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arXiv:0809.0326 · AIP conference proceedings

Nondeterministic Noiseless Linear Amplification of Quantum Systems

Timothy C. Ralph, Austin P. Lund, Alexander Lvovsky

Published Jan 1, 2009• 163 citations
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Abstract

We introduce the concept of non‐deterministic noiseless linear amplification. We propose a linear optical realization of this transformation that could be built with current technology. We discuss the application of the device to distillation of continuous variable entanglement. We demonstrate that highly pure entanglement can be distilled from transmission over a lossy channel.

DOI
10.1063/1.3131295

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We introduce the concept of non‐deterministic noiseless linear amplification. We propose a linear optical realization of this transformation that could be built with current technology. We discuss the application of the device to distillation of continuous variable entanglement. We demonstrate that highly pure entanglement can be distilled from transmission over a lossy channel.
Nondeterministic quantum noiseless linear amplifiers are a new technology with interest in both fundamental understanding and new applications. With a noiseless linear amplifier it is possible to perform tasks such as improving the performance of quantum key distribution, purifying lossy channels, and distilling entanglement. Previous designs for noiseless linear amplifiers involving linear optics and photon counting are nonoptimal because they have a probability of success lower than the bound given by the theory of generalized quantum measurement. This paper develops a theoretical model using unitary interactions and projective measurements which reaches this limit. We calculate the fidelity and probability of success of this model for coherent states and Einstein-Podolsky-Rosen entangled states. Finally, we explore some examples of the complex interplay between the fidelity, probability, and the distilling and purifying power of the model.
The unavoidable addition of noise during amplification is a well known signature of quantum mechanics. It is at the heart of fundamental results such as the no-cloning theorem, quantum limited metrology, quantum key distribution and the impossibility of increasing entanglement by local operations. Nonetheless one can still avoid the unavoidable by moving to a non-deterministic protocol. This novel concept and a linear optics implementation have been proposed [1] and experimentally realised for the case of amplifying coherent states [2-4], qubits [5,6] and the concentration of phase information [7]. All these were extremely challenging experiments, with only [2] demonstrating entanglement distillation and none directly showing the EPR distillation necessary for application to CV QKD. Furthermore the success probability of these experiments was substantially worse than the theoretical considerations would imply. However as has been noted in [8,9] it is possible to virtually implement noiseless amplification (NLA) and hence entanglement distillation via post-selective measurements, achieving significant distillation with a much improved probability of success.
Entanglement distillation is an indispensable ingredient in extended quantum communication networks. Distillation protocols are necessarily non-deterministic and require non-trivial experimental techniques such as noiseless amplification. We show that noiseless amplification could be achieved by performing a post-selective filtering of measurement outcomes. We termed this protocol measurement-based noiseless linear amplification (MBNLA). We apply this protocol to entanglement that suffers transmission loss of up to the equivalent of 100km of optical fibre and show that it is capable of distilling entanglement to a level stronger than that achievable by transmitting a maximally entangled state through the same channel. We also provide a proof-of-principle demonstration of secret key extraction from an otherwise insecure regime via MBNLA. Compared to its physical counterpart, MBNLA not only is easier in term of implementation, but also allows one to achieve near optimal probability of success.
We discuss the recently introduced concept of non-deterministic noiseless linear amplification, demonstrating that such an operation can only be performed perfectly with vanishing probability of success. We show that a weak measurement, which imprints the weak value of an observable of a pre-selected and post-selected system onto a probe system, can be used to approximate probabilistic noiseless amplification. This result may be applied to various tasks in continuous variable quantum information, including entanglement concentration, probabilistic cloning, and in quantum repeaters. We discuss the application of our scheme to probabilistic cloning of weak coherent states.
Quantum entanglement distillation is a probabilistic process which protects entanglement from environment-induced decoherence. In this paper, we investigate the distillation of a continuousvariable optic entangled state with noiseless linear amplification (NLA). NLA schemes perform better than the conventional photon-subtraction-based distillation scheme, particularly in distributing entanglement over extremely low efficiency quantum channels. Finally, a comparison between the NLA-based scheme and the local squeezing-enhanced photon subtraction scheme is also investigated.