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Quantum cryptography without detector vulnerabilities using optically-seeded lasers
L. C. Comandar, M. Lucamarini, B. Fröhlich, J. F. Dynes, A. W. Sharpe, S. Tam, Z. L. Yuan, R. V. Penty, A. J. Shields
TL;DR
MDI-QKD needs higher key rates while avoiding detector vulnerabilities. The paper uses pulsed laser seeding to produce high-visibility two-photon interference, measuring 0.482 visibility.
Problem
MDI-QKD requires higher key rates while preserving its detector-vulnerability-free operation.
Method
The paper uses pulsed laser seeding with master–slave gain-switched lasers to generate phase-randomised pulses for two-photon interference.
Results
0.482 visibility was measured for two-photon interference using superconducting single-photon detectors and a 350 ps time window.
Takeaways & Limitations
Using three intensity settings rather than four allows higher key rates in the protocol.
Abstract
from arXiv · showhide
Security in quantum cryptography is continuously challenged by inventive attacks targeting the real components of a cryptographic setup, and duly restored by new counter-measures to foil them. Due to their high sensitivity and complex design, detectors are the most frequently attacked components. Recently it was shown that two-photon interference from independent light sources can be exploited to avoid the use of detectors at the two ends of the communication channel. This new form of detection-safe quantum cryptography, called Measurement-Device-Independent Quantum Key Distribution (MDI-QKD), has been experimentally demonstrated, but with modest delivered key rates. Here we introduce a novel pulsed laser seeding technique to obtain high-visibility interference from gain-switched lasers and thereby perform quantum cryptography without detector vulnerabilities with unprecedented bit rates, in excess of 1 Mb/s. This represents a 2 to 6 orders of magnitude improvement over existing implementations and for the first time promotes the new scheme as a practical resource for quantum secure communications.
METHODS · Experimental setup
The experimental setup uses independently seeded, phase-randomized pulsed lasers and decoy-state polarization encoding to send weak coherent states to Charlie. High-speed gated detectors, temperature-dependent operation, and interference-based temporal alignment support the measurement procedure.
- Experimental setup: Two independent sources generate phase-randomized 35 ps pulses at 1550 nm and 1 GHz repetition rate.Variable 20 GHz optical band-pass filters remove spurious emission, while fibre Bragg gratings pre-compensate pulse broadening in fibre experiments.
- Experimental setup: Polarization and intensity are controlled while power meters monitor average photon fluxes, enabling preparation of weak coherent states.The four polarization states are H, V in the Z basis and D, A in the X basis.
- Experimental setup: The Z basis distils key bits, whereas the X basis tests quantum-channel noise.Alice and Bob choose among four intensity classes: s (signal), u (decoy 1), v (decoy 2), and w (vacuum).
- Experimental setup: Four intensity settings instead of three are used, allowing higher key rates.The classes are s (signal), u (decoy 1), v (decoy 2), and w (vacuum).
- Experimental setup: Charlie splices beam-splitter outputs to polarizing beam-splitter inputs to align polarization to the rectilinear basis and reduce losses.Four InGaAs self-differencing avalanche photodiodes are gated at 1 GHz and synchronized to photon arrival times.
- Experimental setup: Temporal overlap is optimized first by maximizing gated-detector counts and then by directly measuring interference visibility in the matched Z basis.At 20 °C and 0 °C, afterpulse probabilities are 6.5% and 8.6%, while dark-count probabilities per gate are 6.50×10−5 and 2.64×10−5, respectively.
Pulsed laser seeding
Pulsed laser seeding uses a below-threshold master laser to generate random-phase pulses that seed a slave laser, producing narrow pulses and high-visibility two-photon interference. The setup achieves a measured visibility of 0.482 under the reported acquisition conditions.
- Pulsed laser seeding: The master laser operates below threshold to provide random-phase pulses of ∼250 ps that seed the slave laser.The master’s DC level is sufficiently high to minimize turn-on delay, while the slave cannot lase without master photons.
- Pulsed laser seeding: The interference visibility was tested with superconducting single-photon detectors at approximately 10^6 counts/s per detector.Measurements used a 350 ps time window around the central peak and 50 seconds of acquisition.
- Pulsed laser seeding: 0.482 visibility was measured in a two-photon interference experiment using a 350 ps time window around the central peak.The photon count rate was tuned to ∼10^6 counts/s per detector, with data acquired for 50 seconds.
SUPPLEMENTARY INFORMATION · A. Protocol · B. Distillation procedure
The supplementary sections describe an optimized four-intensity MDI-QKD protocol and a distillation procedure that separately processes singlet and triplet data before summing their key-rate contributions. The protocol uses basis-dependent photon fluxes, decoy-state estimation, Bell-event sifting, and post-processing to obtain the final key.
- A. Protocol: A. Protocol: The optimized protocol uses four intensity settings to decouple the data basis Z from the test basis X.The settings are signal, two decoys, and vacuum.
- A. Protocol: A. Protocol: 0.7 photons/pulse in the Z basis produces count rates of tens of millions counts per second over short distances.The X basis instead uses a small photon flux suited to decoy-state parameter estimation.
- A. Protocol: A. Protocol: Decoy-state quantities are estimated with a linear-programming routine that increases the resulting key-rate size and stability.The protocol’s experimental settings and rates are provided in Tables II–V.
- A. Protocol: A. Protocol: Alice and Bob send phase-randomised weak coherent states, while Charlie performs a Bell measurement and announces detector coincidences.Users retain successful events associated with orthogonal H/V polarizations, announce bases, and keep matching-basis results.
- A. Protocol: A. Protocol: The users estimate single-photon gains and error rates from X-basis data using decoy states, then infer the key-rate bound.Only rectilinear-basis results undergo error correction and privacy amplification; diagonal-basis results support estimation.
- B. Distillation procedure: B. Distillation procedure: The protocol distills separate key rates for the singlet |Ψ−⟩ and triplet |Ψ+⟩ states, whose contributions are summed.The procedure can be applied separately to each state or to a combined data set.
- B. Distillation procedure: B. Distillation procedure: Key bits come only from the s class, whereas u, v, and w classes provide decoy-state estimates.The s class is selected whenever basis Z is chosen, so ps coincides with pZ.
- B. Distillation procedure: B. Distillation procedure: The single-photon yield y1,1 and error rate e1,1 are not directly measurable and must be estimated using decoy states.The simultaneous single-photon emission probability follows the product of two Poisson distributions for independent weak coherent states.
Decoy state estimation
Decoy-state estimation uses constrained optimization to lower-bound the single-photon yield and maximize its error rate in the X basis. The procedure combines low-count classes into cumulative constraints, reducing yield constraints from 18 to 14 and producing 21 constraints for error-rate maximization.
- Single-photon yield estimation: 7 + 7 = 14 constraints remain after combining the vw, wv, and ww classes into one cumulative constraint because their counts are much smaller and fluctuate more.The optimization also constrains all yields to be probabilities.
Finite size key rate
Finite-size statistical fluctuations loosen the decoy-state constraints and reduce the secure key rate relative to the asymptotic case. Combining singlet and triplet data yields a key rate of 366 kbit/s, while at 2.33 dB attenuation and a sample of ∼2.4×10^7, the finite-size rate is about 30% of the asymptotic rate.
- Statistical estimation: 5.4 × 10−11: Choosing n = 7 gives ε = 2.56 × 10−12 and keeps the overall parameter-estimation failure probability below this value across 21 constraints.The statistical fluctuations are assumed Gaussian, and the failure probability is set through the estimation procedure.
- Finite-size effects: 30%: At 2.33 dB channel attenuation and total sample size ∼2.4×10^7, the finite-size key rate is about 30% of the asymptotic rate.Looser finite-size constraints make the finite-size solution worse than the asymptotic solution, reducing the key rate.
- Data-set combination: 366 kbit/s: Joining the singlet and triplet data sets produces this key rate.The total sample is formed by combining counts from both data sets to maximize the finite-size key rate.
C. Key rates
This section presents key rate R as a function of channel attenuation or equivalent distance in a single-mode optical fibre. The fibre is characterized by 0.2 dB/km attenuation.
- Key rates: Key rate R is reported against channel attenuation in dB.The table specifies channel attenuation as one independent variable.
- Key rates: Key rate R is also reported against equivalent distance in km.Equivalent distance is the second independent variable listed for the rate comparison.
- Key rates: 0.2 dB/km attenuation characterizes the single-mode optical fibre.The passage identifies the fibre attenuation used for the channel.
D. Count and error rates in the rectilinear basis
The rectilinear-basis measurements report coincidence counts and error rates separately for singlet and triplet states, using 80 ms acquisition for each attenuation/distance value.
- Measured rectilinear-basis coincidence counts are reported separately for singlet and triplet states.
- Measured rectilinear-basis error rates are reported separately for singlet and triplet states.
- 80 ms acquisition was used for each attenuation/distance value.
E. Count rates in the diagonal basis
This section reports measured diagonal-basis coincidence counts for singlet and triplet states, using 25-second acquisitions except for finite-size data collected over 12,000 seconds.
- Measured diagonal-basis coincidence counts are reported separately for the singlet and triplet states.
- 25 seconds was used for each combination, except the finite-size dataset, which was acquired over 12,000 seconds.
F. Error rates in the diagonal basis · G. Theoretical estimation of the visibility
The paper reports measured diagonal-basis error rates for singlet and triplet states, with acquisition times matching Table IV. It models two-photon interference visibility from independent gain-switched lasers using timing jitter, pulse bandwidth, frequency differences, pulse profiles, and chirp.
- F. Error rates in the diagonal basis: Measured diagonal-basis error rates EXX are reported separately for the singlet and triplet states.
- F. Error rates in the diagonal basis: Acquisition times for the diagonal-basis measurements are the same as those listed in Table IV.
- G. Theoretical estimation of the visibility: Visibility V(στ, ∆ν) from two independent gain-switched laser diodes depends on time jitter τ and interfering-pulse bandwidth ∆ν.
- G. Theoretical estimation of the visibility: Figure 2(a) uses τ and ∆ν as its horizontal and vertical axes, with measured seeded and unseeded slave-laser values shown by two empty circles.
- G. Theoretical estimation of the visibility: The model assumes time jitter follows a Normal distribution Nτ(0, στ) centred at 0 and plots visibility using the stated expression.
- G. Theoretical estimation of the visibility: Visibility is derived from Alice’s and Bob’s emitted electric fields to estimate coincidence counts at Charlie’s detectors.
- G. Theoretical estimation of the visibility: The formulation includes relative central-frequency difference ωij, Gaussian pulse intensity profiles, measurable pulse width, and frequency chirp parameter β.
- G. Theoretical estimation of the visibility: Assuming chirp is the sole cause of excess bandwidth, measured σt and the time-bandwidth product allow inversion of the bandwidth relation to determine β.