Reinhold A. Bertlmann

Bloch vectors for qudits

We present three different matrix bases that can be used to decompose density matrices of d-dimensional quantum systems, so-called qudits: the generalized Gell–Mann matrix basis, the polarization operator basis and the Weyl operator basis. Such a decomposition can be identified with a vector—the Bloch vector, i.e. a generalization of the well-known qubit case—and is a convenient expression for comparison with measurable quantities and for explicit calculations avoiding the handling of large matrices. We present a new method to decompose density matrices via so-called standard matrices, consider the important case of an isotropic two-qudit state and decompose it according to each basis. In the case of qutrits we show a representation of an entanglement witness in terms of expectation values of spin-1 measurements, which is appropriate for an experimental realization.

A Geometric picture of entanglement and Bell inequalities

We work in the real Hilbert space

Two-dimensional gravitational anomalies, Schwinger terms and dispersion relations

{\mathcal{H}}_{s}

Relativistic entanglement of two massive particles

of Hermitian Hilbert-Schmidt operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set

Decoherence of entangled kaons and its connection to entanglement measures

S\ensuremath{\subset}{\mathcal{H}}_{s}

Bell inequality and CP violation in the neutral kaon system

of separable states. This violation equals the Euclidean distance in

Residual entanglement of accelerated fermions is not nonlocal

{\mathcal{H}}_{s}

Optimal entanglement witnesses for qubits and qutrits

of the entangled state to S and thus entanglement, GBI, and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.

Entanglement or separability: the choice of how to factorize the algebra of a density matrix

Abstract 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.

Multipartite entanglement detection via structure factors.

We describe the spin and momentum degrees of freedom of a system of two massive spin--