  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 non-idealities:
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.

Quantum Physics