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Physical Review A

Amplification of maximally-path-entangled number states

G. S. Agarwal, S. Chaturvedi, Amit Rai

Published Apr 29, 2010• 15 citations
Publisher

Abstract

We examine the behavior of a non-Gaussian state like the maximally path-entangled number state commonly known as a $N00N$ state under phase-insensitive amplification. We derive an analytical result for the density matrix of the $N00N$ state for arbitrary gain of the amplifier. We consider cases of both symmetric and antisymmetric amplification of the two modes of the $N00N$ state. We quantitatively evaluate the loss of entanglement by the amplifier in terms of the logarithmic negativity parameter. We find that $N00N$ states are more robust than their Gaussian counterparts.

DOI
10.1103/physreva.81.043843

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We examine the behavior of a non-Gaussian state like the maximally path-entangled number state commonly known as a N00NN00NN00N state under phase-insensitive amplification. We derive an analytical result for the density matrix of the N00NN00NN00N state for arbitrary gain of the amplifier. We consider cases of both symmetric and antisymmetric amplification of the two modes of the N00NN00NN00N state. We quantitatively evaluate the loss of entanglement by the amplifier in terms of the logarithmic negativity parameter. We find that N00NN00NN00N states are more robust than their Gaussian counterparts.
We examine the behavior of a Non Gaussian state like NOON state under phase insensitive amplification. We derive analytical result for the density matrix of the NOON state for arbitrary gain of the amplifier. We consider cases of both symmetric and antisymmetric amplification of the two modes of the NOON state. We quantitatively evaluate the loss of entanglement by the amplifier in terms of the logarithmic negativity parameter. We find that NOON states are more robust than their Gaussian counterparts.
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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.