Paulina Marian

Continuous-variable teleportation in the characteristic-function description

We give a description of the continuous-variable teleportation protocol in terms of the characteristic functions of the quantum states involved. The Braunstein-Kimble protocol is written for an unbalanced homodyne measurement and arbitrary input and resource states. We show that the output of the protocol is a superposition between the input one-mode field and a classical one induced by measurement and classical communication. We choose to describe the input state distortion through teleportation by the average photon number of the measurement-induced field. Only in the case of symmetric Gaussian resource states we find a relation between the optimal added noise and the minimal EPR correlations used to define inseparability.

Uhlmann fidelity between two-mode Gaussian states

We analyze the Uhlmann fidelity of a pair of

Quantum degrees of polarization

n

Entanglement of Formation for an Arbitrary Two-Mode Gaussian State

-mode Gaussian states of the quantum radiation field. This quantity is shown to be the product of an exponential function depending on the relative average displacement and a factor fully determined by the symplectic spectrum of the covariance matrix of a specific Gaussian state. However, it is difficult to handle our general formula unless the Gaussian states commute or at least one of them is pure. On the contrary, in the simplest cases

Inseparability of mixed two-mode Gaussian states generated with a SU(1,1) interferometer

n=1

Bures distance as a measure of entanglement for symmetric two-mode Gaussian states

and

Relative entropy is an exact measure of non-Gaussianity

n=2

Measures of non-Gaussianity for one-mode field states

, it leads to explicit analytic formulas. Our main result is a calculable expression of the fidelity of two arbitrary two-mode Gaussian states. This can be applied to build reliable measures of quantum correlations between modes in various branches of quantum physics.

Hellinger distance as a measure of Gaussian discord

We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results. Still, we argue that these operators and their properties should be basic for any measure of polarization. We compare alternative quantum degrees and put forth that they order various states differently. This is to be expected, since, despite being rooted in the Stokes operators, each of these measures only captures certain characteristics. Therefore, it is likely that several quantum degrees of polarization will coexist, each one having its specific domain of usefulness.

Quantum Fisher information on two manifolds of two-mode Gaussian states

We write the optimal pure-state decomposition of any two-mode Gaussian state and show that its entanglement of formation coincides with the Gaussian one. This enables us to develop an insightful approach of evaluating the exact entanglement of formation. Its additivity is finally proven.