Conference key agreement allows multiple remote parties to establish a shared secret key with information-theoretical security. In device-independent conference key agreement, security can be guaranteed with minimal assumptions on the devices used, provided that a violation of a Bell inequality is observed. However, implementations are extremely challenging because high detection efficiency is required to observe loophole-free Bell violations. Here, we enhance the robustness of device-independent conference key agreement by introducing a new family of multipartite Bell inequalities called the asymmetric parity-Clauser-Horne-Shimony-Holt (CHSH) inequalities. We derive a tight analytical lower bound on the conditional von Neumann entropy of the outcomes of one of the parties in a protocol based on this inequality, including noisy preprocessing. Using this bound, we analyze robustness to detection inefficiencies as well as local and global depolarizing noise. We show that the combination of the asymmetric parity-CHSH inequality and noisy preprocessing can significantly improve the robustness to imperfections.
Conference key agreement allows multiple remote parties to establish a shared secret key with information-theoretical security. In device-independent conference key agreement, security can be guaranteed with minimal assumptions on the devices used, provided that a violation of a Bell inequality is observed. However, implementations are extremely challenging because high detection efficiency is required to observe loophole-free Bell violations. Here, we enhance the robustness of device-independent conference key agreement by introducing a new family of multipartite Bell inequalities called the asymmetric parity-Clauser-Horne-Shimony-Holt (CHSH) inequalities. We derive a tight analytical lower bound on the conditional von Neumann entropy of the outcomes of one of the parties in a protocol based on this inequality, including noisy preprocessing. Using this bound, we analyze robustness to detection inefficiencies as well as local and global depolarizing noise. We show that the combination of the asymmetric parity-CHSH inequality and noisy preprocessing can significantly improve the robustness to imperfections.
Device-independent conference key agreement (DI-CKA) lets a group of parties establish a shared secret key from untrusted quantum devices, with security certified by non-locality. Existing DI-CKA protocols are each built around a single Bell inequality, typically a multiparty variant of the CHSH game. DI-QKD protocols, in contrast, have been built from a much richer landscape of non-local games, and it has remained unclear how to carry this landscape over to the conference setting. We introduce $\textit{Parity-$G$ games}$, which extend any two-player game G to N players, for every N, provided G has an optimal strategy in which one player measures Pauli observables. The extension preserves the quantum and classical values of G, and the security of the resulting N-party protocol follows from an analysis of the two-player game alone. Our framework recovers the Parity-CHSH game of Ribeiro, Murta and Wehner (Phys. Rev. A, 2018) as a special case. Applied to the Mermin--Peres Magic Square Game, it yields a new N-player pseudo-telepathy game, the Parity Magic Square Game, which ideal devices win in every round. We use it to construct the first DI-CKA protocol based on a pseudo-telepathy game. We prove the protocol secure against coherent attacks. It produces up to two key bits per round, and at low noise its key rate exceeds that of the DI-CKA protocol based on the Parity-CHSH game.
Device-independent conference key agreement (DI-CKA) enables N>2 distant parties to establish a common secret key without detailed characterization of the source or measurement devices. Many existing protocols rely on full-body Bell correlators, whose measurement can be demanding for a large number of parties. Here, we show that two-body correlators alone suffice for DI-CKA using balanced Dicke states for every even N≥4. We construct two-body Bell inequalities and derive a tight analytical lower bound on the conditional von Neumann entropy by comparing their Bell operators with those of asymmetric Clauser-Horne-Shimony-Holt inequalities. In the ideal setting, certified key rates can approach 1−h[(N−2)/(4(N−1))], where h is the binary entropy function. This rate remains bounded away from zero as N→∞, tending to 1−h(1/4)≈0.189 bits per key-generation round. We show that the honest implementation of our protocol is invariant under collective phase noise. Moreover, a complementary full-body Bell construction certifies positive conference-key rates from correlations arbitrarily close to the local set.
Bell nonlocality provides a device-independent (DI) way to certify quantum randomness, based on which true random numbers can be extracted from the observed correlations without detail characterizations on devices for quantum state preparation and measurement. However, the efficiency of current strategies for DI randomness certification is still heavily constrained when it comes to non-maximal Bell values, especially for multiple parties. Here, we present a family of multipartite Bell inequalities that allows to certify optimal quantum randomness and self-test GHZ (Greenberger-Horne-Zeilinger) states, which are inspired from the stabilizer group of the GHZ state. Due to the simple representation of stabilizer group for GHZ states, this family of Bell inequalities is of simple structure and can be easily expanded to more parties. Compared with the Mermin-type inequalities, this family of Bell inequality is more efficient in certifying quantum randomness when non-maximal Bell values achieved. Meanwhile, the general analytical upper bound for the Holevo quantity is presented, and achieves better performance compared with the MABK (Mermin-Ardehali-Belinskii-Klyshko) inequality, Parity-CHSH (Clauser-Horne-Shimony-Holt) inequality and Holz inequality at N=3, which is of particular interests for experimental researches on DI quantum cryptography in quantum networks.
Conference key agreement aims to establish shared, private randomness among many separated parties in a network. Device-independent conference key agreement (DICKA) is a variant in which the source and the measurement devices used by each party need not be trusted. So far, DICKA protocols largely fall into two categories: those that rely on violating a joint Bell inequality using genuinely multipartite entangled states and those that concatenate many bipartite protocols. The question of whether a hybrid protocol exists, where a multipartite Bell inequality can be violated using only bipartite entanglement, was asked by Grasselli et al. [Quantum 7, 980 (2023)2521-327X10.22331/q-2023-04-13-980]. We answer this question affirmatively, by constructing an asymptotically secure DICKA protocol achieving the same rate as the concatenation of bipartite device-independent quantum key distribution, yet relying on a single joint Bell violation. Our results prompt further discussion on the benefits of multipartite entanglement for DICKA over its bipartite alternative, and we give an overview of different arguments for near-term devices.
Given a pair of isolated devices that accept random binary inputs and return binary outputs, a user can deduce from the observed data alone if the underlying mechanism can be explained classically. Bell's theorem further states that a classical explanation can be ruled out if the devices perform certain measurements on an entangled quantum state, underpinning the security of cryptographic protocols that are device-independent (DI). For certain protocols, such as those performed in a tight space, it might be difficult to perfectly enforce the non-signaling assumption required in Bell's theorem. This prompts the question: is quantum nonlocality robust to such imperfections? We show that if a binary channel sends a noisy copy of one party's input to the other before any measurements take place, the answer is yes. We completely characterize the vertices and facets of the local polytope in this scenario, and identify Bell inequalities that certify non-signaling quantum correlations. This is possible even when a near perfect copy of the input is sent. We go on to show that the identified inequalities are more robust to depolarizing noise than the Clauser-Horne-Shimony-Holt inequality when certifying DI randomness in this scenario. In addition, we characterize the local polytope when both parties receive a noisy copy of each other's input and make similar conclusions, leaving many new potential Bell inequalities to be explored.
Multipartite device-independent quantum key distribution (DI-QKD), also known as device-independent conference key agreement, enables more than two remote parties to share a common key with information-theoretic security even without trusting the devices. So far, several multipartite DI-QKD protocols have been proposed where Greenberger-Horne-Zeilinger (GHZ) states are used as multipartite entanglement. A natural question is then whether one can construct multipartite DI-QKD with the other type of multipartite entanglement. W state is of particular interest since it is intrinsically different from GHZ state and in some cases, easier to optically implement. In this paper, we show that multipartite DI-QKD is possible with W states. To this end, we construct Bell inequalities largely violated by W states, which can be used for the multipartite DI-QKD. Furthermore, we consider several different implementation scenarios. First, we analyze the minimum required detection efficiencies to extract finite amount of keys. Then we propose a long-distance multipartite DI-QKD protocol with single-photon interference and make detailed analyses with several physical implementation scenarios. We show that the protocol enables secret key distribution over longer distances than the existing multipartite DI-QKD protocols based on GHZ states. This study provides new insight about the relationship between multipartite entanglement and device-independent quantum information processing as well as opens an alternative path toward long-distance multipartite DI-QKD.