Communications in Mathematical Physics

, Volume 327, Issue 2, pp 481–519

Symplectic Geometry of Quantum Noise


DOI: 10.1007/s00220-014-1937-9

Cite this article as:
Polterovich, L. Commun. Math. Phys. (2014) 327: 481. doi:10.1007/s00220-014-1937-9


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.

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael