Non-deterministic noiseless amplification via non-symplectic phase space transformations

Abstract

We analyse the action of an ideal noiseless linear amplifier operator, $g^\hat{n}$, 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 optimising the use of the amplification in quantum information protocols.

12 pages, 9 figures, missing reference added

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• Optimal architecture for a non-deterministic noiseless linear amplifier
• Noiseless Linear Amplifiers in Entanglement-Based Continuous-Variable Quantum Key Distribution
• Simulation of Gaussian channels via teleportation and error correction of Gaussian states
• Coherent-state discrimination via non-heralded probabilistic amplification
• Quantum enhancement of signal-to-noise ratio with a heralded linear amplifier
• Noiseless Linear Amplification and Quantum Channels
• Channel purification via continuous-variable quantum teleportation with Gaussian post-selection
• A robust W-state encoding for linear quantum optics
• Models of reduced-noise, probabilistic linear amplifiers
• Coherence of Quantum States after Noiseless Attenuation
• Multi-mode CV-QKD with Noiseless Attenuation and Amplification
• Decoding Protocols for Classical Communication on Quantum Channels