Quantum entanglement has become a resource for the fascinating developments in quantum information and quantum communication during the last decades. It quantifies a certain nonclassical correlation ...property of a density matrix representing the quantum state of a composite system. We discuss the concept of how entanglement changes with respect to different factorizations of the algebra which describes the total quantum system. Depending on the considered factorization a quantum state appears either entangled or separable. For pure states we always can switch unitarily between separability and entanglement, however, for mixed states a minimal amount of mixedness is needed. We discuss our general statements in detail for the familiar case of qubits, the GHZ states, Werner states and Gisin states, emphasizing their geometric features. As theorists we use and play with this free choice of factorization, which for an experimentalist is often naturally fixed. For theorists it offers an extension of the interpretations and is adequate to generalizations, as we point out in the examples of quantum teleportation and entanglement swapping.
Relevant aspects for testing Bell inequalities with entangled meson–antimeson systems are analyzed. In particular, we argue that the results of Go J. Mod. Opt. 51 (2004) 991, which nicely illustrate ...the quantum entanglement of
B-meson pairs, cannot be considered as a Bell-test refuting local realism.
We are dealing with two-dimensional gravitational anomalies, specifically with the Einstein anomaly and the Weyl anomaly, and we show that they are fully determined by dispersion relations ...independent of any renormalization procedure (or ultraviolet regularization). The origin of the anomalies is the existence of a superconvergence sum rule for the imaginary part of the relevant formfactor. In the zero mass limit the imaginary part of the formfactor approaches a δ-function singularity at zero momentum squared, exhibiting in this way the infrared feature of the gravitational anomalies. We find an equivalence between the dispersive approach and the dimensional regularization procedure. The Schwinger terms appearing in the equal time commutators of the energy momentum tensors can be calculated by the same dispersive method. Although all computations are performed in two dimensions the method is expected to work in higher dimensions too.
For the entangled neutral kaon system we formulate a Bell inequality sensitive to
CP violation in mixing. Via this Bell inequality we obtain a bound on the leptonic
CP asymmetry which is violated by ...experimental data. Furthermore, we connect the Bell inequality with a decoherence approach and find a lower bound on the decoherence parameter which practically corresponds to Furry's hypothesis.
I want to give an impression of the time I spent together with John S. Bell, of the atmosphere of our collaboration and friendship. I briefly review our work, the methods of nonrelativistic ...approximations to quantum field theory for calculating the properties of heavy quark-antiquark bound states.
We consider the time evolution of the density matrix
ρ in a 2-dimensional complex Hilbert space. We allow for dissipation by adding to the von Neumann equation a term
D
ρ, which is of Lindblad type ...in order to assure complete positivity of the time evolution. We present five equivalent forms of
D
ρ. In particular, we connect the familiar dissipation matrix
L with a geometric version of
D
ρ, where
L consists of a positive sum of projectors onto planes in
R
3
. We also study the minimal number of Lindblad terms needed to describe the most general case of
D
ρ. All proofs are worked out comprehensively, as they present at the same time a practical procedure how to determine explicitly the different forms of
D
ρ. Finally, we perform a general discussion of the asymptotic behaviour
t→∞ of the density matrix and we relate the two types of asymptotic behaviour with our geometric version of
D
ρ.
The gravitational anomalies in two dimensions, specifically the Einstein anomaly and the Weyl anomaly, are fully determined by means of dispersion relations. In this approach the anomalies originate ...from the peculiar infrared feature of the imaginary part of the relevant formfactor which approaches a
δ-function singularity at zero momentum squared when
m→0.
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