## Similar books

**Symplectic, Poisson, and Noncommutative Geometry**

by

**Tohru Eguchi, et al.**-

**Cambridge University Press**

Symplectic geometry has its origin in physics, but has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics ...

(

**1221**views)

**Introduction to the Basics of Heegaard Floer Homology**

by

**Bijan Sahamie**-

**arXiv**

This is an introduction to the basics of Heegaard Floer homology with some emphasis on the hat theory and to the contact geometric invariants in the theory. It is designed to be comprehensible to people without any prior knowledge of the subject.

(

**4006**views)

**Introduction to Symplectic Field Theory**

by

**Y. Eliashberg, A. Givental, H. Hofer**-

**arXiv**

We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifolds in the spirit of topological field theory.

(

**8369**views)

**Introduction to Symplectic and Hamiltonian Geometry**

by

**Ana Cannas da Silva**

The text covers foundations of symplectic geometry in a modern language. It describes symplectic manifolds and their transformations, and explains connections to topology and other geometries. It also covers hamiltonian fields and hamiltonian actions.

(

**9933**views)