Minimal Entanglement Witness from Electrical Current Correlations

Abstract

Despite great efforts, an unambiguous demonstration of entanglement of mobile electrons in solid state conductors is still lacking. Investigating theoretically a generic entangler-detector setup, we here show that a witness of entanglement between two flying electron qubits can be constructed from only two current cross correlation measurements, for any nonzero detector efficiencies and non-collinear polarization vectors. We find that all entangled pure states, but not all mixed ones, can be detected with only two measurements, except the maximally entangled states, which require three. Moreover, detector settings for optimal entanglement witnessing are presented. [19,20], even when the number of entangled particles is large [21].The prospects of few-measurement entanglement detection make witnesses particularly interesting for flying qubits in solid state conductors, where an unambiguous demonstration of entanglement is still lacking. Here, detection schemes for spatially separated, spin [22,23] or orbitally [24][25][26][27] entangled, electrons have been proposed based on experimentally accessible current cross correlations [28]. However, the required set of measurements, with different, non-collinear detector settings and correlations between two or more pairs of detector terminals, are experimentally highly challenging. Aiming for less demanding measurements, works [29,30] on witnesses have proposed schemes with only two or three settings and less than ten cross correlations, allowing detection of certain classes of entangled states. Yet, two fundamental questions remain unanswered: (i) What is the minimum number of current cross correlation measurements needed for an entanglement witness? (ii) Which entangled states can be detected by such a witness?Here we answer these two questions within a generic solid state entangler-detector model, see Fig. 1. We find that only two cross correlation measurements -two detector settings with one measurement per setting -are sufficient to constitute a witness. Moreover, we show that all entangled pure (but not all mixed) states can be detected by the witness, except the maximally entangled, which require three measurements. In addition, the

Real-time observation of Cooper pair splitting showing strong non-local correlations

“…Alternatively, ferromagnetic leads may be used to determine the spin state of the electrons 41 , 42 . Thus, by combining the fast charge detection with the spin readout, one may witness and certify the quantum entanglement of the split Cooper pairs 43 , 44 . Ultimately, several Cooper pair splitters may be combined to realize the first rudimentary quantum information algorithms using split Cooper pairs.…”

From Cooper pair splitting to the non-local spectroscopy of a Shiba state

“…Theoretically, several ways were proposed to test the performance of a Cooper pair splitter device, starting from current or noise correlations, [19][20][21] through spin selective measurements [22][23][24][25] to proving the entanglement by demonstrating the violation of the Bellinequality 18,[26][27][28][29][30][31][32] or using more complex spin-qubit or circuit quantum electrodynamics architectures 17,33,34 or even time domain measurements. 35 The experiments primarily focused on spatial current correlations.…”

Noise and full counting statistics of a Cooper pair splitter

“…1. To certify the entanglement of the split Cooper pairs, it has been suggested that Bell inequalities can be formulated for the cross correlations of the output currents, using ferromagnetic leads as spin filters [3][4][5][6][7][8].…”