Covariance matrices under Bell-like detections

TY - JOUR

T1 - Covariance matrices under Bell-like detections

AU - Spedalieri, Gae

AU - Ottaviani, Carlo

AU - Pirandola, Stefano

PY - 2013/6

Y1 - 2013/6

N2 - We derive a simple formula for the transformation of an arbitrary covariance matrix of (n+2) bosonic modes under general Bell-like detections, where the last two modes are combined in an arbitrary beam splitter (i.e., with arbitrary transmissivity) and then homodyned. In particular, we consider the realistic condition of non-unit quantum efficiency for the homodyne detectors. This formula can easily be specialized to describe the standard Bell measurement and the heterodyne detection, which are exploited in many contexts, including protocols of quantum teleportation, entanglement swapping and quantum cryptography. In its general form, our formula can be adopted to study quantum information protocols in the presence of experimental imperfections and asymmetric setups, e.g., deriving from the use of unbalanced beam splitters.

AB - We derive a simple formula for the transformation of an arbitrary covariance matrix of (n+2) bosonic modes under general Bell-like detections, where the last two modes are combined in an arbitrary beam splitter (i.e., with arbitrary transmissivity) and then homodyned. In particular, we consider the realistic condition of non-unit quantum efficiency for the homodyne detectors. This formula can easily be specialized to describe the standard Bell measurement and the heterodyne detection, which are exploited in many contexts, including protocols of quantum teleportation, entanglement swapping and quantum cryptography. In its general form, our formula can be adopted to study quantum information protocols in the presence of experimental imperfections and asymmetric setups, e.g., deriving from the use of unbalanced beam splitters.

U2 - 10.1142/S123016121350011X

DO - 10.1142/S123016121350011X

M3 - Article

SN - 1230-1612

VL - 20

JO - Open Systems and Information Dynamics

JF - Open Systems and Information Dynamics

IS - 2

M1 - 1350011

ER -