Entangling quantum memories via heralded photonic Bell measurement

A common way to entangle quantum memories is via photonic entanglement swaps. Each of two memories, connected by an optical channel, emits a photonic qubit entangled with itself, and the photonic qubits undergo an entanglement swap on a beamsplitter in the middle of the channel. We compare two choices of encoding of the photonic qubit: single rail and dual rail. At low channel loss the dual-rail scheme outperforms the single-rail scheme. However, as expected, the high-loss rate asymptote for the dual-rail scheme scales quadratically worse with loss compared with single rail. Considering the following nonidealities: imperfect mode matching at the swap, carrier-phase mismatch across the interfered photonic qubits, and detector excess noise, we evaluate the density operator of the heralded two-qubit entangled state. We calculate a lower bound on its distillable entanglement per copy, and its fidelity (with the ideal Bell state). For both schemes, imperfect swap-visibility results in a constant-factor decrease in the rate, while excess noise results in a dropoff of distillable entanglement beyond a certain total channel loss threshold, to zero. Despite the single-rail scheme's better rate-loss scaling, it is more severely affected by excess noise. The single-rail scheme is adversely affected by stochastic carrier-phase mismatch, which does not affect the dual-rail scheme. We study entanglement distillation on the heralded noisy entangled states for both methods and outline a suite of quantum networking studies that our work could incite.