Application of an Improved Version of McDiarmid Inequality in Finite-Key-Length Decoy-State Quantum Key Distribution

Abstract

In practical decoy-state quantum key distribution, the raw key length is finite. Thus, deviation of the estimated single photon yield and single photon error rate from their respective true values due to finite sample size can seriously lower the provably secure key rate $R$. Current method to obtain a lower bound of $R$ follows an indirect path by first bounding the yields and error rates both conditioned on the type of decoy used. These bounds are then used to deduce the single photon yield and error rate, which in turn are used to calculate a lower bound of the key rate $R$. Here we report an improved version of McDiarmid inequality in statistics and show how use it to directly compute a lower bound of $R$ via the so-called centering sequence. A novelty in this work is the optimization of the bound through the freedom of choosing possible centering sequences. The provably secure key rate of realistic 100~km long quantum channel obtained by our method is at least twice that of the state-of-the-art procedure when the raw key length ${\ell }_{\text{raw}}$ is $\approx 10^5$ to $10^6$. In fact, our method can improve the key rate significantly over a wide range of raw key length from about $10^5$ to $10^{11}$. More importantly, it is achieved by pure theoretical analysis without altering the experimental setup or the post-processing method. In a boarder context, this work introduces powerful concentration inequality techniques in statistics to tackle physics problem beyond straightforward statistical data analysis especially when the data are correlated so that tools like the central limit theorem are not applicable.

arXiv comment14 pages, 1 table, superseding the result reported in arXiv:1806.05063, to appear in New J Phys

References in corpus (18)

• Decoy State Quantum Key Distribution
• Measurement-device-independent quantum key distribution
• Beating the PNS attack in practical quantum cryptography
• Overcoming the rate-distance barrier of quantum key distribution without using quantum repeaters
• Practical Decoy State for Quantum Key Distribution
• Practical challenges in quantum key distribution
• An information-theoretic security proof for QKD protocols
• Concise Security Bounds for Practical Decoy-State Quantum Key Distribution
• Lower and upper bounds on the secret key rate for QKD protocols using one--way classical communication
• Making the decoy-state measurement-device-independent quantum key distribution practically useful
• Practical issues in quantum-key-distribution post-processing
• General theory of decoy-state quantum cryptography with source errors
• Security of decoy-state quantum key distribution with inexactly controlled source
• Security analysis of the decoy method with the Bennett-Brassard 1984 protocol for finite key lengths
• General theory for decoy-state quantum key distribution with arbitrary number of intensities
• Sine gating detector with simple filtering for low-noise infra-red single photon detection at room temperature
• Finite-key security analysis for multilevel quantum key distribution
• Decoy State Quantum Key Distribution With More Than Three Types Of Photon Intensity Pulses

Cited by in corpus (4)

• Zigzag approach to higher key rate of sending-or-not-sending twin field quantum key distribution with finite key effects
• Composable security for practical quantum key distribution with two way classical communication
• Security Of Finite-Key-Length Measurement-Device-Independent Quantum Key Distribution Using Arbitrary Number Of Decoys
• Security proofs for practical QKD: variations, techniques, gaps, and limitations