Viable entanglement detection of unknown mixed states in low dimensions

We explore procedures to detect entanglement of unknown mixed states, which can be experimentally viable. The heart of the method is a hierarchy of simple feasibility problems, which provides sufficient conditions to entanglement. Our numerical investigations indicate that the entanglement is detected with a cost which is much lower than full state tomography. The procedure is applicable to both free and bound entanglement, and involves only single copy measurements.Comment: 8 pages, 9 figures, 4 table

Schmidt balls around the identity

Robustness measures as introduced by Vidal and Tarrach [PRA, 59, 141-155] quantify the extent to which entangled states remain entangled under mixing. Analogously, we introduce here the Schmidt robustness and the random Schmidt robustness. The latter notion is closely related to the construction of Schmidt balls around the identity. We analyse the situation for pure states and provide non-trivial upper and lower bounds. Upper bounds to the random Schmidt-2 robustness allow us to construct a particularly simple distillability criterion. We present two conjectures, the first one is related to the radius of inner balls around the identity in the convex set of Schmidt number n-states. We also conjecture a class of optimal Schmidt witnesses for pure states.Comment: 7 pages, 1 figur

Optimal measurement bases for Bell-tests based on the CH-inequality

The Hardy test of nonlocality can be seen as a particular case of the Bell tests based on the Clauser-Horne (CH) inequality. Here we stress this connection when we analyze the relation between the CH-inequality violation, its threshold detection efficiency, and the measurement settings adopted in the test. It is well known that the threshold efficiencies decrease when one considers partially entangled states and that the use of these states, unfortunately, generates a reduction in the CH violation. Nevertheless, these quantities are both dependent on the measurement settings considered, and in this paper we show that there are measurement bases which allow for an optimal situation in this trade-off relation. These bases are given as a generalization of the Hardy measurement bases, and they will be relevant for future Bell tests relying on pairs of entangled qubits.Comment: 8 pages, 6 figure

Quantifying Quantum Correlations in Fermionic Systems using Witness Operators

We present a method to quantify quantum correlations in arbitrary systems of indistinguishable fermions using witness operators. The method associates the problem of finding the optimal entan- glement witness of a state with a class of problems known as semidefinite programs (SDPs), which can be solved efficiently with arbitrary accuracy. Based on these optimal witnesses, we introduce a measure of quantum correlations which has an interpretation analogous to the Generalized Robust- ness of entanglement. We also extend the notion of quantum discord to the case of indistinguishable fermions, and propose a geometric quantifier, which is compared to our entanglement measure. Our numerical results show a remarkable equivalence between the proposed Generalized Robustness and the Schliemann concurrence, which are equal for pure states. For mixed states, the Schliemann con- currence presents itself as an upper bound for the Generalized Robustness. The quantum discord is also found to be an upper bound for the entanglement.Comment: 7 pages, 6 figures, Accepted for publication in Quantum Information Processin

Mutations in the intellectual disability gene Ube2a cause neuronal dysfunction and impair parkin-dependent mitophagy

The prevalence of intellectual disability is around 3%; however, the etiology of the disease remains unclear in most cases. We identified a series of patients with X-linked intellectual disability presenting mutations in the Rad6a (Ube2a) gene, which encodes for an E2 ubiquitin-conjugating enzyme. Drosophila deficient for dRad6 display defective synaptic function as a consequence of mitochondrial failure. Similarly, mouse mRad6a (Ube2a) knockout and patient-derived hRad6a (Ube2a) mutant cells show defective mitochondria. Using in vitro and in vivo ubiquitination assays, we show that RAD6A acts as an E2 ubiquitin-conjugating enzyme that, in combination with an E3 ubiquitin ligase such as Parkin, ubiquitinates mitochondrial proteins to facilitate the clearance of dysfunctional mitochondria in cells. Hence, we identify RAD6A as a regulator of Parkin-dependent mitophagy and establish a critical role for RAD6A in maintaining neuronal function