Abstract
Discrete-modulated (DM) continuous-variable quantum key distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity. While tight security analyses in the asymptotic limit exist, proofs in the finite-size regime are still subject to active research. We present a composable finite-size security proof against independently and identically distributed collective attacks for a general DM CV-QKD protocol. We introduce a new energy testing theorem to bound the effective dimension of Bob’s system and rigorously prove security within Renner’s -security framework and address the issue of acceptance sets in protocols and their security proof. We want to highlight that our method also allows for nonunique acceptance statistics, which is necessary in practise. Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate. To demonstrate our method, we apply it to a quadrature phase-shift keying protocol for both untrusted, ideal and trusted, nonideal detectors. The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 72 km transmission distance.
- Received 23 January 2023
- Revised 10 August 2023
- Accepted 8 September 2023
DOI:https://doi.org/10.1103/PRXQuantum.4.040306
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum key distribution (QKD) enables two remote parties to establish a shared secret key even in the presence of an eavesdropper that has access to a quantum computer. The obtained key then can be used to encrypt secret messages. Continuous-variable QKD (CV-QKD) protocols with discrete modulation (DM) are promising candidates for commercial implementations because the required components are already used in current telecommunications infrastructure.
We prove the security of a general DM CV-QKD protocol against so-called collective independently and identically distributed (i.i.d.) attacks. Key rates for this class of attacks are believed to be optimal up to some de Finetti reduction terms. One of the main challenges when proving security arises from the fact that DM CV-QKD protocols must be analyzed in an infinite-dimensional Hilbert space. We state and prove a new energy-testing theorem that bounds the effective weight of the analyzed quantum states outside a finite-dimensional cutoff space. We rigorously take this cutoff into account and then prove composable security against i.i.d. collective attacks. Composable security means that the obtained secure key can safely be used in larger cryptographic settings. Finally, we use a numerical method to calculate tight lower bounds on the secure key rate both for ideal and nonideal detectors.
Our results show that nonzero key rates can be achieved up to more than 70 km transmission distances under experimentally viable conditions.
