Abstract
We analyse the action of an ideal noiseless linear amplifier operator, , using the Wigner function phase space representation. In this setting we are able to clarify the gain g for which a physical output is produced when this operator is acted upon inputs other than coherent states. We derive compact closed form expressions for the action of N local amplifiers, with potentially different gains, on arbitrary N-mode Gaussian states and provide several examples of the utility of this formalism for determining important quantities including amplification and the strength and purity of the distilled entanglement, and for optimizing the use of the amplification in quantum information protocols.
Highlights
Optical quantum communication has resulted in numerous protocols that achieve classically impossible tasks including teleportation [1, 2], quantum key distribution [3, 4] and super-dense coding [5, 6]
We address the scenarios in which, dependent upon the state to be amplified, the noiseless linear amplifier (NLA) fails to transform into a physical output in the limiting procedure described above
We show that previous attempts to represent the action of the NLA and an effective channel of the same form but with different parameters are in general insufficient
Summary
Optical quantum communication has resulted in numerous protocols that achieve classically impossible tasks including teleportation [1, 2], quantum key distribution [3, 4] and super-dense coding [5, 6]. An ingenious recent approach is to circumvent these limits by designing devices that achieve genuinely noiseless amplifications in a non-deterministic but heralded manner [17] This noiseless linear amplifier (NLA) has been the subject of considerable theoretical [18,19,20,21,22,23,24,25,26,27,28,29,30,31] and experimental [32,33,34,35,36,37,38,39] work. In the amplification regime (g > 1) this is an unbounded operator, for any particular input state one can always write down a new operator of the form Π N ga†awhere Π N is a projector onto the subspace spanned by the first N + 1 energy eigenstates This operation will result in an arbitrarily good approximation of an ideal NLA as N increases at the price of a decreased, but finite, success probability.
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