Entanglement detection in Cooper pair splitters from dc current measurements without the efficiency limit of magnetic detectors

We present theoretical studies on models for experimental determination of spin correlations and detection of quantum entanglement of spatially separated electrons of Cooper pairs. These models are based on both electric current cross-correlations and simpler dc current measurements. By proper optimization of the entanglement witness method, we demonstrate that entanglement detection is possible with any magnetic detectors regardless of their efficiency. This allows us to break the relatively high previously established limit of detector efficiency (spin polarization), $p>1/\sqrt{3}\ensuremath{\approx}58%$.