Generalized constraints on quantum amplification

The generalized constraints on amplifier noise performance were analyzed which is valid regardless of whether the commutators of the components of the current operator are c numbers or operators. The constraints were found to be valid for both fermionic and bosonic currents. The nonequilibrium Kubo formula was used to generalize the usual noise limits of amplifiers to the case in which the commutator of the signal components was not a c number. It was concluded that the analysis could allow for the possibility of phase sensitive fermion based devices which contributes no noise to the component of the signal that is amplified.