Source-linked AI summary
Measurement-device-independent quantum key distribution
Hoi-Kwong Lo, Marcos Curty, Bing Qi
TL;DR
The paper establishes unconditional security for measurement-device-independent quantum key distribution. It develops a security analysis using virtual qubits and decoy-state estimation, showing tolerance to high channel loss and low Bell-measurement success probability.
Problem
The paper addresses how to establish unconditional security for measurement-device-independent quantum key distribution.
Method
The protocol uses a security proof based on time-reversed EPR-based QKD and decoy states, with a virtual-qubit formulation and practical phase-randomized weak coherent pulses.
Results
The protocol is unconditionally secure and remains secure with very high channel loss and very low Bell-measurement success probability.
Takeaways & Limitations
Successful Bell-measurement events can be post-selected, while decoy states allow Alice and Bob to estimate the parameters needed for the asymptotic secret-key rate.
Abstract
from arXiv · showhide
How to remove detector side channel attacks has been a notoriously hard problem in quantum cryptography. Here, we propose a simple solution to this problem---*measurement* device independent quantum key distribution. It not only removes all detector side channels, but also doubles the secure distance with conventional lasers. Our proposal can be implemented with standard optical components with low detection efficiency and highly lossy channels. In contrast to the previous solution of full device independent QKD, the realization of our idea does not require detectors of near unity detection efficiency in combination with a qubit amplifier (based on teleportation) or a quantum non-demolition measurement of the number of photons in a pulse. Furthermore, its key generation rate is many orders of magnitude higher than that based on full device independent QKD. The results show that long-distance quantum cryptography over say 200km will remain secure even with seriously flawed detectors.
Appendix A: Security analysis
The protocol is proven unconditionally secure by combining a virtual-qubit, entanglement-based perspective with decoy-state estimation. Security remains valid despite imperfect preparation, high channel loss, and low Bell-measurement success probability.
- Appendix A: Security analysis: MDI-QKD is unconditionally secure for practical phase-randomized weak coherent pulses generated by lasers.The proof is inspired by time-reversed EPR-based QKD and the decoy-state method.
- Appendix A: Security analysis: Alice and Bob prepare decoy-state BB84 weak coherent pulses and send them to Charlie, who performs a Bell measurement and announces successful outcomes.They retain only transmission events associated with a specified Bell-state result.
- Appendix A: Security analysis: Decoy states let Alice and Bob obtain the gain and QBER for events in which both users send single-photon states.These quantities support the subsequent virtual-qubit security analysis.
- Appendix A: Security analysis: The virtual-qubit formulation makes the protocol equivalent to an entanglement-based protocol, with QBER computed on Alice’s and Bob’s stored qubits in the XX and ZZ bases.Alice and Bob can delay measuring their virtual qubits until Charlie announces a successful Bell-measurement result.
- Appendix A: Security analysis: Basis-independent single-photon signals are sufficient for the security proof, while basis-dependent preparation flaws can be handled with a quantum-coin analysis of the combined emitted states.The treatment covers simultaneous imperfections in Alice’s and Bob’s preparation processes.
- Appendix A: Security analysis: Very high channel loss and very low Bell-measurement success probability do not compromise security because Alice and Bob post-select successful Bell-measurement events.The security argument uses a virtual-memory picture in which losses do not affect security.
Appendix B: Estimation procedure
The estimation procedure extends decoy-state QKD to MDI-QKD, allowing Alice and Bob to infer the photon-number-dependent yields and error parameters needed for the key-rate formula. In the asymptotic regime, the relevant single-photon quantities are obtainable, while practical implementations require only finitely many decoy states.
- Appendix B: Estimation procedure: The decoy-state method applied to MDI-QKD allows Alice and Bob to estimate the relevant parameters for the asymptotic secret-key-rate formula.In particular, the procedure targets the single-photon gain and related error quantities.
- Appendix B: Estimation procedure: Alice and Bob use different decoy settings, indexed by i and j, to form linear equations for MDI-QKD gains and error-related parameters.The two indices correspond to the decoy settings used by Alice and Bob, respectively.
- Appendix B: Estimation procedure: Varying Alice’s and Bob’s decoy settings lets them estimate photon-number-dependent yields in the rectilinear and diagonal bases.The procedure proceeds from one-party-indexed quantities to the joint yields Y_n,m in each basis.
- Appendix B: Estimation procedure: The same estimation strategy recovers error parameters, including e1,1, after the relevant yields have been determined.The error equations are treated analogously to the gain equations.
- Appendix B: Estimation procedure: In the asymptotic case, Alice and Bob can estimate Y_n,m for all n and m and obtain the relevant quantities Y_1,1.The single-photon parameters are the quantities needed for evaluating the key-rate expression.
- Appendix B: Estimation procedure: Practical applications require only a finite number of decoy states, similarly to standard finite-decoy-state QKD protocols.The asymptotic estimation result therefore has a finite-decoy practical counterpart.
Appendix C: Experimental setup of proof of concept experiment
The proof-of-concept experiment tests interference between independently generated laser pulses by matching their timing, polarization, pulse shape, and spectral properties in a fiber-based setup.
- Experimental motivation: Interference between independent lasers is central to implementing MDI-QKD and also underlies related quantum-information applications.The experiment addresses this requirement using two independent laser sources.
- Laser sources and timing: Two unconnected continuous-wave lasers generate narrow pulses whose relative delay is adjustable with picosecond resolution.S1 operates at 1550 nm, while S2 is wavelength tunable; intensity modulators and a delay generator shape and synchronize the pulses.
- Optical preparation: Variable attenuators set the average photon number per pulse, and a phase modulator scans the phase of one pulse train.The two pulse trains interfere at a symmetric 2×2 fiber coupler.
- Mode matching and detection: Single-mode telecom-fiber components and polarization controllers make the spatial modes identical and align the pulse trains in polarization at the beam splitter.Coincident measurements are performed with single-photon detectors and a time-interval analyzer.
- Pulse matching: Matched electrical driving produces approximately Gaussian pulses with 200ps FWHM and about 5GHz bandwidth, exceeding the below-30MHz central-frequency mismatch.These conditions support spectral indistinguishability during interference.