"From billion photons to single photon experimental setups for QKD"

Workshop on Quantum Key Distribution (QKD) Systems, 18 September 2023 From billion photons to single photon experimental setups for QKD Giannis Giannoulis, PhD Photonics Communications Research Laboratory, School of Electrical and Computer Engineering, National Technical University of Athens Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 Talk overview •QKD system implementation in Lab •Quantum Layer Implementation ✓Single-photon emission station ✓Polarisation encoder @ Alice station and Polarisation analysis @Bob station ✓Fiber links for quantum and classical/quantum coexistence ✓Single-photon detection •Quantum Layer Evaluation ✓Quantum BER ✓Secure Key Rate estimation Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 3 What we need to install QKD setups in lab? Quantum channel (optical fiber/FSO link) Polarisation analysis station Polarization Encoder QRNG Single-photons 𝑋= 𝐷, 𝐴 𝑍= 𝐻, 𝑉 Single-photon detectors Eleni Diamanti, Photonics@be doctoral school May 10, 2016 The talk today will focus on the quantum channel implementation Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 4 Photon number states ത𝑛=1,𝛥𝑛=0 Ideal single photons Generating single-photons Practical single photons Attenuated laser sources 𝑃 𝑛 =ത𝑛𝑛 𝑛!𝑒−ത 𝑛,𝑛=0,1,2,⋯ Quantum Light Sampling billions of photons provided by classical lasers down to single-photon regime Poissonian statistics –the discrete equivalent of Gaussian statistics – are obtained! Mark Fox, Quantum Optics –An Introduction Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 5 Polarisation as an attractive encoding scheme! Polarisation encoding for QKD •Polarisation optics are part of every photonic laboratory, allowing for orthonormal bases implementation (e.g., X,Z) with simple laboratory equipment (PER of ~30dB) •Robust encoding scheme for FSO links and stable operation for installed fiber links •Deployment-friendly approach for QKD setups offering simple polarization control Generating polarization bases in the lab! 𝜓1=12H +𝑒𝑖𝜑1V 𝜓2=12H +𝑒𝑖 𝜑1+𝜋 V 𝜒2=12H +𝑒𝑖 𝜑1+Τ 3𝜋 2 V 𝜒1=12H +𝑒𝑖 𝜑1+Τ 𝜋 2 V 𝜑1=0 Vol. 25, No. 23 | 13 Nov 2017 | OPTICS EXPRESS 28886 #304476 Opt. Lett 44(10) 2398 (2019) Controlling the phase difference between the horizontal ( ↔) and vertical ( ↕) components Encoding path Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 6 Lossy fibers in quantum links Fiber loss in classical photonic links 𝑑𝑃 𝑑𝑧=−𝐴𝑧⇒𝑃 𝑧 =𝑃 0𝑒−𝐴𝑧 Exponential law in fiber loss for classical systems comes as the result of averaging the effect of loss mechanisms in fiber in billions of photons Fiber loss parameter A decreases exponentially the received power Fiber loss in singlephoton links The effect of a lossy medium with transmission Ton a beam of light can be modelled as a beam splitter with splitting ratio T:(1-T).The beam splitting process is probabilistic at the level of the individual photons, so every photon can see its own fiber loss!! From received power levels to detection probabilities Mark Fox, Quantum Optics –An Introduction Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 [Fiber Quantum Link scenario]: Assume an ideal single-photon source at Alice station emitting photons with a repetition rate of 10 GHz. The ideal single-photon pulse train is detected through noiseless ideal photon detectors (η=100%). Which is the detection probability of one photon after the propagation of the above pulse train over 2000Km of telecom fiber with loss of 0.2dB/Km? The loss-limits on the detection probability As a first step, we calculate the loss of the telecom fiber: 𝐿=0.2 Τ 𝑑𝐵 𝐾𝑚×1000𝐾𝑚=200𝑑𝐵 20 orders of magnitude! Hence, the transmittance of the fiber channel is:𝜂=10−20 Since we have assumed ideal detector of 100%DE:𝜂𝐷𝐸 =𝜂𝑓𝑖𝑏𝑒𝑟 =10−20 On the detection station the rate of detected photons can be then calculated: 𝑅𝐴𝑙𝑖𝑐𝑒×𝜂𝐷𝐸 =10×109×10−20 =10−10𝑐𝑝𝑠 ~ 0.3 photon detections/century!! Within the next 3-4 centuries, one photon from Alice station will will succeed to overcome all the obstacles within the fiber core (absorption, Rayleigh scattering, etc.) and it will finally offer a click at the Bob’s measurement station!! Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 The loss-limits on the detection probability The result from a philosophical perspective: Be positive in your difficult times: Everything is possible with a non-zero probability! ~ 0.3 photon detections/century!! The result from a technology perspective: •Quantum repeaters will revolutionize the landscape of Quantum Links!! •Satellite QKD offers an alternative approach to the fundamental loss-limit on the detection probability!! QKD in Space, satellite-toground QKD links 2nd Day: 10:00-10:45 Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 Classical/Quantum Coexistence in the fibers N A Peters et al 2009 New J. Phys. 11 045012 Coexistence topology The scattered photons are generated at frequencies above and below that of the pump light, corresponding to anti-Stokes and Stokes scattering. A. Ntanos, et al., "Deployment-Oriented Classical/Quantum coexistence in X-haul fiber link for B5G Networks," in CLEO 2023, paper AM3N.5. Raman noise photons Intense classical light Raman scattering arises from an inelastic interaction of a pump light with vibrational modes (optical phonons) in a fiber. Contamination photons on quantum channel D. Zavitsanos et al., "Feasibility Analysis of QKD Integration in Real-World FTTH Access Networks," in Journal Lightwave Technology (Early Access) Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 Decoy states against the PNS Decoy QKD protocol Signal states - μ Decoy states - v 𝑄𝑠𝑖𝑔𝑛𝑎𝑙 =#det𝑒𝑐𝑡𝑒𝑑𝑠𝑖𝑔𝑛𝑎𝑙 #𝑝𝑟𝑒𝑝𝑎𝑟𝑒𝑑𝑠𝑖𝑔𝑛𝑎𝑙 𝜂𝑠𝑖𝑔𝑛𝑎𝑙 =−ln1+𝑌0−𝑄𝑠𝑖𝑔𝑛𝑎𝑙 𝜇 𝜂𝑑𝑒𝑐𝑜𝑦 =−ln1+𝑌0−𝑄𝑑𝑒𝑐𝑜𝑦 𝜈 𝑄𝑑𝑒𝑐𝑜𝑦 =#det𝑒𝑐𝑡𝑒𝑑𝑑𝑒𝑐𝑜𝑦 #𝑝𝑟𝑒𝑝𝑎𝑟𝑒𝑑𝑑𝑒𝑐𝑜𝑦 𝜂𝑠𝑖𝑔𝑛𝑎𝑙 ≠𝜂𝑑𝑒𝑐𝑜𝑦 𝜂𝑠𝑖𝑔𝑛𝑎𝑙 =𝜂𝑑𝑒𝑐𝑜𝑦 PNS attack! No PNS attack! Alice/Bob calculate the transmittance for both categories of pulses PRL 94, 230504 (2005) PHYSICAL REVIEW A 72, 012326 2005 Decoy states boost the SKRs of QKD! Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 17 Polarisation as an attractive encoding scheme! Polarisation analysis in Bob’s measurement station Linearly polarized photon with polarization angle θ: ↕ۄ ↔=0(2) 𝜃 =cos𝜃↕+sin𝜃↔ 𝑃𝑉=↕ۄ 𝜃2⇒𝑃𝑉=↕ۄ cos𝜃↕+sin𝜃↔2 (1) (1) ⇒𝑃𝑉= cos𝜃↕ۄ ↕+sin𝜃↕ۄ ↔2(2) ⇒𝑃𝑉=cos2𝜃 𝑃Η=↔ۄ 𝜃2⇒𝑃𝐻=↔ۄ cos𝜃↕+sin𝜃↔2 ⇒𝑃𝐻= cos𝜃↔ۄ ↕+sin𝜃↔ۄ ↔2⇒𝑃𝐻=sin2𝜃 Detection probabilities in the photon detectors D1 &D2: D1 (2) (1) D2 ↕ۄ ↕=1 Polarisation analysis at Bob station •DSP algorithms to mitigate the polarization drifts through the quantum channel (e.g., Polarisation Mode Dispersion in telecom fibers) •Measurements of states of polarization by selecting random base. Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 [True or False] If a circularly polarized photon 𝐿 = 12𝐻 +𝑖𝑉 inserted into a Polarisation Beam Splitter (PBS), the detection probability of the photon exiting the horizontal polarization axis (H) and vertical polarization axis ports is 50%. 𝐿 Quiz Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 If a Circularly polarized photon 𝐿 = 12𝐻 +𝑖𝑉 inserted into Polarisation Beam Splitter (PBS), the detection probability of the photon exiting the horizontal polarization axis (H) and vertical polarization axis ports is 50%. Assuming an ideal single-photon detector of η=100%, we can calculate the detection probabilities through the bracket calculations: 𝑃𝐻= 𝐻 ۄ 𝐿2⇒𝑃𝐻= 𝐻 ۄ 12𝐻 + 𝑖2𝑉2 (1) (1) ⇒𝑃𝐻=12𝐻ۄ 𝐻 + 𝑖2𝐻ۄ 𝑉2 𝐻ۄ 𝐻 =1 𝐻ۄ 𝑉 =0 (2) ⇒𝑃𝐻=12×12=1 2=50% (2) TRUE 𝐿 𝐿 = 12𝐻 +𝑖𝑉 Following the same methodology, the probability for the other PBS port is: 𝑃𝑉= 𝑉 ۄ 𝐿2=50% 𝑃𝑉=1−𝑃𝐻=50% Assuming the preservation of photon number: Quiz Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 Photon Detection Quantum Efficiency 𝑛= ഥ 𝑁 ത𝑛 •Quantum efficiency is defined as the ratio between the number of photon counts and the number of incoming photons. •Quantum theory of photodetection aims to relate the photocount statistics observed in a particular experiment to those of the incoming photons 𝛥𝑁 2=𝜂2𝛥𝑛 2+𝜂 1−𝜂 ത𝑛 Theoretical background & equipment description for hands-on experiments 2nd Day: 10:00-10:45 Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 21 In the case of installing a laboratory setup, additional optical losses which significantly degrade the system detection efficiency should be considered. We need also to include the non-ideal quantum efficiency (QE<100%) of the single-photon detector. Incoming photons Loss of fiber patch cords Loss due to the mismatch between the mode diameter and the active area of SPD Percentage of absorbed photons that successfully generate electrical pulses Percentage of photons arriving at the active area and finally absorbed. 𝜂𝑓𝑖𝑏𝑒𝑟×𝜂𝑐𝑜𝑢𝑝𝑙𝑒 𝑜𝑢𝑡 ×𝜂𝑎𝑏𝑠×𝜂𝑄𝐸 𝑖 𝜂𝐷𝐸 =𝜂𝑓𝑖𝑏𝑒𝑟×𝜂𝑐𝑜𝑢𝑝𝑙𝑒 𝑜𝑢𝑡 ×𝜂𝑎𝑏𝑠×𝜂𝑄𝐸 𝑖 Detection efficiency in laboratory setups Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 Synchronized photon detection @Bob station ΟΝ ΟΝ OFF OFF OFF Photon arrival SPAD operation The pulse carving at Alice station ensures that the photons arrives at Bob station are expected within the time window of the pulse. They are packed within the pulse! By transferring synchronized time windows for driving the SPADs, we provide ON detection gates synched with the pulses carrying the single-photons. Out of the pulsewidth the SPAD is on OFF state. Gated mode Synchronization channel •Synchronizing the pulses consisting of photons together with the SPADs is essential for minimizing the error counts •Optical clock recovery techniques have been proposed, where innovative solutions based on SPAD outputs have been also proposed (Qubit4Sync) Opt. Express 12, 2011-2016 (2004) Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 QBER measurement 𝑄𝐵𝐸𝑅= 𝑓𝑎𝑙𝑠𝑒 𝑓𝑎𝑙𝑠𝑒+𝑟𝑖𝑔ℎ𝑡 General definition: 𝑄𝐵𝐸𝑅=1 2𝑝𝜇1−𝑉 +2𝑝𝑑𝑐+𝑝𝑎𝑝+𝑝𝑟𝑎𝑚+𝑝𝑋𝑡𝑎𝑙𝑘 𝑝𝜇+2𝑝𝑑𝑐+𝑝𝑎𝑝+𝑝𝑟𝑎𝑚+𝑝𝑋𝑡𝑎𝑙𝑘 Signal detection probability Visibility Dark count rates Afterpulsing probability Spectral profile of SpRS P Eraerds et al 2010 New J. Phys. 12 063027 QBER anatomy in coexistence scenarios Quantum Bit Error Rate (QBER): The ratio between the number of false detections and total detections (right + false) Example: Solar radiance in FSO/satellite-QKD links 𝑉 𝐻 Non-ideal basis construction Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 Classical vs Quantum BER •~ 1.5 ×105 photons for each transmitted bit level ‘1’ •~ 1.5 × 102photons for each transmitted bit level ‘0’ BER < 10-9 QBER < ~ 8-9 ×10-2 Acceptable BER values Acceptable QBER values Photons per bit Photons per qubit Less than 1 photon per encoded pulse Non-reproduceable block for QBER measurement Each block of detected events after SPADs is unique! Every sequence of bits can be reproduced (e.g., stored) OOK link parameters: 𝑃𝑎𝑣𝑔 =−10𝑑𝐵𝑚 𝛣=10𝐺𝑏𝑝𝑠 𝜆=1550𝑛𝑚 Giannis Giannoulis, Postdoctoral Researcher, PCRL-NTUA/GRNET HellasQCI Training Event, 18-22 September 2023 The final step: Secure Key Rates SKR estimation 𝑅≥𝑞−𝑓 𝐸𝜇𝑄𝜇𝐻2𝐸𝜇+𝑄11−𝐻2𝑒1 Lo, H. K., Ma, X., & Chen, K. (2005). Decoy state quantum key distribution. PRL, 94(23), 230504 QBER measurement Cryptographic apps A. Ntanos et al., submitted for publication to IEEE JLT