Restoring quantum communication efficiency over high loss optical fibres

TL;DR

The work addresses the fundamental barrier to long-distance quantum communication in optical fibres by showing that memory effects in the environment can be engineered to neutralise noise. It introduces the concept of environment-controlled general attenuators $\Phi_{\lambda,\sigma}$ and a noise-attenuation protocol that uses trigger pulses to prepare the environment in favorable states, enabling unassisted quantum communication at a fixed positive rate even as $\lambda \to 0^+$ and, with pre-shared entanglement, entanglement-assisted rates that match the noiseless ideal. The authors provide exact results for EC and EA capacities of thermal attenuators, prove a constructive two-trigger-pulse scheme that suffices for small $\lambda$, and establish continuity bounds showing robustness to the environment state and energy constraints. These findings suggest a feasible path toward reliable quantum communication over arbitrarily long fibres and have significant implications for experimental tests of memory effects in optical channels.

Abstract

In the absence of quantum repeaters, quantum communication proved to be nearly impossible across optical fibres longer than $\gtrsim 20\text{ km}$ due to the drop of transmissivity below the critical threshold of $1/2$. However, if the signals fed into the fibre are separated by a sufficiently short time interval, memory effects must be taken into account. In this paper we show that by properly accounting for these effects it is possible to devise schemes that enable unassisted quantum communication across arbitrarily long optical fibres at a fixed positive qubit transmission rate. We also demonstrate how to achieve entanglement-assisted communication over arbitrarily long distances at a rate of the same order of the maximum achievable in the unassisted noiseless case.

Figures (2)

• Figure 1: The quantity $I_{\mathrm{coh}}(\Phi_{\lambda,\ket{n}\!\bra{n}},\tau_N)$ plotted with respect to $\lambda$ for $N=0.5$ and for several values of $n$ from $10$ to $100$. In the inset we plot the function $H\left(q(N,c(N))\right)-H\left(p(N,c(N))\right)$ (see Lemma \ref{['teo_lowtrasm']}) with respect to $N$ for several choices of $c(N)$ of the form $c(N)=N+\alpha$.
• Figure 2: Steps 2 and 3 of the noise attenuation protocol. At the beginning of step 2, the environment is initialised in $\tau_\nu$. By sending the signals $S_1,S_2,\ldots,S_k$, Alice aims to turn the environment into a state $\sigma$, where the latter is such that $\Phi_{\lambda,\sigma}$ is less noisy than $\Phi_{\lambda,\tau_\nu}$. Right after the environment has transformed into $\sigma$, step 3 starts with Alice sending the information-carrying signal $S$.

Theorems & Definitions (34)

• Theorem 1: die-hard
• Conjecture 2
• Lemma 3
• Theorem 4
• Theorem 5
• Definition S1
• Lemma S2
• proof
• Lemma S3
• proof