# In-Field Quantum-Protected Control-Based Key Distribution with a Lossy Urban Fiber Link
## 2 Protocol Description  
Conceptually, the realized protocol is equivalent to that presented in Ref. [22] and follows the logic outlined in Ref. [19]. It is assumed that the users are connected via a quantum channel (optical fiber) and an authenticated classical communication channel. The procedure can be summarized as follows:  
**Scheme Adjustment**  
(i) _OTDR_--[PERSON] and [PERSON] carry out optical time-domain reflectometry (OTDR) to identify local leakages that could be exploited by [PERSON] and to measure the natural, homogeneous scattering losses which are considered non-interceptible [19]. Once this baseline is established, subsequent additional losses, determined at the later stage, will be attributed to [PERSON]. The resulting reflectogram is shared over the classical channel. For details, see Section 7.1 in Methods. (ii) _Auto-tuning procedure_-- [PERSON] transmits to [PERSON] a series of phase-randomized pulses encoding a bit sequence (via their intensities), while the same bit sequence is sent over the classical channel. [PERSON]'s detector produces a sequence of voltages, which he compares against the known bit sequence from [PERSON]. Based on this comparison, [PERSON] and [PERSON] set the postselection parameters to optimize the trade-off between bit error ratio (BER) and bit loss ratio (BLR) (see Section 4). **Transmission & Control**  
1. _Transmitometry_-- For the purpose of the loss control, [PERSON] sends a sinusoidal signal through the quantum channel for loss estimation. The signal is modulated at a high frequency to suppress \(1/f\) noise at [PERSON]'s detection stage. 2. _Quantum information transmission_-- [PERSON] transmits a sequence of low-intensity pulses (633,600 pulses in one transmission). Each 33 rd pulse serves as a synchronization marker. The 32 phase-randomized pulses between two consecutive synchronization pulses encode informational bits. Informational pulses are two times weaker than synchronization pulses. 3. _Measurements_-- [PERSON] measures all received signals. By analyzing the known baseline losses with the measured amplitude of the transmitometry signal, [PERSON] estimates the exploitable leaked fraction photons \(r_{\mathrm{E}}\) of the bit-encoding signals. This estimate is sent to [PERSON] over the classical channel. In turn, the synchronization pulses identify the start positions of each bit series, ensuring [PERSON] that he has obtained the full series. **Postprocessing**
4. _Postselection_-- [PERSON] reports to [PERSON] via the classical channel the positions of inconclusive measurement outcomes as determined by the agreed postselection criteria. Then both parties remove these bits from their respective bit strings. 5. _Error correction_-- Disclosing a small selection of bits through the classical channel, the users estimate the BER. If the error is above a certain level, see Section 4 for details, the users apply the advantage distillation procedure [23]. Once the effective BER is sufficiently reduced, low-density parity-check (LDPC) code correction is employed to remove the remaining errors. The protocol verifies that the collision probability remains below \(10^{-6}\). 6. _Privacy amplification_-- To ensure that [PERSON] does not know any bits from the final key, privacy amplification is performed [24]. Knowing the observed channel losses \(r_{\mathrm{E}}\) and the amount of information revealed during error correction, the users evaluate the amount of information leaked to [PERSON]. If the leaked information exceeds the users' own shared information, they discard the entire bit sequence from that round. Otherwise, they apply a suitable hashing technique to compress the sequence into a shorter key, about which [PERSON] holds no information. The compression factor is determined by the evaluated leaked information. The resulting key is added to the key storage. The protocol leverages the non-orthogonality of bit-encoding states, implemented as phase-randomized low-intensity coherent states with different mean photon numbers.