TY - JOUR
T1 - Symplectic Geometry of Quantum Noise
AU - Polterovich, Leonid
N1 - Funding Information:
Partially supported by the National Science Foundation grant DMS-1006610, the Israel Science Foundation grants 509/07, 178/13 and the European Research Council Advanced grant 338809.
PY - 2014/4
Y1 - 2014/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84897579517&partnerID=8YFLogxK
U2 - 10.1007/s00220-014-1937-9
DO - 10.1007/s00220-014-1937-9
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AN - SCOPUS:84897579517
SN - 0010-3616
VL - 327
SP - 481
EP - 519
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -