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.Quantum key distribution (QKD) represents one of the primary applications of quantum information science. Since the proposal of the first QKD protocols [1, 2], major advancements have been achieved both on the theoretical and experimental side [3,4]. A QKD protocol provides a systematic procedure through which two honest parties (Alice and Bob) generate a secret shared key, when connected by an insecure quantum channel and an authenticated insecure classical channel.Recently the generalization of such protocols to multipartite schemes has been investigated [5,6]. It has been shown that there are quantum-network configurations [5] or noise regimes [6] in which the execution of a multipartite scheme is advantageous with respect to establishing a multipartite secret key via many independent bipartite protocols. However, the analysis of multipartite QKD protocols has only been carried out in the unrealistic scenario of infinitely many signals exchanged through the quantum channel.We compare the performances of two multipartite QKD protocols, which constitute the N-partite versions of the asymmetric BB84 [1] and the asymmetric six-state protocol [7], and will be denoted as N-BB84 and N-sixstate protocol. While the N-six-state protocol was first proposed in [5], the N-BB84 constitutes a novel multipartite QKD protocol.Our analysis is conducted in the practical case of a finite amount of resources (signals) at the N parties' disposal. The action of a potential eavesdropper (Eve) on the insecure quantum channel is not restricted at all, as she is allowed to perform any kind of attack (coherent attacks) on the exchanged signals. What is assumed is that the parties have access to true randomness and that the devices performing measurements on the quantum systems work according to their ideal functionality.The article is structured as follows. In section 1 we extend notions and results of bipartite QKD security analysis to the multipartite scenario. In section 2 we review the N-six-state protocol and introduce the N-BB84 protocol. Then we obtain a computable expression for their secret key lengths in the case of finite resources. In section 3 we compare the achievable key rates of the two NQKD protocols in the presence of finite and infinite resources. We conclude the article in section 4. Multipartite QKD: general framewo...

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Twin-field (TF) quantum key distribution (QKD) represents a novel QKD approach whose principal merit is to beat the point-to-point private capacity of a lossy quantum channel, thanks to performing single-photon interference in an untrusted node. Indeed, recent security proofs of various TF-QKD type protocols have confirmed that the secret key rate of these schemes scales essentially as the square root of the transmittance of the channel. Here, we focus on the TF-QKD protocol introduced by Curty et al, whose secret key rate is nearly an order of magnitude higher than previous solutions. Its security relies on the estimation of the detection probabilities associated to various photon-number states through the decoy-state method. We derive analytical bounds on these quantities assuming that each party uses either two, three or four decoy intensity settings, and we investigate the protocol's performance in this scenario. Our simulations show that two decoy intensity settings are enough to beat the point-to-point private capacity of the channel, and that the use of four decoys is already basically optimal, in the sense that it almost reproduces the ideal scenario of infinite decoys. We also observe that the protocol seems to be quite robust against intensity fluctuations of the optical pulses prepared by the parties.The last few decades have witnessed major advancements in the field of quantum communication [1, 2], with quantum key distribution (QKD) [3-13] being its most developed application. Recent experiments over about 400 km of optical fibers [14,15] and over about 1000 km of satellite-to-ground links [16,17] demonstrated that QKD over long distances is possible. Despite such remarkable experimental achievements, the private capacity of point-to-point QKD is intrinsically limited by fundamental bounds [18,19]. These bounds state that in the high-loss regime the key rate scales basically linearly with the transmittance of the channel connecting the endusers Alice and Bob, i.e. it decreases exponentially with the total channel length. This imposes strict practical constraints on the possibility of achieving point-to-point QKD over arbitrary long distances.A way to overcome this limitation is to employ one or more intermediate nodes in the quantum channel connecting the parties. For instance, the use of quantum repeaters [20] yields a polynomial scaling of the communication efficiency with the distance [21]. Moreover, a quantum repeater scheme can be arbitrarily iterated along the quantum channel, thus increasing in principle the total communication distance between Alice and Bob as much as desired. Unfortunately, however, quantum repeaters are very challenging to build in practice with current technology: they either require quantum memories [20][21][22] or quantum error correction [23,24]. Of course, technology is improving, and quantum repeaters may become viable in the future.Other solutions, which attain a square-root improvement in the scaling of the key rate with respect to the transmittance of the channel, ...

We address parameter estimation for complex/structured systems and suggest an effective estimation scheme based on continuous-variables quantum probes. In particular, we investigate the use of a single bosonic mode as a probe for Ohmic reservoirs, and obtain the ultimate quantum limits to the precise estimation of their cutoff frequency. We assume the probe prepared in a Gaussian state and determine the optimal working regime, i.e. the conditions for the maximization of the quantum Fisher information in terms of the initial preparation, the reservoir temperature and the interaction time. Upon investigating the Fisher information of feasible measurements we arrive at a remarkable simple result: homodyne detection of canonical variables allows one to achieve the ultimate quantum limit to precision under suitable, mild, conditions. Finally, upon exploiting a perturbative approach, we find the invariant sweet spots of the (tunable) characteristic frequency of the probe, able to drive the probe towards the optimal working regime.

The intense research activity on Twin-Field (TF) quantum key distribution (QKD) is motivated by the fact that two users can establish a secret key by relying on single-photon interference in an untrusted node. Thanks to this feature, variants of the protocol have been proven to beat the point-to-point private capacity of a lossy quantum channel. Here we generalize the main idea of the TF-QKD protocol introduced by Curty et al to the multipartite scenario, by devising a conference key agreement (CKA) where the users simultaneously distill a secret conference key through single-photon interference. The new CKA is better suited to high-loss scenarios than previous multipartite QKD schemes and it employs for the first time a W-class state as its entanglement resource. We prove the protocol's security in the finite-key regime and under general attacks. We also compare its performance with the iterative use of bipartite QKD protocols and show that our truly multipartite scheme can be advantageous, depending on the loss and on the state preparation.The most mature and developed application of quantum communication [1, 2] is certainly quantum key distribution (QKD) [3][4][5][6][7][8]. The majority of the QKD protocols proposed so far involve just two end-users, Alice and Bob, who want to establish a secret shared key. Nowadays there is a vibrant research towards protocols which are proven to be secure in the most adversarial situation possible (i.e. reducing the assumption on the devices) [9-14], but at the same time are also implementable with today's technology [15][16][17][18]. In this context, a protocol which recently received great attention is the Twin-Field (TF) QKD protocol originally proposed by Lucamarini et al [19], further developed to prove its security [20][21][22][23][24][25][26][27] and experimentally implemented [28][29][30][31]. Indeed, the TF-QKD protocol relies only on single-photon interference occurring in an untrusted node, making it a measurement-device-independent (MDI) QKD protocol capable of overcoming the repeaterless bounds [32,33].In a scenario where several users are required to share a common secret key, one can for instance perform bipartite QKD protocols between pairs of users and then use the secret keys established in this way to encode the final common secret key. Alternatively, one can perform a truly multipartite QKD scheme-also known as conference key agreement (CKA)-whose purpose is to deliver the same secret key to all the parties involved in the protocol [35][36][37][38][39]. In order to accomplish such a task, a resource which seems necessary is the multipartite Greenberger-Horne-Zeilinger (GHZ) state [34][35][36][37][38] or a multipartite private state-a 'twisted' version of the GHZ state [40,41].In this work we introduce a CKA which exploits for the first time the multipartite entanglement of a W-class state [42], in order to deliver the same secret key to all users. Despite having a number of users involved, the scheme relies on single-photon interference in an untrusted no...

Conference key agreement (CKA), or multipartite key distribution, is a cryptographic task where more than two parties wish to establish a common secret key. A composition of bipartite quantum key distribution protocols can accomplish this task. However, the existence of multipartite quantum correlations allows for new and potentially more efficient protocols, to be applied in future quantum networks. Here, the existing quantum CKA protocols based on multipartite entanglement are reviewed, both in the device‐dependent and the device‐independent scenario.

Twin-Field (TF) quantum key distribution (QKD) is a major candidate to be the new benchmark for far-distance QKD implementations, since its secret key rate can overcome the repeaterless bound by means of a simple interferometric measurement. Many variants of the original protocol have been recently proven to be secure. Here, we focus on the TF-QKD type protocol proposed by Curty et al (2019 NPJ Quantum Inf. 5 64), which can provide a high secret key rate and whose practical feasibility has been demonstrated in various recent experiments. The security of this protocol relies on the estimation of certain detection probabilities (yields) through the decoy-state technique. Analytical bounds on the relevant yields have been recently derived assuming that both parties use the same set of decoy intensities, thus providing sub-optimal key rates in asymmetric-loss scenarios. Here we derive new analytical bounds when the parties use either two, three or four independent decoy intensity settings each. With the new bounds we optimize the protocol's performance in asymmetric-loss scenarios and show that the protocol is robust against uncorrelated intensity fluctuations affecting the parties' lasers.

Quantum networks will provide multinode entanglement enabling secure communication on a global scale. Traditional quantum communication protocols consume pair-wise entanglement, which is suboptimal for distributed tasks involving more than two users. Here, we demonstrate quantum conference key agreement, a cryptography protocol leveraging multipartite entanglement to efficiently create identical keys between N users with up to N-1 rate advantage in constrained networks. We distribute four-photon Greenberger-Horne-Zeilinger (GHZ) states, generated by high-brightness telecom photon-pair sources, over optical fiber with combined lengths of up to 50 km and then perform multiuser error correction and privacy amplification. Under finite-key analysis, we establish 1.5 × 106 bits of secure key, which are used to encrypt and securely share an image between four users in a conference transmission. Our work highlights a previously unexplored protocol tailored for multinode networks leveraging low-noise, long-distance transmission of GHZ states that will pave the way for future multiparty quantum information processing applications.