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High-Dimensional Quantum Key Distribution based on Multicore Fiber using Silicon Photonic Integrated Circuits
Yunhong Ding, Davide Bacco, Kjeld Dalgaard, Xinlun Cai, Xiaoqi Zhou, Karsten Rottwitt, Leif Katsuo Oxenløwe
TL;DR
Traditional binary QKD is limited to 1 bit/photon, motivating higher-dimensional protocols that can improve information efficiency. This paper implements HD-QKD with multicore-fiber space division multiplexing and silicon photonic circuits, realizing three mutually unbiased bases in a four-dimensional Hilbert space. The experiment achieves a stable 13% average QBER over 10 minutes and demonstrates a trade-off between security and secret-key rate when increasing the number of bases.
Problem
Traditional binary QKD has an information-efficiency limit of 1 bit/photon, while long-distance fiber transmission of alternative spatial modes faces inter-modal crosstalk challenges.
Method
The paper uses space division multiplexing in multicore fiber with silicon photonic integrated circuits to prepare and measure four-dimensional quantum states in three mutually unbiased bases.
Results
13% average QBER was obtained over 10 minutes, and the experiment demonstrated stable HD-QKD operation with two of the three prepared mutually unbiased bases.
Takeaways & Limitations
Multicore fiber and silicon photonics provide a compact approach for manipulating high-dimensional quantum states and support higher-information-efficiency QKD.
Takeaways & Limitations
The experiment's 10 kHz and 5 kHz pulse rates limit long-link deployment because the thermally tunable interferometer heaters switch slowly.
Abstract
from arXiv · showhide
Quantum Key Distribution (QKD) provides an efficient means to exchange information in an unconditionally secure way. Historically, QKD protocols have been based on binary signal formats, such as two polarisation states, and the transmitted information efficiency of the quantum key is intrinsically limited to 1 bit/photon. Here we propose and experimentally demonstrate, for the first time, a high-dimensional QKD protocol based on space division multiplexing in multicore fiber using silicon photonic integrated lightwave circuits. We successfully realized three mutually unbiased bases in a four-dimensional Hilbert space, and achieved low and stable quantum bit error rate well below both coherent attack and individual attack limits. Compared to previous demonstrations, the use of a multicore fiber in our protocol provides a much more efficient way to create high-dimensional quantum states, and enables breaking the information efficiency limit of traditional QKD protocols. In addition, the silicon photonic circuits used in our work integrate variable optical attenuators, highly efficient multicore fiber couplers, and Mach-Zehnder interferometers, enabling manipulating high-dimensional quantum states in a compact and stable means. Our demonstration pave the way to utilize state-of-the-art multicore fibers for long distance high-dimensional QKD, and boost silicon photonics for high information efficiency quantum communications.
Introduction
Traditional QKD encodes information in binary formats with an efficiency limit of 1 bit/photon, motivating higher-dimensional approaches. This paper demonstrates HD-QKD using multicore fiber and silicon photonic integrated circuits.
- Introduction: 1 bit/photon is the information-efficiency limit of traditional binary QKD systems.BB84 uses polarization encoding and two mutually unbiased bases in a two-dimensional Hilbert space.
- Introduction: Multicore fibers provide separate spatial channels with low inter-core crosstalk for high-dimensional quantum-state transmission.This offers an alternative to optical angular momentum modes, whose long-distance fiber transmission is challenged by inter-modal crosstalk.
- Introduction: The paper demonstrates HD-QKD over multicore fiber using silicon photonic integrated circuits.The reported system prepares three mutually unbiased bases with four-dimensional quantum states and transmits them through a 7-core fiber.
- Introduction: Silicon photonic integration is used to manipulate high-dimensional quantum states in compact, phase-stable circuits.The fabricated Alice and Bob chips are shown alongside a 1 euro coin to indicate their compact size.
Protocol definition
The protocol uses three mutually unbiased bases in a four-dimensional Hilbert space, with basis states formed from superpositions of four core states. Silicon photonic Mach-Zehnder interferometers prepare and measure these states through multicore-fiber interference.
- Protocol definition: Mutually unbiased bases produce equally probable measurement outcomes when preparation and measurement use different bases.This property underlies the basis-selection structure of the protocol.
- Protocol definition: Three mutually unbiased bases are used in a four-dimensional Hilbert space.The protocol restricts the analysis to three bases even though the maximum number for dimension four is five.
- Protocol definition: The three bases satisfy pairwise unbiasedness through equal squared overlaps of 1/4.The construction is summarized by |⟨M0|M1⟩|2 = |⟨M0|M2⟩|2 = |⟨M1|M2⟩|2 = 1/4.
- Protocol definition: The four basis states are represented by the four individual multicore-fiber cores.They are denoted |A⟩, |B⟩, |C⟩, and |D⟩.
- Protocol definition: Alice prepares basis states by tuning transmitter-chip Mach-Zehnder interferometers to create superpositions between cores.Bob randomly selects one of the three bases and tunes the corresponding interferometer to measure the state.
Secret key rate
The four-dimensional QKD analysis defines secret-key-rate bounds through Alice–Bob and Eve mutual information, considering individual and general attacks. It relates fidelity and disturbance to security thresholds and allowable QBER.
- Secret key rate: The secret key rate measures the useful key Alice and Bob can generate in bit/s or bit/pulse.The paper introduces this as the major criterion for a QKD communication system.
- Secret key rate: The four-dimensional secret-key-rate formulation uses Alice–Bob mutual information and an Eve-information term under a trusted-device assumption.The analysis considers Alice–Eve information and assumes Eve cannot modify Bob’s detector efficiency.
- Eavesdropping models: Individual attacks treat ququart states independently, whereas general attacks allow Eve to monitor multiple quantum states jointly.The paper describes general attacks as less conservative than individual attacks.
- Eavesdropping models: For individual attacks, the analysis uses a universal quantum cloning machine for qudits to bound Eve’s information and the disturbance introduced by eavesdropping.The bound is formulated for four-state ququart encoding and depends on the relevant fidelity.
- Security thresholds: The disturbance limit increases with Hilbert-space dimension, allowing higher QBER during key generation as N increases.This relationship is presented as a consequence of the individual-attack analysis.
- Security thresholds: Security under coherent attacks is sufficient when IAB ≥ log2(N), assuming the key dimension is much greater than the number of ququart pulses.The stated bounds assume infinite key length; finite-key security requires a different treatment.
Experimental results
The experiment implements high-dimensional state preparation and decoy-state operation with silicon photonic circuits and multicore fiber. Three mutually unbiased bases were experimentally verified, and stable QBER below both stated attack limits was achieved.
- Experimental setup: Silicon photonic circuits prepare high-dimensional quantum states from weak coherent pulses using variable attenuation and configurable interferometers.Alice’s chip prepares the states, while VOA1 controls pulse power for decoy-state operation.
- Experimental setup: Alice randomly transmits one of four states in one of three bases, while decoy-state sequences are introduced every 2 minutes.The decoy sequence lasts 10 seconds and is generated by tuning VOA1.
- State verification: Theoretical and experimental quantum tomography show good agreement for all three mutually unbiased bases.The agreement indicates that the three bases were well prepared.
- Performance: 13% average QBER remained stable for more than 10 minutes, below both coherent-attack and individual-attack limits.The measurement used a 5 kHz repetition rate and mean photon number µ = 0.26 per pulse.
Discussion
The experiment demonstrates stable HD-QKD performance while exposing practical trade-offs and deployment constraints. The discussion identifies multicore-fiber phase drift, heater speed, insertion loss, and integration advances as key considerations for long-distance operation.
- Experimental performance: 13% average QBER over 10 minutes provided a stable demonstration and a basis for key extraction.The measurement used the HD-QKD protocol discussed in the experiment.
- State characterization: Three MUBs were characterized by comparing theoretical and experimental state tomography under 30-second measurements.The tomography used a 1550 nm continuous-wave laser with 10 ns pulses at 10 kHz and 0.2 mean photons per pulse.
- Decoy-state operation: The protocol used real-time decoy-state control through Alice’s on-chip VOA1, with signal and decoy sifted bits reported separately.The average estimated photon numbers were µ = 0.26 and v = 0.15 photon/pulse.
- Security-rate trade-off: Using more than three MUBs creates a security-rate trade-off: in four dimensions, less than 2% additional QBER tolerance corresponds to a 2/5 reduction in key rate.The appropriate choice depends on actual channel conditions.
- Long-distance constraints: Long-distance transmission must address independent phase and polarization drift in multicore-fiber cores and match inter-core delays at Bob.The short experimental link mitigated these effects, but a real QKD system must consider them.
- Hardware limitations: The 10 kHz and 5 kHz pulse rates limit long-link deployment because thermal MZI switching is slow, while the receiver chip adds 8 dB insertion loss.The discussion proposes faster phase shifters and improved grating couplers as remedies.
Methods
The methods combine silicon photonic fabrication and electronic control with simulations of HD-QKD performance over distance. The simulated comparison evaluates Hilbert-space dimension, attack strategy, decoy-state key rates, and channel loss.
- Device fabrication: Silicon PICs were fabricated on a 250 nm silicon, 1 µm BOX SOI wafer using standard lithography and ICP etching.The fabrication sequence formed the silicon photonic circuit before subsequent oxide and heater processing.
- Performance simulation: The simulations compare mutual-information thresholds and secret key rate versus distance for qubit and ququart decoy-state encodings.They use fixed detector, dark-count, loss, and decoy-rate parameters and include three experimental points.
- Device fabrication: A 1 µm SiO2 isolation layer and titanium heaters were added to enable thermally controlled photonic operation.The heaters were fabricated after oxide deposition and thinning, followed by contact-layer processing and wire bonding.
- Electronic control: Real-time control of the transmitter and receiver MZIs used FPGA-generated electrical signals to tune the silicon-chip interferometers.The electronic design supports chip-to-chip HD-QKD based on space-division multiplexing.
Experimental setup
The experimental setup generated weak coherent pulses and injected them into Alice’s silicon chip for spatially multiplexed quantum-state preparation. Time-tagged measurements characterized the resulting pulse shape and modulation behavior.
- Optical preparation: A continuous-wave laser, intensity modulator, FPGA, polarization controller, and fiber-grating coupler generated and injected pulsed light into Alice’s chip.The laser operated from 1540–1560 nm, with pulses generated at a 5 kHz repetition rate and injected in TE mode.
- Pulse characterization: 45-second time-tagged measurements indicated a 10 ns pulse width, with out-of-pulse counts attributed to limited modulation extinction ratio.
Characterization of switching time
The switching characterization measured tunable-MZI transmission under applied voltage and quantified heater-driven switching dynamics. The thermal response was asymmetric between rising and falling transitions.
- Voltage response: A 5 V drive produced an almost one-FSR MZI transmission shift, while the FPGA’s 4.1 V maximum guaranteed a π phase shift.
- System context: The experimental setup used FPGA-controlled intensity modulation and DAC-generated analog signals to prepare spatially multiplexed weak coherent pulses.
- Switching dynamics: 66 µs rise time and 27 µs fall time were measured for the heater-driven tunable MZI.Rise time is measured from 10% to 90% switched power, while fall time is measured from 90% to 10%.
Mutual information
QBER disturbance thresholds depend on Hilbert-space dimension, Eve’s attack strategy, and the number of mutually unbiased bases used. The supporting figure and table frame these limits through mutual-information intersections and dimension-specific values.
- For qudit encoding, the tolerable QBER threshold can exceed the BB84 value.The threshold is represented by the intersection of solid and dashed mutual-information curves.
- A complete set of N + 1 MUBs slightly increases the limit compared with two MUBs.The reported thresholds vary across Hilbert-space dimensions and Eve’s strategies.
- Under individual attacks with two MUBs, the intersection of Alice–Bob and Alice–Eve mutual-information curves marks the disturbance threshold beyond which no key can be extracted.
BOB BOB
Figure S. 5 compares theoretical and experimental two-dimensional representations of three mutually unbiased bases measured using a weak, pulsed laser setup.
- The figure presents theoretical and experimental two-dimensional views of the three MUBs.
- Measurements used a 1540 nm laser operating at 10 kHz with 10 ns-wide pulses and mean photon number µ around 0.2.
- Each pixel was collected over several 30 s measurement slots, totaling 34 million pulses.