The minimal Kitaev chain that emulates a topological superconductor with three quantum dots offers a tunable platform for potentially hosting poor man's Majorana (PMM) modes. Asserting the need to go beyond differential conductance spectroscopy, we introduce current-current correlations as a viable framework for verifying their true non-locality. The robustness of the PMM modes, specifically with respect to delocalization as the system is tuned away from sweet spots, we show, is embedded in the relative magnitudes of the nonlocal transport processes. This aspect is adeptly captured by current cross-correlations, whose features show remarkable stability around the PMM sweet spot, specifically with respect to the detuning of an outer dot. We establish this as a prominent feature and a diagnostic for true PMMs even in the short chain limit. Our results accentuate the need for current cross-correlation measurements as a diagnostic framework for unambiguously verifying true non-locality of entangled states as well as topologically protected states.
Generating non-locally entangled electron pairs via Cooper-pair splitting is vital for solid-state quantum information processing. However, isolating the underlying crossed Andreev reflection (CAR) is challenging due to competing transport processes like electron tunneling (ET) and local Andreev reflection (AR). Here, we propose a flux-tunable four-terminal normal metal-superconductor junction that achieves deterministic, 100\% efficient CAR. We demonstrate that at exactly half a magnetic flux quantum (
φ=π), exact destructive Aharonov-Bohm and Peierls interferences structurally forbid ET and AR respectively. By tuning the central junction hopping, electron reflection is also suppressed to zero. Using the Cauchy argument principle, we prove that this suppression manifests as a quantized topological winding number, guaranteeing a topologically protected unit CAR probability. We establish that this regime is characterized by a strictly positive cross-correlation shot noise, providing an unambiguous experimental signature of Cooper-pair splitting. Furthermore, this perfect CAR is nearly broadband within the superconducting gap and remarkably robust against structural disorder, offering a highly resilient architecture for deterministic nonlocal entanglement generation.
Charge and spin current correlations are analyzed in a source of spin-entangled electrons built from a superconductor and two quantum dots in parallel. In addition to the ideal (crossed Andreev) channel, parasitic channels (direct Andreev and cotunneling) and spin flip processes are fully described in a density matrix framework. The way they reduce both the efficiency and the fidelity of the entangler is quantitatively described by analyzing the zero-frequency noise correlations of charge current as well as spin current in the two output branches. Spin current noise is characterized by a spin Fano factor, equal to 0 (total current noise) and -1 (crossed correlations) for an ideal entangler. The violation of the Bell inequalities, as a test of non-locality (entanglement) of split pairs, is formulated in terms of the correlations of electron charge and spin numbers counted in a specific time window
τ. The efficiency of the test is analyzed, comparing
τ to the various time scales in the entangler operation.