The Price of a Secret Bit: Energy per Delivered Key Bit in Quantum Key Distribution

Quantum key distribution is sold on security, never on energy. This paper prices a stated decoy-state BB84 link end to end: the secret-key rate is computed from the standard asymptotic decoy-state yield model (Lo, Ma and Chen 2005; Ma et al. 2005) at a 1 GHz clock, mean photon number 0.5, 0.2 dB/km fibre loss, and published detector classes, and divided into the stated total wall-plug power including detector cooling and classical post-processing. With InGaAs avalanche photodiodes (190 W total) the link delivers 7.68 Mbit/s at zero distance at 2.48e-05 J per secret bit and 57.37 kbit/s at 100 km at 3.31e-03 J per bit, with no key beyond about 134 km. With superconducting nanowire detectors (1690 W total, including a 1500 W closed-cycle cryocooler) it delivers 44.72 Mbit/s at zero distance at 3.78e-05 J per bit, 431.62 kbit/s at 100 km at 3.92e-03 J per bit, and 41.32 kbit/s at 150 km at 4.09e-02 J per bit, with no key beyond about 222 km. Energy per bit rises by a factor of 133.8 (avalanche) and 103.6 (nanowire) between 0 km and 100 km. A stated classical X25519 handshake costs 1.00e-03 J, or 3.91e-06 J per key bit, so the quantum link is 848 times (avalanche) and 1002 times (nanowire) as expensive per key bit at 100 km. Information-theoretic key security costs microjoules per bit at short range and millijoules per bit at 100 km, rising exponentially thereafter. Model calculations are labelled SIMULATED, NOT MEASURED. The deposit includes the paper PDF and text, the computation script (compute.py) that produces every number in the paper, and its outputs (results.json, results.txt).