The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation. © 2007 IOP Publishing Ltd.
Symplectic entropy / S., De Nicola; Fedele, Renato; M. A., Man'Ko; V. I., Man'Ko. - In: JOURNAL OF PHYSICS. CONFERENCE SERIES. - ISSN 1742-6588. - STAMPA. - 70:1(2007), pp. 012007-1-012007-14. [10.1088/1742-6596/70/1/012007]
Symplectic entropy
FEDELE, RENATO;
2007
Abstract
The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation. © 2007 IOP Publishing Ltd.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.