Inseparability Criterion for Continuous Variable Systems

Abstract

As with discrete systems, quantum entanglement also plays the basic role in quantum information protocols with continuous variables. A problem of great importance is then to check whether a continuous variable state, generally mixed, is entangled (inseparable). For discrete systems, there is the Peres-Horodecki inseparability criterion [1,2], based on the negativity of the partial transpose of the composite density operator. This negativity provides a necessary and sufficient condition for inseparability of 2 × 2 or 2 × 3 —dimensional systems. In this section, we will describe an entirely different inseparability criterion for continuous variable states, which was first proposed in Ref. [3]. The Peres-Horodecki criterion was also successfully extended to the continuous variable systems shortly afterwards, which will be described in the next section by Simon.