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 $\eta$, the channel's transmissivity. The rate is proportional to $\eta$ ideal Bell states (ebits) per mode. The quantum capacity, $C(\eta) = -\log_2(1-{\eta})$ ebits per mode, which $\approx 1.44\eta$ for high loss, i.e., $\eta \ll 1$, thereby making these schemes near rate-optimal. However, $C(\eta) \to \infty$ as $\eta \to 1$, making the known schemes highly rate-suboptimal for shorter ranges. We show that a cavity-assisted memory-photon interface 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.