Quantum Optical Communication in the presence of strong attenuation noise

TL;DR

This work addresses quantum and entanglement-assisted classical communication over optical fibres with strong attenuation. It develops a memory-enabled framework using general attenuators and introduces a noise-attenuation protocol that leverages trigger signals to steer the environment into favorable states, enabling die-hard HQCOM and enhanced entanglement-assisted capacities even for arbitrarily small $\lambda$. The authors derive a simple Kraus representation of the thermal attenuator via a Lindblad master equation (the master equation trick) and prove that, in the vanishing-$\lambda$ limit, suitable Fock-state preparations yield positive coherent information and thus nonzero capacities; with a conjecture on coherence positivity this extends to stronger entanglement-assisted gains. They show that a two-trigger scheme suffices for small $\lambda$ to realize a channel with positive quantum capacity and discuss operational procedures to generate the trigger states using an interferometer, highlighting the potential for repeaterless, long-distance quantum communication. The results recast memory as a resource in quantum communication and offer concrete steps toward practical implementation, while identifying experimental challenges and promising directions for future work.

Abstract

Is quantum communication possible over an optical fibre with transmissivity $λ\leq 1/2$ ? The answer is well known to be negative if the environment with which the incoming signal interacts is initialised in a thermal state. However, in [PRL 125:110504, 2020] the quantum capacity was found to be always bounded away from zero for all $λ>0$, a phenomenon dubbed "die-hard quantum communication" (D-HQCOM), provided that the initial environment state can be chosen appropriately (depending on $λ$). Here we show an even stronger version of D-HQCOM in the context of entanglement-assisted classical communication: entanglement assistance and control of the environment enable communication with performance at least equal to that of the ideal case of absence of noise, even if $λ>0$ is arbitrarily small. These two phenomena of D-HQCOM have technological potential provided that we are able to control the environment. How can we achieve this? Our second main result answers this question. Here we provide a fully consistent protocol to activate the phenomena of D-HQCOM without directly accessing the environment state. This is done by sending over the channel "trigger signals", i.e. signals which do not encode information, prior to the actual communication, with the goal of modifying the environment in an advantageous way. This is possible thanks to the memory effects which arise when the sender feeds signals separated by a sufficiently short temporal interval. Our results may offer a concrete scheme to communicate across arbitrarily long optical fibres, without using quantum repeaters. As a by-product of our analysis, we derive a simple Kraus representation of the thermal attenuator exploiting the associated Lindblad master equation.

Figures (12)

• Figure 1: The functions $I_{\text{coh}}\left(\Phi_{\lambda,\ket{n}\!\bra{n}},\tau_N\right)$ plotted with respect to the variable $\lambda$ for $N=0.5$ and for several values of $n$ from $3$ to $100$. We have computed $I_{\text{coh}}\left(\Phi_{\lambda,\ket{n}\!\bra{n}},\tau_N\right)$ by using \ref{['cohprob']}.
• Figure 2: The function $\bar{n}_N(\lambda)$ plotted with respect to the transmissivity $\lambda$ with a step of $\Delta\lambda=0.0002$ for several values of the energy-constraint $N$. The continuous lines are functions of the form $K(N)/\lambda$.
• Figure 3: An estimate of the function $K(N)$ plotted with respect to the energy-constraint $N$.
• Figure 4: The functions $H\left(q\left(N,c(N)\right)\right)-H\left(p\left(N,c(N)\right)\right)$ plotted with respect to the variable $N$ for several choices of the function $c(N)$.
• Figure 5: The probability distributions $P_l(2,n,\frac{3}{n})$ and $P_l(2,n,1-\frac{3}{n})$ plotted with respect to the index $l$ for several values of $n$. These probability distributions are computed by using \ref{['simpler']}.

Theorems & Definitions (57)

• Lemma 1
• Theorem 2
• Lemma 3
• Lemma 4
• Theorem 5
• Conjecture 6
• Theorem 7
• Conjecture 8
• Theorem 9
• proof : Proof of Theorem \ref{['congl0']}