**Quantum Noise in the Mapping of the Phase Space
**

**D. Kuznetsov* and D. Rohrlich**
**

** National University of Mexico, Mexico
*

*** School of Physics and Astronomy, Tel Aviv University, Tel Aviv, 69978 Israel
*

Received October 29, 1996

**Abstract**—Quadrature components of a single-mode field are interpreted as coordinates of the phase space.

Itis assumed that a quantum amplifier transforms the state of a single mode and the initial state of the field in

this mode is a coherent squeezed one. The transfer function relating the average values of the field in the initial

and final states determines mapping of the phase state. In the case of amplification, the field uncertainty in the

final state is usually greater than in the initial state. This increase is interpreted as quantum noise of the ampli-

fier. The lower bounds of this noise are estimated in terms of the derivatives of the transfer function. A degen-

erate parametric amplifier with pumping depletion is considered to be an illustration. Transformation of an ini-

tially orthogonal rectangular net in the phase space and deformation of the body of uncertainty given by the

Wigner function are constructed for such an amplifier.

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