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Horia Scutaru

Publications and source records attributed to Horia Scutaru.

7 recordsLinked to original sources
arXiv2006

Entanglement and Teleportation of Gaussian States of the Radiation Field

We propose a reliable entanglement measure for a two-mode squeezed thermal state of the quantum electromagnetic field in terms of its Bures distance to the set of all separable states of the same kind. The requisite Uhlmann fidelity of a pair of two-mode squeezed thermal states is evaluated as the maximal transition probability between two four-mode purifications. By applying the Peres-Simon criterion of separability we find the closest separable state. This enables us to derive an insightful expression of the amount of entanglement. Then we apply this measure of entanglement to the study of the Braunstein-Kimble protocol of teleportation. We use as input state in teleportation a mixed one-mode Gaussian state. The entangled state shared by the sender (Alice) and the receiver (Bob) is taken to be a two-mode squeezed thermal state. We find that the properties of the teleported state depend on both the input state and the entanglement of the two-mode resource state. As a measure of the quality of the teleportation process, we employ the Uhlmann fidelity between the input and output mixed one-mode Gaussian states.

quant-ph↗
arXiv1999

On Lieb's conjecture

The reformulation of Lieb's conjecture, in the frame of the harmonuic analysis on the SO(3) group, makes it evident that the exact value of the classical entropy of a pure quantum state, which belongs to the Hilbert space of a (2J+1)-dimensional, unitary, irreducible representation of the SO(3) group, depends only on the parameters which characterize the orbits of this representation. In the case J=1 we give the exact analytic dependence of the classical entropy of a quantum state on the parameters which characterize the orbits and as a consequence we obtain a verification of Lieb's entropy conjecture. We verify this conjecture also for any value of J for the states of the canonical basis of the Hilbert space of the representation. A natural generalization of Lieb's entropy conjecture, which is a new "phenomenon" in the harmonic analysis on SO(3), is discussed in the case J=1.

math-ph↗
arXiv1999

Coherent states and uncertainty relations

A sharp estimation of the $L^p$-norms of some matrix coefficients of the square integrable representations is conjectured. The conjecture can be proved for integer values of $p$ using a result of J. Burbea.

math-ph↗
arXiv1999

A new measure of nonclassical distance

We propose a new measure of the nonclassical distance in the case of Gaussian states. Let us consider two Gaussian states one of which is fixed and the other runs through the set of Gaussian classical states. The maximum value of the fidelity between these two states can be used as a nonclassical distance of the fixed state to the set of classical states, in the same extent as the Hillery measure. This measure increases when on the fixed state acts a Gaussian noise map i.e. the selected state becomes closer to the classical states.

quant-ph↗
arXiv1999

Transition probabilities between quasifree states

We obtain a general formula for the transition probabilities between any state of the algebra of the canonical commutation relations (CCR-algebra) and a squeezed quasifree state. Applications of this formula are made for the case of multimode thermal squeezed states of quantum optics using a general canonical decomposition of the correlation matrix valid for any quasifree state. In the particular case of a one mode CCR-algebra we show that the transition probability between two quasifree squeezed states is a decreasing function of the geodesic distance between the points of the upper half plane representing these states. In the special case of the purification map it is shown that the transition probability between the state of the enlarged system and the product state of real and fictitious subsystems can be a measure for the entanglement.

quant-ph↗
arXiv1999

Bures distance between two displaced thermal states

The Bures distance between two displaced thermal states and the corresponding geometric quantities (statistical metric, volume element, scalar curvature) are computed. Under nonunitary (dissipative) dynamics, the statistical distance shows the same general features previously reported in the literature by Braunstein and Milburn for two--state systems. The scalar curvature turns out to have new interesting properties when compared to the curvature associated with squeezed thermal states.

quant-ph↗