Xb. Wang et al., Detecting the inseparability and distillability of continuous variable states in Fock space - art. no. 137903, PHYS REV L, 8713(13), 2001, pp. 7903
The partial transposition (PT) operation is an efficient tool in detecting
the inseparability of a mixed state. We give an explicit formula for the PT
operation for the continuous variable states in Fock space. We then give t
he necessary and sufficient condition for the positivity of Gaussian operat
ors. Based on this, a number of criteria on the inseparability and distilla
bility for the multimode Gaussian states are naturally drawn. We finally gi
ve an explicit formula for the state in a subspace of a global Gaussian sta
te. This formula, together with the known results for Gaussian states, give
s the criteria for the inseparability and distillability in a subspace of t
he global Gaussian state.