¨¸Ó³ ¢ —Ÿ. 2009. ’. 6, º 7(156). ‘. 96Ä101 ŠŒœ’…›… ’…•‹ƒˆˆ ‚ ”ˆ‡ˆŠ… QUANTUM FIDELITY OF GAUSSIAN STATES IN OPEN SYSTEMS A. Isar 1 National Institute for Physics and Nuclear Engineering, Bucharest-Magurele, Romania Using the expression of the ˇdelity for the most general Gaussian quantum states, the behaviour of the quantum ˇdelity is described for the states of a harmonic oscillator interacting with an environment, in particular with a thermal bath. By taking a correlated squeezed Gaussian state as initial state, we calculate the quantum ˇdelity for both kinds of undisplaced and displaced states, and for different values of the squeezing and correlation parameters and of the environment temperature. ‘ ¨¸¶μ²Ó§μ¢ ´¨¥³ ¢Ò· ¦¥´¨Ö Éμδμ¸É¨ ¤²Ö ´ ¨¡μ²¥¥ μ¡Ð¨Ì £ Ê¸¸μ¢ÒÌ ±¢ ´Éμ¢ÒÌ ¸μ¸ÉμÖ´¨° 춨¸ ´μ ¶μ¢¥¤¥´¨¥ ±¢ ´Éμ¢μ° Éμδμ¸É¨ ¤²Ö ¸μ¸ÉμÖ´¨° £ ·³μ´¨Î¥¸±μ£μ μ¸Í¨²²ÖÉμ· , ¢§ ¨³μ¤¥°¸É¢Ê- ÕÐ¥£μ ¸ μ±·Ê¦¥´¨¥³, ¢ Π¸É´μ¸É¨ ¸ É¥¶²μ¢Ò³ ·¥§¥·¢Ê ·μ³. …¸²¨ ¢§ÖÉÓ ±μ··¥²¨·μ¢ ´´μ¥ ¸¦ Éμ¥ £ Ê¸¸μ¢μ ¸μ¸ÉμÖ´¨¥ ± ± ´ Î ²Ó´μ¥ ¸μ¸ÉμÖ´¨¥, ³μ¦´μ ¢ÒΨ¸²¨ÉÓ ±¢ ´Éμ¢ÊÕ Éμδμ¸ÉÓ ± ± ¤²Ö ´¥- ¸³¥Ð¥´´ÒÌ, É ± ¨ ¸³¥Ð¥´´ÒÌ ¸μ¸ÉμÖ´¨° ¶·¨ · §²¨Î´ÒÌ §´ Î¥´¨ÖÌ μ±·Ê¦ ÕÐ¥° É¥³¶¥· ÉÊ·Ò ¨ ¶ · ³¥É·μ¢ ¸¦ É¨Ö ¨ ±μ··¥²Öͨ¨. PACS: 03.67.Mn, 01.30.Cc, 03.67.-a INTRODUCTION In recent years there has been an increased interest in the study of Gaussian states of continuous variable systems used in quantum information processing. Usually, the quantum ˇdelity for quantum optics experiments, in particular quantum teleportation experiments, is calculated for pure coherent states as input states. However, in real experiments the in- put quantum states have some non-negligible degree of mixedness, achieved mainly due to the decoherence phenomenon which takes place during the interaction of the system with its environment. In the framework of the theory of open systems based on quantum dy- namical semigroups, we consider a one-dimensional harmonic oscillator interacting with an environment, in particular with a thermal bath. Our purpose is to study the inuence of the environment on the time evolution of the quantum ˇdelity for Gaussian states of the con- sidered system. The structure of the paper is the following. In Sec. 1 we briey review the basic formalism for the calculation of the quantum ˇdelity for a general pair of single-mode Gaussian states. The time evolution of the harmonic oscillator in the theory of open quantum systems is described in Sec. 2. By taking a correlated squeezed Gaussian state as initial state, the quantum ˇdelity of this initial pure state and an arbitrary time mixed state of the considered system is calculated in Sec. 3. A summary is given in the ˇnal section. 1 E-mail: isar@theory.nipne.ro