We investigate the creation of squeezing via operations subject
to noise and losses and ask for the optimal use of such devices
when supplemented by noiseless passive operations. Both, single
and repeated uses of the device are optimized and it is proven
that in the latter case the squeezing converges exponentially fast
to its asymptotic optimum, which we determine explicitly. For the
case of multiple iterations we show that the optimum can be
achieved with fixed intermediate passive operations. Finally, we
relate the results to the generation of entanglement and derive
the maximal two-mode entanglement achievable within the considered
scenario.
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