On von Neumann and Bell theorems applied to quantumness tests

The issues, raised in arXiv:0809.011, concerning the relevance of the von Neumann theorem for the single-system's quantumness test proposed in arXiv:0704.1962 and performed for the case of single photon polarization in arXiv:0804.1646, and the usefulness of Bell's inequality for testing the idea of macroscopic quantum systems are discussed in some details. Finally, the proper quantum mechanical description of the experiment with polarized photon beams is presented.Comment: 6 pages, no figure

Connections and Metrics Respecting Standard Purification

Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert-Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one-to-one. Our methods are borrowed from elementary *-representation and fibre space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and ``add noise'' to a curve of pure states.Comment: Latex, 27 page

Alice falls into a black hole: Entanglement in non-inertial frames

Two observers determine the entanglement between two free bosonic modes by each detecting one of the modes and observing the correlations between their measurements. We show that a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated. This phenomenon, which is a consequence of the Unruh effect, shows that entanglement is an observer-dependent quantity in non-inertial frames. In the high acceleration limit, our results can be applied to a non-accelerated observer falling into a black hole while the accelerated one barely escapes. If the observer escapes with infinite acceleration, the state's distillable entanglement vanishes.Comment: I.F-S published before with maiden name Fuentes-Guridi Replaced with published version. Phys. Rev. Lett. in pres

Research of Gravitation in Flat Minkowski Space

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession, i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the $n$-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order $c^{-2}$.Comment: 28 page

Entanglement of Dirac fields in non-inertial frames

We analyze the entanglement between two modes of a free Dirac field as seen by two relatively accelerated parties. The entanglement is degraded by the Unruh effect and asymptotically reaches a non-vanishing minimum value in the infinite acceleration limit. This means that the state always remains entangled to a degree and can be used in quantum information tasks, such as teleportation, between parties in relative uniform acceleration. We analyze our results from the point of view afforded by the phenomenon of entanglement sharing and in terms of recent results in the area of multi-qubit complementarity.Comment: 15 pages, with 8 figures (Mar 2006); accepted to Physical Review A, July 2006 - slightly revise

Degradation of non-maximal entanglement of scalar and Dirac fields in non-inertial frames

The entanglement between two modes of the free scalar and Dirac fields as seen by two relatively accelerated observers has been investigated. It is found that the same initial entanglement for an initial state parameter $\alpha$ and its "normalized partner" $\sqrt{1-\alpha^{2}}$ will be degraded by the Unruh effect along two different trajectories except for the maximally entangled state, which just shows the inequivalence of the quantization for a free field in the Minkowski and Rindler coordinates. In the infinite acceleration limit the state doesn't have the distillable entanglement for any $\alpha$ for the scalar field but always remains entangled to a degree which is dependent of $\alpha$ for the Dirac field. It is also interesting to note that in this limit the mutual information equals to just half of the initially mutual information, which is independent of $\alpha$ and the type of field.Comment: 9 pages, 4 figure

Speeding up Entanglement Degradation

Entanglement between two free bosonic modes can be determined via detection of each mode by different observers and then observing the correlations between their measurements. We show that such entanglement is degraded as a function of time if one observer begins in a state of inertial motion but ends in a state of uniform acceleration while the other remains inertial. At late times we recover previously established results for observers in relative uniform acceleration.Comment: 5 pages, 2 figure

Quantum discord dynamical behaviors due to initial system-cavity correlations

We analyze the roles of initial correlations between the two-qubit system and a dissipative cavity on quantum discord dynamics of two qubits. Considering two initial system-cavity states, we show that the initial system-cavity correlations not only can initially increase the two-qubit quantum discord but also would lead to a larger long-time quantum discord asymptotic value. Moreover, quantum discord due to initial correlations is more robust than the case of the initial factorized state. Finally, we show the initial correlations' importance for dynamics behaviors of mutual information and classical correlation

Entanglement Creation in Low-Energy Scattering

We study the entanglement creation in the low-energy scattering of two particles in three dimensions, for a general class of interaction potentials that are not required to be spherically symmetric. The incoming asymptotic state, before the collision, is a product of two normalized Gaussian states. After the scattering the particles are entangled. We take as a measure of the entanglement the purity of one of them. We provide a rigorous explicit computation, with error bound, of the leading order of the purity at low-energy. The entanglement depends strongly in the difference of the masses. It takes its minimum when the masses are equal, and it increases rapidly with the difference of the masses. It is quite remarkable that the anisotropy of the potential gives no contribution to the leading order of the purity, on spite of the fact that entanglement is a second order effect.Comment: The paper has been edited and some comments have been adde