1209.4810 (Gaetana Spedalieri et al.)

Transformation rule for covariance matrices under Bell-like detections    [PDF]

Gaetana Spedalieri, Carlo Ottaviani, Stefano Pirandola

Starting from the transformation rule of a covariance matrix under homodyne detections, we can easily derive a formula for the transformation of a covariance matrix of (n+2) bosonic modes under Bell-like detections, where the last two modes are combined in an arbitrary beam splitter (i.e., with arbitrary transmissivity) and then homodyned. This formula can be specialized to describe the standard Bell detection and the heterodyne measurement, which are exploited in many contexts, including protocols of quantum teleportation, entanglement swapping and quantum cryptography. Our general formula can be adopted to study these protocols in the presence of experimental imperfections or asymmetric setups, e.g., deriving from the use of unbalanced beam splitters.

View original: http://arxiv.org/abs/1209.4810