Abstract
The photon counting is an important task in quantum optics and photonic quantum information. The simplest photon counter found in the literature is a multi-photon number resolving detector (MPNRD), composed by a threshold single-photon detector and a time-multiplexing scheme usually built with a fiber ring. The correct photon number estimation is hampered by the optical losses and the non-unit quantum efficiency of the single-photon detector used. In this work we provide an analytical expression that improves the performance of the multi-photon number resolving detector when coherent states are measured. This transform the static MPNRD device in a dynamic MPNRD.
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References
Banaszek, K., Walmsley, I.A.: Photon counting with a loop detector. Opt. Lett. 28, 52–54 (2003)
Bezerra, P., Vasconcelos, H.M., Glancy, S.: Quadrature squeezing and temperature estimation from the Fock distribution. Quantum Inf. Process. 21, 365 (2022). https://doi.org/10.1007/s11128-022-03677-5
Brod, D.J., Galvão, E.F., Crespi, A., Osellame, R., Spagnolo, N., Sciarrino, F.: Photonic implementation of boson sampling: a review. Adv. Photonics 1(3), 034001 (2019). https://doi.org/10.1117/1.AP.1.3.034001
Bromley, T.R., Arrazola, J.M., Jahangiri, S., Izaac, J., Quesada, N., Gran, A.D., Schuld, M., Swinarton, J., Zabaneh, Z., Killoran, N.: Applications of near-term photonic quantum computers: software and algorithms. Quantum Sci. Technol. 5, 034010 (2020)
Cai, Y., Chen, Y., Chen, X., Ma, J., Xu, G., Wu, Y., Xu, A., Wu, E.: Quantum calibration of photon-number-resolving detectors based on multi-pixel photon counters. Appl. Sci. 9(13), 2638 (2019). https://doi.org/10.3390/app9132638
Castro, G.S., Ramos, R.V.: Enhancing eavesdropping detection in quantum key distribution using disentropy measure of randomness. Quantum Inf. Process. 21, 79 (2022). https://doi.org/10.1007/s11128-022-03422-y
Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the Lambert W function. Adv. Comput. Math. 5, 329–359 (1996)
Curado, E.M.F., Tsallis, C.: Generalized statistical mechanics: connection with thermodynamics. J. Phys. A 24, L69 (1991) [Corrigenda: 24, 3187 (1991) and 25, 1019 (1992)]
Da Silva, J.L.M., Mendes, F.V., Ramos, R.V.: Radial basis function network using Lambert–Tsallis function. Physica A 534(15), 122168 (2019). https://doi.org/10.1016/j.physa.2019.122168
da Silva, G.B., Ramos, R.V.: The Lambert–Tsallis Wq function. Physica A 525, 164–170 (2019)
da Silva, J.R., Ramos, R.V.: Applications of the Lambert–Tsallis Function in X-ray free electron laser. IEEE Trans. Plasma Sci. 50(10), 3578–3582 (2022). https://doi.org/10.1109/TPS.2022.3205545
Davis, S.I., Mueller, A., Valivarthi, R., Lauk, N., Narvaez, L., Korzh, B., Beyer, A.D., et al.: Heralding single photons using photon-number-resolving superconducting nanowires. In: CLEO: QELS_Fundamental Science. Optica Publishing Group, Washington, D.C. (2022). https://doi.org/10.1364/cleo_qels.2022.fth5o.5
de Almeida, F.J.L., Ramos, R.V.: Disentropy in astronomy. Eur. Phys. J. plus 138, 20 (2023). https://doi.org/10.1140/epjp/s13360-022-03640-4
de Andrade, J.S., Nobrega, K.Z., Ramos, R.V.: Analytical solution of the current-voltage characteristics of circuits with power-law dependence of the current on the applied voltage using the Lambert–Tsallis Wq function. IEEE Trans. Circuits Syst. II Express Briefs 69(3), 769–773 (2021). https://doi.org/10.1109/TCSII.2021.3110407
Fujiwara, M., Sasaki, M.: Photon number resolving detector at telecom wavelengths: charge integration photon detector (CIPD). IEEE J. Sele. Top. Quantum Electron. 13(4), 952–958 (2007). https://doi.org/10.1109/jstqe.2007.903857
Fukuda, D., Fujii, G., Numata, T., Amemiya, K., Yoshizawa, A., Tsuchida, H., Fujino, H., et al.: Titanium superconducting photon-number-resolving detector. IEEE Trans. Appl. Supercond. 21(3), 241–245 (2011). https://doi.org/10.1109/tasc.2010.2089953
Inoue, K.: Differential phase-shift quantum key distribution systems. IEEE Sel. Top. Quant. Electron. 21(3), 6600207 (2015)
Kardynał, B.E., Yuan, Z.L., Shields, A.J.: An avalanche-photodiode-based photon-number-resolving detector. Nat. Photonics 2(7), 425–428 (2008). https://doi.org/10.1038/nphoton.2008.101
Li, Y.-P., Chen, W., Wang, F.-X., Yin, Z.-Q., Zhang, L., Liu, H., Wang, S., He, D.-Y., Zhou, Z., Guo, G.-C., Han, Z.-F.: Experimental realization of a reference-frame independent decoy BB84 quantum key distribution based on Sagnac interferometer. Opt. Lett. 44(18), 4523–4526 (2019)
Lo, H.-K., Curty, M., Tamaki, K.: Secure quantum key distribution. Nat. Photonics 18, 595–604 (2014)
Mendes, F.V., Lima, C., Ramos, R.V.: Applications of the Lambert-Tsallis Wq function in quantum photonic Gaussian boson sampling. Quantum Inf. Process. 21, 215 (2022). https://doi.org/10.1007/s11128-022-03559-w
Ramos, R.V.: Disentropy of the Wigner function. JOSA B 36(8), 2244–2249 (2019). https://doi.org/10.1364/JOSAB.36.002244
Ramos, R.V.: Estimation of the randomness of continuous and discrete signals using the disentropy of the autocorrelation. SN Comput. Sci. 2, 254 (2021). https://doi.org/10.1007/s42979-021-00666-w
Ramos, R.V.: Analytical solutions of cubic and quintic polynomials in micro and nanoelectronics using the Lambert–Tsallis Wq function. J. Comput. Electron. 21, 396–400 (2022). https://doi.org/10.1007/s10825-022-01852-6
Ramos, R.V.: Solving the Fermat and Fibonacci equations with the Lambert–Tsallis Wq function. Available on Researchgate (2023)
Rehacek, J., Hradil, Z., Haderka, O., Perina, J., Hamar, M.: Multiple-photon resolving fiber-loop detector. Phys. Rev. A 67, 061801 (2003)
Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Dušek, M., Lütkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301–1350 (2009)
Sonoyama, T., Endo, M., Matsuyama, M., Okamoto, F., Miki, S., Terai, H., Yabuno, M., China, F., Furusawa, A.: Detector tomography of superconducting-nanowire photon-number-resolving detector. In: 2021 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference (CLEO/Europe-EQEC). (2021). https://doi.org/10.1109/cleo/europe-eqec52157.2021.9542157
Thé, G.A.P., Ramos, R.V.: Multiple-photon number resolving detector using fibre ring and single-photon detector. J. Mod. Opt. 54(8), 1187–1202 (2007). https://doi.org/10.1080/09500340601124825
Thekkadath, G.S., Bell, B.A., Walmsley, I.A., Lvovsky, A.I.: Engineering Schrödinger cat states with a photonic even-parity detector. Quantum 4, 239 (2020). https://doi.org/10.22331/q-2020-03-02-239
Tiedau, J., Meyer-Scott, E., Nitsche, T., Barkhofen, S., Bartley, T.J., Silberhorn, C.: A logarithmic optical detector for single photons and bright light. In: 25th Central European Workshop on Quantum Optics (CEWQO) (2018)
Tsallis, C.: Possible generalization of Boltzmann–Gibbs statistics. J. Stat. Phys. 52, 479-487 (1988)
Valluri, S.R., Jeffrey, D.J., Corless, R.M.: Some applications of the Lambert W function to physics. Can. J. Phys. 78(9), 823–831 (2000)
Webb, J.G., Huntington, E.H.: Photostatistics reconstruction via loop detector signatures. Opt. Express 17, 11799–11812 (2009)
Zhang, G.Q., Zhai, X.J., Zhu, C.J., Liu, H.C., Zhang, Y.T.: The silicon photomultiplier—a new detector for single-photon-number-resolving at room temperature. Int. J. Quantum Inform. 10(03), 1230002 (2012). https://doi.org/10.1142/s0219749912300021
Funding
This work was supported by the Brazilian agencies CNPq via Grant no. 309374/2021-9, CAPES via no. Grant 001 and FUNCAP. Also, this work was performed as part of the Brazilian National Institute of Science and Technology for Quantum Information.
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RVR and FAM had the main idea of the paper. IKA da Silva and RV Ramos made the calculations and numerical simulations. RV Ramos wrote the paper.
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da Silva, I.K.A., Mendonca, F.A. & Ramos, R.V. Dynamic multi-photon number resolving detector with fiber ring and single-photon detector. Opt Quant Electron 55, 1063 (2023). https://doi.org/10.1007/s11082-023-05391-7
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DOI: https://doi.org/10.1007/s11082-023-05391-7