Witnessed Entanglement

We present a new measure of entanglement for mixed states. It can be approximately computable for every state and can be used to quantify all different types of multipartite entanglement. We show that it satisfies the usual properties of a good entanglement quantifier and derive relations between it and other entanglement measures.Comment: Revised version. 7 pages and one figur

Entangled inputs cannot make imperfect quantum channels perfect

Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the non-additivity of several quantities relevant for quantum information science. In this work, we answer the converse question (whether entangled inputs can ever render noisy quantum channels have maximum capacity) to the negative: No sophisticated entangled input of any quantum channel can ever enhance the capacity to the maximum possible value; a result that holds true for all channels both for the classical as well as the quantum capacity. This result can hence be seen as a bound as to how "non-additive quantum information can be". As a main result, we find first practical and remarkably simple computable single-shot bounds to capacities, related to entanglement measures. As examples, we discuss the qubit amplitude damping and identify the first meaningful bound for its classical capacity.Comment: 5 pages, 2 figures, an error in the argument on the quantum capacity corrected, version to be published in the Physical Review Letter

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

Measuring the extent of convective cores in low-mass stars using Kepler data: towards a calibration of core overshooting

Our poor understanding of the boundaries of convective cores generates large uncertainties on the extent of these cores and thus on stellar ages. Our aim is to use asteroseismology to consistently measure the extent of convective cores in a sample of main-sequence stars whose masses lie around the mass-limit for having a convective core. We first test and validate a seismic diagnostic that was proposed to probe in a model-dependent way the extent of convective cores using the so-called $r_{010}$ ratios, which are built with $l=0$ and $l=1$ modes. We apply this procedure to 24 low-mass stars chosen among Kepler targets to optimize the efficiency of this diagnostic. For this purpose, we compute grids of stellar models with both the CESAM2k and MESA evolution codes, where the extensions of convective cores are modeled either by an instantaneous mixing or as a diffusion process. Among the selected targets, we are able to unambiguously detect convective cores in eight stars and we obtain seismic measurements of the extent of the mixed core in these targets with a good agreement between the CESAM2k and MESA codes. By performing optimizations using the Levenberg-Marquardt algorithm, we then obtain estimates of the amount of extra-mixing beyond the core that is required in CESAM2k to reproduce seismic observations for these eight stars and we show that this can be used to propose a calibration of this quantity. This calibration depends on the prescription chosen for the extra-mixing, but we find that it should be valid also for the code MESA, provided the same prescription is used. This study constitutes a first step towards the calibration of the extension of convective cores in low-mass stars, which will help reduce the uncertainties on the ages of these stars.Comment: 27 pages, 15 figures, accepted in A&

Comment on Baltic provenance of top-Famennian siliciclastic material of the northern Rhenish Massif, Rhenohercynian zone of the Variscan orogen, by Koltonik et al., International Journal of Earth Sciences (2018) 107:2645–2669

Koltonik et al. (Int J Earth Sci 107:2645–2669, 2018) evidence that the Late Devonian siliciclastic rocks from the Rheno- Hercynian Zone, in Germany, derived from Baltica and Scandinavian Caledonides. This finding together with what is known about the provenance of the Pulo do Lobo and South Portuguese zones, in Portugal and Spain, reinforces the probability that Late Devonian basins may have been sourced from distinct terranes placed along the Variscan suture. Our comment intends to underline changes in the provenance of the Late Devonian basins along the active margin of Laurussia, and also, to improve the correlation model for the Variscan tectonic units from SW Iberia and Germany

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

Experimental implementation of a NMR entanglement witness

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance (NMR) experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW's are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance