Detection of entanglement by helical Luttinger liquids
  A Cooper-pair or electron-hole splitter is a device capable of spatially separating entangled fermionic quasiparticles into mesoscopic solid-state systems such as quantum dots or quantum wires. We theoretically study such a splitter based on a pair of helical Luttinger liquids, which arise naturally at the edges of a quantum spin Hall insulator. Equipping each helical liquid with a beam splitter, current-current cross correlations can be used to construct a Bell inequality whose violation would indicate nonlocal orbital entanglement of the injected electrons and/or holes. Due to Luttinger-liquid correlations, however, the entanglement is exponentially suppressed at finite temperatures. 
Koji Sato and Yaroslav Tserkovnyak
cond-mat.mes-hall