Entangling Quantum Memories at Channel Capacity

Entangling quantum memories, mediated by optical-frequency or microwave channels, at high rates and fidelities is key for linking qubits across short and long ranges. All well-known protocols encode up to one qubit per optical mode, hence entangling one pair of memory qubits per transmitted mode over the channel, with probability η, the channel's transmissivity. The rate is proportional to η ideal Bell states (ebits) per mode. The quantum capacity, C(η) = -log₂(1-η) ebits per mode, which ≈ 1.44η for high loss, i.e., η << 1, thereby making these schemes near rate-optimal. However, C(η) →∞ as η →1, making the known schemes highly rate-suboptimal for shorter ranges. We propose a cavity-assisted memory-photon interface that can be used to entangle matter memories with Gottesman-Kitaev-Preskill (GKP) photonic qudits, which along with dual-homodyne entanglement swaps that retain analog information, enables entangling memories at capacity-approaching rates at low loss. We benefit from loss resilience of GKP qudits, and their ability to encode multiple qubits in one mode. Our memory-photon interface further supports the preparation of needed ancilla GKP qudits. We expect our result to spur research in low-loss high-cooperativity cavity-coupled qubits with high-efficiency optical coupling, and demonstrations of high-rate short-range quantum links.