Twin-Field QKD in 2D: The Loss-Budget View

Twin-Field QKD Link

Total distance L 250 km

Mean photon number μ 0.50

Interference visibility V 98.0%

Detector dark-count rate 1.0e-6

Live Key Rate

R (twin-field)

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R (ordinary BB84)

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QBER

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Crossover distance

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Twin-field R(L) BB84 R(L)

How it works

This is a 2D, no-camera companion to the 3D twin-field QKD scene: a flat schematic of the same fibre link, plus two extra chart panels that make the physics reasoning visible instead of just animated. In ordinary point-to-point QKD (BB84) the secret key rate falls off linearly with the channel's transmittance η(L), because a single photon must survive the whole fibre. Twin-field QKD splits the same distance in half: Alice and Bob each send a weak coherent pulse only as far as an untrusted central node, where the two pulses interfere on a beamsplitter. A detector click reveals the parity of Alice's and Bob's phase-encoded bits without exposing either one — so the accessible key rate scales with √η(L) instead of η(L):

η(L)   = 10^(−αL/10)            fibre transmittance, α ≈ 0.2 dB/km
R_BB84 = ½μ·η(L)·[1−2h₂(QBER)]         (repeaterless PLOB-type bound)
R_TF   = ½μ·√η(L)·s·[1−2h₂(QBER)]      s ≈ system overhead of phase-locked interference
h₂(x)  = −x·log₂x − (1−x)·log₂(1−x)     binary (error-correction) entropy

Because √η(L) decays half as fast (in dB) as η(L), the twin-field rate eventually overtakes BB84 even though it starts lower — the crossover distance shown above is where that happens for the current settings. The two mini-panels under the fibre diagram make this concrete: the left one plots η_total(L) against η_arm(L) = √η_total(L) on a log scale, where the twin-field curve is visibly the straight-line average slope of the BB84 curve; the right one turns the same numbers into a dB loss budget — BB84 pays αL dB end-to-end, twin-field effectively pays only αL/2 dB per arm before the interference stage, which is the entire reason it can reach further.

Distance L — total Alice–Bob fibre length; each arm to the central node carries L/2.
Mean photon number μ — average photons per pulse; higher μ raises the raw rate but also the multi-photon leakage risk in a real decoy-state analysis (simplified here).
Visibility V — how precisely the two lasers' phases are locked at the central node; lower visibility directly raises the QBER.
Dark-count rate — spurious detector clicks with no photon present; at long distance these start to dominate the true signal, which is what ultimately caps the reach of any QKD link.
Drag / scroll on the diagram — pan and zoom the fibre-link view; it never affects the physics, only what you're looking at.

drag to pan · scroll to zoom

Alice's pulses Bob's pulses Detector click (sifted bit)

sifted bits: 0
clicks/s: 0.0