Separability Criteria from Uncertainty Relations

We explain several separability criteria which rely on uncertainty relations. For the derivation of these criteria uncertainty relations in terms of variances or entropies can be used. We investigate the strength of the separability conditions for the case of two qubits and show how they can improve entanglement witnesses.Comment: 4 pages, 2 figures, contribution for the proceedings of QCMC 2004 in Glasgo

Two measurement settings can suffice to verify multipartite entanglement

We present entanglement witnesses for detecting genuine multi-qubit entanglement. Our constructions are robust against noise and require only two local measurement settings, independent of the number of qubits. Thus they allow to verify entanglement of many qubits in experiments while requiring only a small effort. In contrast, usual methods need an effort which increases exponentially with the number of qubits. The witnesses detect states close to GHZ states and cluster states.Comment: 4 pages including a figure, LaTeX; to appear in the conference proceedings of QCMC0

Multipartite entanglement in spin chains

We investigate the presence of multipartite entanglement in macroscopic spin chains. We discuss the Heisenberg and the XY model and derive bounds on the internal energy for systems without multipartite entanglement. Based on this we show that in thermal equilibrium the above mentioned spin systems contain genuine multipartite entanglement, even at finite modest temperatures.Comment: 5 pages, 1 figure, to appear in New J. Phy

Memory cost of quantum contextuality

The simulation of quantum effects requires certain classical resources, and quantifying them is an important step in order to characterize the difference between quantum and classical physics. For a simulation of the phenomenon of state-independent quantum contextuality, we show that the minimal amount of memory used by the simulation is the critical resource. We derive optimal simulation strategies for important cases and prove that reproducing the results of sequential measurements on a two-qubit system requires more memory than the information carrying capacity of the system.Comment: 18 pages, no figures, v2: revised for clarit

Enhanced entanglement criterion via symmetric informationally complete measurements

We show that a special type of measurements, called symmetric informationally complete positive operator-valued measures (SIC POVMs), provide a stronger entanglement detection criterion than the computable cross-norm or realignment criterion based on local orthogonal observables. As an illustration, we demonstrate the enhanced entanglement detection power in simple systems of qubit and qutrit pairs. This observation highlights the significance of SIC POVMs for entanglement detection

Bounding the quantum dimension with contextuality

We show that the phenomenon of quantum contextuality can be used to certify lower bounds on the dimension accessed by the measurement devices. To prove this, we derive bounds for different dimensions and scenarios of the simplest noncontextuality inequalities. Some of the resulting dimension witnesses work independently of the prepared quantum state. Our constructions are robust against noise and imperfections, and we show that a recent experiment can be viewed as an implementation of a state-independent quantum dimension witness