Fig. 4: High-dimensional time-frequency entanglement distribution of a 45.32 GHz singly-filtered biphoton frequency comb at 10 km distances.
From: High-dimensional time-frequency entanglement in a singly-filtered biphoton frequency comb
a Illustrative experimental scheme for asymmetric entanglement distribution of high-dimensional time-frequency entanglement of a singly-filtered BFC. The singly-filtered BFC is generated by only passing the signal photons through an FFPC, while the idler photons are distributed via a 10 km fiber link. After distribution, a pair of tunable bandpass filters are used to select frequency bins for the signal and idler photons, which are then analyzed by a Franson interferometer for energy-time entanglement. The inset shows the Franson interference fringes for 5 symmetric frequency-bin pairs after 10 km distribution. The error bars represent one standard deviation of the mean assuming Poissonian statistics. b The measured visibilities of Franson-interference recurrences (black dots) and Schmidt eigenvalues (green bars) after 10 km distribution from 0th to 15th time-bin with (without) background subtracted: 98.81 (63.90) ± 0.61%, 89.28 (55.29) ± 1.55%, 80.54 (49.44) ± 1.15%, 71.28 (40.10) ± 1.35%, 64.81 (32.90) ± 1.57%, 58.54 (28.83) ± 1.68%, 52.57 (20.92) ± 1.80%, 47.52 (19.87) ± 1.84%, 42.03 (17.40) ± 1.95%, 37.18 (14.67) ± 2.03%, 33.50 (14.62) ± 2.06%, 29.46 (13.78) ± 2.12%, 27.90 (13.64) ± 2.15%, 24.93 (13.06) ± 2.26%, 22.79 (11.21) ± 2.24%, 19.83 (10.79) ± 2.35%. The error bars represent one standard deviation of the mean. The insets show the interference fringe for the 0th, 7th and 15th time-bin. The Franson interference visibility decay matches well with our theoretical prediction after 10 km distribution, full data of the Franson interference fringes for 16 time bins is provided in Supplementary Note 3. The time-bin Schmidt number after 10 km distribution is measured to be 12.99, which only shows degradation of 0.92% compared to Fig. 2e. Detailed Schmidt eigenvalues are presented in Supplementary Note 4. c The measured frequency-binned Franson-interference visibilities (black inverse triangular and red dots) and the coincidence counts for 5 symmetric frequency-bin pairs (different colors represent corresponding frequency-bin pairs in the frequency-correlation matrix) of the singly-filtered BFC after 10 km distribution. Frequency-binned Franson interference visibilities after distribution with (without) background subtraction are 94.95 (73.86) ± 2.07% for S2& I-2, 97.99 (84.12) ± 1.04% for S1&I-1, 98.85 (87.60) ± 0.50% for S0&I0, 97.84 (82.77) ± 1.12% for S-1&I1 and 93.89 (70.76) ± 2.71% for S-2&I2, respectively. Averaged frequency-binned Franson visibility of 96.70 ± 1.93% is obtained, with only 1.33% degradation after distribution. These results demonstrate that the frequency-binned energy-time entanglement of our singly-filtered BFC is well preserved after 10 km distribution. The error bars represent one standard deviation of the mean. d Raw key rate (dots) and photon information efficiency (square) of the frequency-multiplexed quantum key distribution using the singly-filtered (red solid line) and doubly-filtered (blue dashed line) BFCs. e Secure key rate (bars) and secure PIE (stars) at different frequency-bin pairs. Three frequency-bin pairs show positive PIE after subtracting Eve’s Holevo information. A total SKR of 1.1 kbits/s is achieved using our singly-filtered BFC. f Secure key rate comparison between singly-filtered BFC and doubly-filtered BFC. The singly-filtered BFC shows ≈ 7.5 × enhancement of secure key rate under the same system condition.
