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Physical Review A

Finite-key-size security of the Phoenix-Barnett-Chefles 2000 quantum-key-distribution protocol

Mhlambululi Mafu, Kevin Garapo, Francesco Petruccione

Published Sep 8, 2014• 11 citations
Publisher

Abstract

The postselection technique was introduced by Christandl, K\"onig, and Renner [Phys. Rev. Lett. 102, 020504 (2009)] in order to simplify the security of quantum-key-distribution schemes. Here, we present how it can be applied to study the security of the Phoenix-Barnett-Chefles 2000 trine-state protocol, a symmetric version of the Bennett 1992 protocol.

DOI
10.1103/physreva.90.032308

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The postselection technique was introduced by Christandl, K"onig, and Renner [Phys. Rev. Lett. 102, 020504 (2009)] in order to simplify the security of quantum-key-distribution schemes. Here, we present how it can be applied to study the security of the Phoenix-Barnett-Chefles 2000 trine-state protocol, a symmetric version of the Bennett 1992 protocol.
The post-selection technique was proposed by Christandl, König, and Renner [Phys. Rev. Lett. 102, 020504 (2009)] to simplify the security of quantum-key-distribution schemes. This work applies this technique to derive the security bounds for the six-state Scarani-Acin-Rigbordy-Gisin 2004 quantum key distribution protocol. This protocol can extract secure keys from a source emitting multi-photons due to its robustness from photon number splitting attacks, making it a good candidate for practical implementations. We also compare the security bounds for this protocol under collective attacks to the security bounds obtained after applying the post-selection technique when using finite resources. Our results demonstrate that the bounds for optimal attack are close to the bound for collective attack for many signals. Notably, the six-state SARG04 protocol proves to be more robust to the PNS attacks when compared to the original four-state SARG04 protocol. This demonstrates the power of the post-selection technique in deriving the security bounds for the six-state protocol when finite resources are used.
We analyze the security of two multipartite quantum key distribution (QKD) protocols, specifically we introduce an N -partite version of the BB84 protocol and we discuss the N -partite six-state protocol proposed by Epping et al (2017 New J. Phys. 19 093012). The security analysis proceeds from the generalization of known results in bipartite QKD to the multipartite scenario, and takes into account finite resources. In this context we derive a computable expression for the achievable key rate of both protocols by employing the best-known strategies: the uncertainty relation and the postselection technique. We compare the performances of the two protocols both for finite resources and infinitely many signals.
We present a finite-size security proof for generic quantum key distribution protocols against independent and identically distributed collective attacks and extend it to coherent attacks using the postselection technique. This work introduces two significant improvements over previous results. First, we achieve tighter finite-size key rates by employing refined concentration inequalities in the acceptance testing phase. Second, we improve second-order correction terms in the key rate expression, by reducing them to scale with the number of sifted rounds rather than the total number of protocol rounds. We apply these advancements to compute finite-size key rates for a qubit and decoy-state BB84 protocol, accommodating arbitrary protocol parameters. Finally, we extend our finite-size security proof to coherent attacks and variable-length protocols and present our results for the decoy-state 4-6 protocol incorporating imperfections such as unequal intensity settings.
The postselection technique is an important proof technique for proving the security of quantum key distribution protocols against coherent attacks via the uplift of any security proof against independent identically distributed collective attacks. In this work, we go through multiple steps to rigorously apply the postselection technique to optical quantum key distribution protocols. First, we place the postselection technique on a rigorous mathematical foundation by fixing a technical flaw in the original postselection paper. Second, we extend the applicability of the postselection technique to prepare-and-measure protocols by using a de Finetti reduction with a fixed marginal. Third, we show how the postselection technique can be used for decoy-state protocols by tagging the source. Finally, we extend the applicability of the postselection technique to realistic optical setups by developing a new variant of the flag-state squasher. We also improve existing de Finetti reductions, which reduce the effect of using the postselection technique on the key rate. These improvements can be more generally applied to other quantum information processing tasks. As an example to demonstrate the applicability of our work, we apply our results to the time-bin-encoded three-state protocol. We observe that the postselection technique performs better than all other known proof techniques against coherent attacks. Published by the American Physical Society 2024
We prove the security of Gaussian continuous-variable quantum key distribution with coherent states against arbitrary attacks in the finite-size regime. In contrast to previously known proofs of principle (based on the de Finetti theorem), our result is applicable in the practically relevant finite-size regime. This is achieved using a novel proof approach, which exploits phase-space symmetries of the protocols as well as the postselection technique introduced by Christandl, Koenig, and Renner [Phys. Rev. Lett. 102, 020504 (2009)].
Quantum key distribution (QKD) protocols are cryptographic techniques with security based only on the laws of quantum mechanics. Two prominent QKD schemes are the Bennett-Brassard 1984 and Bennett 1992 protocols that use four and two quantum states, respectively. In 2000, Phoenix et al. proposed a new family of three-state protocols that offers advantages over the previous schemes. Until now, an error rate threshold for security of the symmetric trine spherical code QKD protocol has been shown only for the trivial intercept-resend eavesdropping strategy. In this Letter, we prove the unconditional security of the trine spherical code QKD protocol, demonstrating its security up to a bit error rate of 9.81%. We also discuss how this proof applies to a version of the trine spherical code QKD protocol where the error rate is evaluated from the number of inconclusive events.