Entangling Quantum Memories at Channel Capacity

Abstract

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, $C(η) = -\log_2(1-η)$ ebits per mode, which $\approx 1.44η$ for high loss, i.e., $η\ll 1$, thereby making these schemes near rate-optimal. However, $C(η) \to \infty$ as $η\to 1$, 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.

Figures (8)

• Figure 1: Overview of the cavity system coupled to the atomic 3-level system. The relevant modes, eigen levels and parameters are labeled. Detailed interaction models have been previously derived Dhara2024-ko (see \ref{['sec:Methods']} for a summary).
• Figure 2: Overview of the interaction of the atomic system with the GKP qubit for the effective CSUM gate -- (a) Overview of the protocol implementing the CSUM gate, involving reflection of coherent pulses from a register of $N$-quantum memories integrated in cavities and memory-state dependent sequential displacement of pre-displaced GKP qudit states. (b) Circuit description of the protocol comprising of sequential controlled phase rotations $(\hat{U}_\mathrm{R})$ and sequential displacements $(\hat{U}_{\mathrm{disp.}})$.
• Figure 3: Layout of high-rate quantum links utilizing GKP qudit basis entanglement swap operation, where each party performs the CSUM gate on local memory registers $(\boldsymbol{M}_1,\boldsymbol{M}_2)$ and GKP qudit states $(G_1,G_2)$ before transmission to the midpoint of a link (of transmissivity $\eta$). The dual-homodyne measurements $\hat{q}_1, \hat{p}_2$ herald the generation of an entangled state of the memory registers $(\tilde{\rho}_{\boldsymbol{M}_1,\boldsymbol{M}_2})$.
• Figure 4: Performance of the qudit-swap assisted link for $N$-qubit memory registers (varying colors) utilizing (a) square lattice and (b) hexagonal lattice GKP qudit encodings $(d=2^N)$ assuming pre-amplification of the transmitted qudits. For both lattice choices, we analyze the performance of protocol for infinite squeezed states (solid), 5 dB (dashed; $\circ$ markers) and 10 dB (dot-dashed; $+$ markers) squeezed states with the channel capacity of $C(\eta)$.
• Figure 5: Performance of the qudit-swap assisted link for $N$-qubit memory registers (varying colors) utilizing (a) square lattice and (b) hexagonal lattice GKP qudit encodings $(d=2^N)$ assuming the CC-amplification of dual-homodyne measurement outcomes. For both lattice choices, we analyze the performance of protocol for infinite squeezed states (solid), 5 dB (dashed; $\circ$ markers) and 10 dB (dot-dashed; $+$ markers) squeezed states with the channel capacity of $C(\eta)$.