Gaussian encoding guarantees ultimate capacity of optical communication channels

What are the fundamental physical limits to the rate of information transmission over optical communication links? Raul García-Patrón, former member of the Theory Division of Professor Ignacio Cirac at the Max Planck Institute of Quantum Optics (MPQ; Garching, Germany), and collaborators from Scuola Normale Superiore and Istituto Nanoscienze-CNR (Pisa, Italy), Université Libre de Bruxelles (Brussels, Belgium), and the Steklov Mathematical Institute and the National Research University Higher School of Economics (both in Moscow, Russia), have now answered this question.¹

A definitive answer to the question on the ultimate limits to optical communication needs to consider the quantum nature of light. The right tools necessary to answer this question were developed in the 1990s by the work of Professor Alexander Holevo (co-author of the new paper), who pioneered quantum communication theory.

Straightforward use of light
Subsequent work conjectured that the optimal strategy to send information over optical communication lines does not need the generation of highly complex quantum states, but instead can use simple light pulses generated by currently existing lasers to reach the optimal communication rates. However, no definitive answer had been given since then.

In a previous work in 2012 (Phys. Rev. Lett. 108, 110505, 2012), Raul García-Patrón (working then at the Theory Division at MPQ), in collaboration with Carlos Navarrete-Benlloch (current member of the Theory Division) and other scientists from the Université Libre and the Massachusetts Institute of Technology (MIT; Cambridge, MA), showed that any realistic optical-communication channel can be modeled by a concatenation of an ideal attenuation channel followed by an ideal process of amplification.

Minimizing entropy
Therefore, the former conjecture on the optimal strategy to encode information could be reduced to a basic question: what is the minimum disorder, or entropy, that is added to the input signal by one of the most studied quantum optical processes -- namely, optical parametric amplification (OPA)?

"Entropy is a measure of disorder," says García-Patrón. "Minimum output entropy of the channel measures how much the channel distorts the input state that you initially sent through the line. The highest achievable bit rate is given by a function that is optimized by minimizing the output entropy of the channel. Intuitively, it means you want to minimize the distortion the channel produces to your input signal."

Keeping things Gaussian
Now the team of scientists has shown that a Gaussian encoding achieves minimum output entropy and hence provides the ultimate capacity of an optical communication channel. Gaussian channels that preserve the “Gaussianity” of the state are the most natural models of optical communication links such as fibers or amplifiers.

Following the road map that was suggested in the researchers' previous work (the Physical Review Letters paper mentioned above), Garcia-Patron and collaborators solved this longstanding open problem, exploiting some known properties of amplifier channels in a novel way.

A few questions remain to be answered. "We know that very simple states achieve an optimal encoding. But we do not know if the same holds for the decoding of the information," García-Patrón. "Our result just gives a proof of existence: we know there is a detector achieving our rate, but further research is needed to find a realistic optimal decoding that could be implemented. As far as future applications are concerned, a simple efficient decoding could be useful for example in regimes where the signals are extremely weak at the reception, as in earth to deep-space communication."

Source: https://www.idw-online.de/en/news604919

REFERENCE:

1. V. Giovannetti et al., Nature Photonics (2014); doi: 10.1038/nphoton.2014.216