Symplectic Geometry of Quantum Noise

Leonid Polterovich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

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. The methods involve Floer theory and Poisson bracket invariants originated in function theory on symplectic manifolds.

Original languageEnglish
Pages (from-to)481-519
Number of pages39
JournalCommunications in Mathematical Physics
Volume327
Issue number2
DOIs
StatePublished - Apr 2014

Funding

FundersFunder number
European Research Council
National Science Foundation
National Science FoundationDMS-1006610
Seventh Framework Programme338809
European Research Council
Israel Science Foundation178/13, 509/07

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