Reliable Quantum Communications based on Asymmetry in Distillation and Coding

TL;DR

This work tackles reliable quantum communication under latency constraints by proposing a hybrid framework that combines entanglement distillation with quantum error correction (QEC). A key insight is that distillation induces asymmetries in the effective quantum channel, which can be exploited by ad-hoc asymmetric QECC to achieve better fidelity with smaller codewords and lower latency. The authors develop a detailed model of the teleportation channel, analyze one-step distillation effects, and demonstrate through numerical results that a few distillation steps plus asymmetric codes significantly outperform symmetric codes or distillation alone, both on a single quantum link and across networks with entanglement swapping. The findings suggest a practical pathway for mid-generation quantum networks where latency and reliability are jointly optimized, and they highlight the value of tailoring coding strategies to the asymmetries introduced by distillation and network operations.

Abstract

The reliable provision of entangled qubits is an essential precondition in a variety of schemes for distributed quantum computing. This is challenged by multiple nuisances, such as errors during the transmission over quantum links, but also due to degradation of the entanglement over time due to decoherence. The latter can be seen as a constraint on the latency of the quantum protocol, which brings the problem of quantum protocol design into the context of latency-reliability constraints. We address the problem through hybrid schemes that combine: (1) indirect transmission based on teleportation and distillation; (2) direct transmission, based on quantum error correction (QEC). The intuition is that, at present, the quantum hardware offers low fidelity, which demands distillation; on the other hand, low latency can be obtained by QEC techniques. It is shown that, in the proposed framework, the distillation protocol gives rise to asymmetries that can be exploited by asymmetric quantum error correcting code (QECC), which sets the basis for unique hybrid distillation and coding design. Our results show that ad-hoc asymmetric codes give, compared to conventional QEC, a performance boost and codeword size reduction both in a single link and in a quantum network scenario.

Figures (12)

• Figure 1: A motivating example of distributed quantum computation. Two quantum computers $C_1$ and $C_2$ share a common task represented by a sequential operation stack. Following certain scheduling related to the computation, whenever two qubits of different quantum computers require an interaction, a quantum communication link is used to send one of these qubits to the other, execute the operation, and send it back.
• Figure 2: Pictorial representation of raw entanglement distribution and one step of entanglement purification. In this example, the transmitter attempts to share $13$ qubits, where each of them is part of a different EPR pair. The receiver successfully detects $7$ qubits among the $13$ transmitted ones. It groups $3$ pairs for purification, performs it, and discards the unpaired one. Finally, it sends the information about which qubit has to be kept and measurements to the original transmitter. Concluding the purification procedure in this example, we have $2$EPR pairs in position $1$ and $8$ of the user's respective quantum memories.
• Figure 3: Equivalence between teleportation protocol using noisy EPR pair and a quantum communication channel based on Pauli errors.
• Figure 4: Evolution of the probability distribution of a EPR pairs mixture described by \ref{['eq:GenMixedState']} due to distillation algorithm \ref{['eq:DeautschProbEvol']}. The initial state is a Werner state with fidelity $\mathcal{F}_0 = 0.8$.
• Figure 5: Evolution of the probability distribution of a EPR pairs mixture described by \ref{['eq:GenMixedState']} due to the STRINGENT distillation algorithm Nickerson2013. The initial state is a Werner state with fidelity $\mathcal{F}_0 = 0.8$.