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arXiv:quant-ph/0508178 · Physical Review A

Experimental purification of coherent states

Ulrik L. Andersen, Radim Filip, Jaromı́r Fiurášek, Vincent Josse, Gerd Leuchs

Published Dec 1, 2005• 30 citations
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Abstract

We propose a scheme for optimal Gaussian purification of coherent states from several imperfect copies. The proposal is experimentally demonstrated for the case of two copies of a coherent state sent through independent noisy channels. Our purification protocol relies on only linear optics and an ancilla vacuum state, rendering this approach an interesting alternative to the more complex protocols of entanglement distillation and quantum error correction.

DOI
10.1103/physreva.72.060301

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We propose a scheme for optimal Gaussian purification of coherent states from several imperfect copies. The proposal is experimentally demonstrated for the case of two copies of a coherent state sent through independent noisy channels. Our purification protocol relies on only linear optics and an ancilla vacuum state, rendering this approach an interesting alternative to the more complex protocols of entanglement distillation and quantum error correction.
By combining multiple copies of noisy coherent states of light (or other bosonic systems), it is possible to obtain a single mode in a state with lesser noise, a process known as distillation or purification of coherent states. We investigate the distillation of coherent states from coherent thermal states under general phase-insensitive operations, and find a distillation protocol that is optimal in the asymptotic regime, i.e., when the number of input copies is much greater than 1. Remarkably, we find that in this regime, the error -- as quantified by infidelity (one minus the fidelity) of the output state with the desired coherent state -- is proportional to the inverse of the purity of coherence of the input state, a quantity obtained from the Right-Logarithmic-Derivative (RLD) Fisher information metric, hence revealing an operational interpretation of this quantity. The heart of this protocol is a phase-insensitive channel that optimally converts an input coherent thermal state with high amplitude, into an output with significantly lower amplitude and temperature. Under this channel, the purity of coherence remains asymptotically conserved. While both the input and desired output are Gaussian states, we find that the optimal protocol cannot be a Gaussian channel. Among Gaussian phase-insensitive channels, the optimal distillation protocol is a simple linear optical scheme that can be implemented with beam splitters.
Quantum-limited amplifiers increase the amplitude of quantum signals at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we investigate a scenario that interpolates between these two extremes. We search for the optimal physical process that generates MMM approximate copies of a pure and amplified coherent state, starting from NNN copies of a noisy coherent state with Gaussian modulation. We prove that the optimal deterministic processes are always Gaussian, whereas non-Gaussianity powers up probabilistic advantages in suitable parameter regimes. The optimal processes are experimentally realizable with current technology, both in the deterministic and in the probabilistic scenario. In view of this fact, we provide benchmarks that can be used to certify the experimental demonstration of the quantum-enhanced amplification and purification of coherent states.
We propose a scheme for purification and distillation of squeezed and entangled continuous-variable states of light transmitted through a channel exhibiting phase fluctuations. The outstanding advantage of the suggested protocol is its experimental feasibility since it only involves an interference of two copies of the decohered state on a balanced beam splitter, a homodyne measurement on one of the output beams, and a conditioning on the measurement outcome. The purification can counteract the detrimental effects of phase fluctuations in optical quantum-communication networks.
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Quantum-limited amplifiers increase the amplitude of the signal at the price of introducing additional noise. Quantum purification protocols operate in the reverse way, by reducing the noise while attenuating the signal. Here we investigate a scenario that interpolates between these two extremes. We search for the physical process that produces the best approximation of a pure and amplified coherent state, starting from multiple copies of a noisy coherent state with Gaussian modulation. We identify the optimal quantum processes, considering both the case of deterministic and probabilistic processes. And we give benchmarks that can be used to certify the experimental demonstration of genuine quantum-enhanced amplification.