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arXiv:1407.6798 · Physical Review A

Heralded noiseless linear amplification and quantum channels

Rémi Blandino, Marco Barbieri, Philippe Grangier, Rosa Tualle-Brouri

Published Jun 5, 2015• 20 citations
arXivHTMLPDF

Abstract

The employ of a heralded noiseless linear amplifier has been proven as a useful tool for mitigating imperfections in quantum channels. Its analysis is usually conducted within specific frameworks, for which the set of input states for a given protocol is fixed. Here we obtain a more general description by showing that a noisy and lossy Gaussian channel followed by a heralded noiseless linear amplifier has a general description in terms of effective channels. This has the advantage of offering a simpler mathematical description, best suited for mixed states, both Gaussian and non-Gaussian. We investigate the main properties of this effective system, and illustrate its potential by applying it to loss compensation and reduction of phase uncertainty.

DOI
10.1103/physreva.91.062305

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The employ of a heralded noiseless linear amplifier has been proven as a useful tool for mitigating imperfections in quantum channels. Its analysis is usually conducted within specific frameworks, for which the set of input states for a given protocol is fixed. Here we obtain a more general description by showing that a noisy and lossy Gaussian channel followed by a heralded noiseless linear amplifier has a general description in terms of effective channels. This has the advantage of offering a simpler mathematical description, best suited for mixed states, both Gaussian and non-Gaussian. We investigate the main properties of this effective system, and illustrate its potential by applying it to loss compensation and reduction of phase uncertainty.
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We present an experimental enhancement of signal-to-noise ratio for arbitrary coherent states using a noise-reduced linear amplifier that profitably combines a heralded measurement-based noiseless linear amplifier and a deterministic linear amplifier. The concatenation of two amplifiers introduces the flexibility that allows one to reach the amplification with high gain for large input coherent amplitude. We demonstrate a signal transfer coefficient of Ts = 2.55 ± 0.08 from input to output, achieved with an amplification gain of 10.54. When Gaussian statistics is retained, our heralded amplifier obtained a signal transfer coefficient of Ts = 1.10 ± 0.04. Our amplification scheme only relies on linear optics and post-selection algorithm, and therefore would be of great usage in loss-sensitive quantum information protocols.
Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still be possible. When the protocol is successful, it can lead to an output that is a noiselessly amplified copy of the input. When the protocol is unsuccessful, the output state is degraded and is usually discarded. Probabilistic protocols may improve the performance of some quantum information protocols, but not for metrology if the whole statistics is taken into consideration. We calculate the precision limits on estimating the phase of coherent states using a noiseless linear amplifier by computing its quantum Fisher information and we show that on average, the noiseless linear amplifier does not improve the phase estimate. We also discuss the case where abstention from measurement can reduce the cost for estimation.
A general framework of quantum state amplification using the language of quantum state transformation is given systematically for the first time. The concept of amplification of quantum states is defined specifically and the amplification of a set of quantum states is formulated generally as the transformation of quantum states. Three different kinds of important quantum amplifications, i.e., deterministic noisy quantum amplification, probabilistic noiseless quantum amplification, and deterministic noiseless quantum amplification are identified and discussed. For deterministic quan- tum amplification, the linearity of amplification is proven to be incompatible with the noiseless amplification while it is not true for probabilistic quantum amplification. However, deterministic noiseless quantum amplification is shown physically attainable if the linearity of amplification is given up. The connection between the gain of amplification and the successful probability is discussed for probabilistic quantum amplification. Assuming that successful probability is the same for all quantum states to be amplified, we obtain a generally valid relation between the gain of amplication and the successful probability. Particular interest is given to phase-preserving quantum amplication of Gaussian states which has been shown of theoretical interest and of practical importance in quantum information and quantum communication recently. Our results of quantum state amplification not only enrich the research of quantum amplification but also can be helpful for further practical applications.
Due to the pervasive nature of decoherence, protection of quantum information during transmission is of critical importance for any quantum network. A linear amplifier that can enhance quantum signals stronger than their associated noise while preserving quantum coherence is therefore of great use. This seemingly unphysical amplifier property is achievable for a class of probabilistic amplifiers that does not work deterministically. Here we present a linear amplification scheme that realises this property for coherent states by combining a heralded measurement-based noiseless linear amplifier and a deterministic linear amplifier. The concatenation of two amplifiers introduces the flexibility that allows one to tune between the regimes of high-gain or high noise-reduction, and control the trade-off of these performances against a finite heralding probability. We demonstrate an amplification signal transfer coefficient of Ts>1\mathcal{T}_s > 1Ts​>1 with no statistical distortion of the output state. By partially relaxing the demand of output Gaussianity, we can obtain further improvement to achieve a Ts=2.55±0.08\mathcal{T}_s = 2.55 \pm 0.08Ts​=2.55±0.08. Our amplification scheme only relies on linear optics and post-selection algorithm. We discuss the potential of using this amplifier as a building block in extending the distance of quantum communication.
Fundamental laws of quantum mechanics impose that arbitrary quantum states cannot be perfectly cloned or amplified without introducing some unavoidable noise in the process. The quantum noise intrinsic to the functioning of a linear phase-insensitive amplifier can however be avoided by relaxing the requirement of a deterministic operation. Non-deterministic noiseless linear amplifiers that do not violate any fundamental quantum law are therefore possible and here we present the first experimental realization of a scheme that allows noiseless amplification of coherent states at the best level of effective gain and final state fidelity ever reached. This scheme, based on a sequence of photon addition and subtraction, and characterized by a significant amplification and low distortions, may become a useful tool for quantum communications and metrology, by enhancing the discrimination between partially overlapping quantum states or by recovering the information transmitted over lossy channels.