All phase-encoded BB84 implementations have signal states with unbalanced amplitudes in practice.Thus the original security analyses a priori do not apply to them.Previous security proofs use signal tagging of multiphoton pulses to recover the behavior of regular BB84.This is overly conservative as for unbalanced signals the photon number splitting attack does not leak full information to Eve.In this work we exploit the flag-state squashing model to preserve some parts of the multiphoton-generated private information in our analysis.Using a numerical proof technique we obtain significantly higher key rates compared with previously published results in the low-loss regime.It turns out that the usual scenario of untrusted dark counts runs into conceptual difficulties in some parameter regimes.Thus we discuss the trusted dark-count scenario in this paper as well.We also report a gain in key rates when part of the total loss is known to be induced by a trusted device.We highlight that all these key rate improvements can be achieved without modification of the experimental setup.
All phase-encoded BB84 implementations have signal states with unbalanced amplitudes in practice.Thus the original security analyses a priori do not apply to them.Previous security proofs use signal tagging of multiphoton pulses to recover the behavior of regular BB84.This is overly conservative as for unbalanced signals the photon number splitting attack does not leak full information to Eve.In this work we exploit the flag-state squashing model to preserve some parts of the multiphoton-generated private information in our analysis.Using a numerical proof technique we obtain significantly higher key rates compared with previously published results in the low-loss regime.It turns out that the usual scenario of untrusted dark counts runs into conceptual difficulties in some parameter regimes.Thus we discuss the trusted dark-count scenario in this paper as well.We also report a gain in key rates when part of the total loss is known to be induced by a trusted device.We highlight that all these key rate improvements can be achieved without modification of the experimental setup.
The squashing model proof technique is a powerful tool in proving security of quantum key distribution (QKD) protocols since it reduces the dimension of the associated computational problem from infinite to finite. In the first half of this thesis, we formally prove that the unconditional asymptotic security of an arbitrary QKD protocol after applying a squashing model implies the same security for the original protocol. We also prove rigorously that the squashing map of the flag-state squashing model is indeed a quantum channel for an infinite-dimensional input Hilbert space. \n \nIn the second half of the thesis, we apply the flag-state squashing model to the phase-encoded BB84 protocol. Since all phase-encoded BB84 implementations have signal states with unbalanced amplitudes in practice, the original security analyses a priori do not apply to them. Previous security proofs use signal tagging of multi-photon pulses to recover the behaviour of regular BB84. This is overly conservative, as for unbalanced signals, the photon-number splitting attack does not leak full information to Eve. In this work, we exploit the flag-state squashing model to preserve some parts of the multi-photon generated private information in our analysis. Using a numerical proof technique, we obtain significantly higher key rates compared with previously published results in the low-loss regime. It turns out that the usual scenario of untrusted dark counts runs into conceptual difficulties in some parameter regime. Thus, we discuss the trusted dark count scenario in this paper as well. We also report a gain in key rates when part of the total loss is known to be induced by a trusted device. We highlight that all these key rate improvements can be achieved without modification of the experimental setup.
In optical implementations of the phase-encoded BB84 protocol, the bit information is usually encoded in the phase of two consecutive photon pulses generated in a Mach-Zehnder interferometer. In the actual experimental realization, the loss in the arms of the Mach-Zehnder interferometer is not balanced, for example because only one arm contains a lossy phase modulator. Therefore, the amplitudes of the pulses are not balanced, and the structure of the signals and measurements no longer corresponds to the (balanced) ideal BB84 protocol. Hence, the BB84 security analysis no longer applies in this scenario. We provide a security proof of the unbalanced phase-encoded BB84. The resulting key rate turns out to be lower than the key rate of the ideal BB84 protocol. Therefore, in order to guarantee security, the loss due to the phase modulator cannot be ignored.
Security proof of practical quantum key distribution (QKD) has attracted a lot of attentions in recent years. Most of real-life QKD implementations are based on phase-coding BB84 protocol, which usually use Unbalanced Mach-Zehnder Interferometer (UMZI) as the information encoder and decoder. However, the long arm and short arm of UMZI will introduce different loss in practical experimental realizations, the state emitted by Alice's side is nolonger perfect BB84 states correspondingly. In this paper, we will give the security analysis in this situation. Counterintuitively, active compensation for this different loss will only lower the secret key bit rate.
In this work we present an improved analysis for decoy-state methods, enhancing both achievable key rates and recovering analytical results for the single intensity scenario. Our primary focus is improving the shortcomings observed in current decoy-state methods, in particular recovering results when employing no decoy intensities. Our methods enable the continuous interpolation across varying numbers of intensity settings. Additionally, we extend decoy-state techniques to encompass scenarios where intensities vary depending on the signal state, thereby relaxing the constraints on experimental implementations. Our findings demonstrate that a minimum of one decoy intensity is sufficient for high asymptotic secret key rates, thereby further softening experimental requirements. We also address inherent imperfections within detection setups like imperfect beamsplitters. We derive provable secure lower bounds on the subspace population estimation, which is required for certain squashing methods such as the flag-state squasher. These analytical bounds allow us to encompass arbitrary passive linear optical setups and, together with intensities varying with each signal state, let us include a broad class of experimental setups. Published by the American Physical Society 2024
In phase-randomized weak coherent pulse (WCP) implementations of Quantum Key Distribution (QKD) BB84 protocol, the decoy method is often used to compensate BB84's vulnerability against photon number splitting (PNS) attacks. However, this typically introduces extra complexities and requirements on experimental devices. In this paper, we are therefore interested in phase-randomized WCP implementations without the decoy method. We examine the performance of three QKD protocols with different classical announcement structures, namely BB84, SARG04, and No Public Announcement of Basis (NPAB) BB84, using numerical security proof techniques. We compare secure key rates of the three protocols in asymptotic and finite-size regimes for lossy and noisy channels. The three protocols show different relative advantages depending on the channel behaviour. Canonical BB84 shows robustness against errors and depolarization, SARG04 demonstrates resilience against high loss channels, and NPAB BB84 shows potential advantages against physical misalignment between QKD devices.
The Bennett-Brassard 1984 (BB84) protocol is the most widely implemented quantum key distribution (QKD) scheme. However, despite enormous theoretical and experimental efforts in the past decades, the security of this protocol with imperfect sources has not yet been rigorously established. In this paper, we address this shortcoming and prove the security of the BB84 protocol in the presence of multiple source imperfections, including state preparation flaws and side channels, such as Trojan-horse attacks, mode dependencies and classical correlations between the emitted pulses. To do so, we consider a modified BB84 protocol that exploits the basis mismatched events, which are often discarded in standard security analyses of this scheme; and employ the reference technique, a powerful mathematical tool to accommodate source imperfections in the security analysis of QKD. Moreover, we compare the achievable secret-key rate of the modified BB84 protocol with that of the three-state loss-tolerant protocol, and show that the addition of a fourth state, while redundant in ideal conditions, significantly improves the estimation of the leaked information in the presence of source imperfections, resulting in a better performance. This paper demonstrates the relevance of the BB84 protocol in guaranteeing implementation security, taking us a step further towards closing the existing gap between theory and practice of QKD.