Quantum key distribution (QKD) enables secure key generation between distant users, yet its standard device-dependent implementations rely on fully characterized and accurately modeled devices. Device-independent (DI) QKD removes this assumption by certifying privacy solely from Bell inequality violations, but its stringent experimental demands severely hinder scalability. In realistic quantum networks, asymmetric levels of device trust can naturally arise from diverse implementation conditions across nodes. Motivated by this, we investigate partially DI scenarios in which only a subset of parties operate trusted devices. Built upon the Brown-Fawzi-Fawzi method [], we employ a semidefinite programming hierarchy tailored to estimate the conditional von Neumann entropies in such settings. This approach provides efficiently computable lower bounds on asymptotic rates of cryptographic protocols with broad applicability. By reexamining representative bipartite and tripartite communication tasks under the partially DI framework, we demonstrate that enforcing trust on the devices of a subset of parties never degrades key or randomness expansion rates and, in certain cases, can substantially increase them owing to the network asymmetry. Our results highlight the impact of device trustworthiness on cryptographic security and facilitate scalable implementations in practical asymmetric network architectures.
Quantum key distribution (QKD) enables secure key generation between distant users, yet its standard device-dependent implementations rely on fully characterized and accurately modeled devices. Device-independent (DI) QKD removes this assumption by certifying privacy solely from Bell inequality violations, but its stringent experimental demands severely hinder scalability. In realistic quantum networks, asymmetric levels of device trust can naturally arise from diverse implementation conditions across nodes. Motivated by this, we investigate partially DI scenarios in which only a subset of parties operate trusted devices. Built upon the Brown-Fawzi-Fawzi method [], we employ a semidefinite programming hierarchy tailored to estimate the conditional von Neumann entropies in such settings. This approach provides efficiently computable lower bounds on asymptotic rates of cryptographic protocols with broad applicability. By reexamining representative bipartite and tripartite communication tasks under the partially DI framework, we demonstrate that enforcing trust on the devices of a subset of parties never degrades key or randomness expansion rates and, in certain cases, can substantially increase them owing to the network asymmetry. Our results highlight the impact of device trustworthiness on cryptographic security and facilitate scalable implementations in practical asymmetric network architectures.
Device-independent security is the gold standard for quantum cryptography: not only is security based entirely on the laws of quantum mechanics, but it holds irrespective of any a priori assumptions on the quantum devices used in a protocol, making it particularly applicable in a quantum-wary environment. While the existence of device-independent protocols for tasks such as randomness expansion and quantum key distribution has recently been established, the underlying proofs of security remain very challenging, yield rather poor key rates, and demand very high quality quantum devices, thus making them all but impossible to implement in practice. We introduce a technique for the analysis of device-independent cryptographic protocols. We provide a flexible protocol and give a security proof that provides quantitative bounds that are asymptotically tight, even in the presence of general quantum adversaries. At a high level our approach amounts to establishing a reduction to the scenario in which the untrusted device operates in an identical and independent way in each round of the protocol. This is achieved by leveraging the sequential nature of the protocol and makes use of a newly developed tool, the “entropy accumulation theorem” of Dupuis, Fawzi, and Renner [ Entropy Accumulation, preprint, 2016]. As concrete applications we give simple and modular security proofs for device-independent quantum key distribution and randomness expansion protocols based on the CHSH inequality. For both tasks, we establish essentially optimal asymptotic key rates and noise tolerance. In view of recent experimental progress, which has culminated in loophole-free Bell tests, it is likely that these protocols can be practically implemented in the near future.
Abstract Device-independent quantum key distribution (DIQKD) provides the strongest form of secure key exchange, using only the input–output statistics of the devices to achieve information-theoretic security. Although the basic security principles of DIQKD are now well understood, it remains a technical challenge to derive reliable and robust security bounds for advanced DIQKD protocols that go beyond the previous results based on violations of the CHSH inequality. In this work, we present a framework based on semidefinite programming that gives reliable lower bounds on the asymptotic secret key rate of any QKD protocol using untrusted devices. In particular, our method can in principle be utilized to find achievable secret key rates for any DIQKD protocol, based on the full input–output probability distribution or any choice of Bell inequality. Our method also extends to other DI cryptographic tasks.
Device-independent (DI) quantum cryptography provides secure cryptography with minimal trust in, or characterisation of, the used quantum devices. An essential component of DI protocols is the use of randomness extractors for privacy amplification, but these typically require an initial seed of randomness that introduces a potential vulnerability. To solve this problem, the security of seedless extractors was proven in Quantum 9, 1654 (2025). The core idea was to use the Bell violation of the raw data, rather than its min-entropy, as the extractor promise. However, the large fluctuations in the Bell inequality used required many rounds to precisely estimate the Bell violation, consuming substantial randomness and making the protocol very inefficient. In this work, we present a new proof technique based on a truncation method that allows the user to estimate the protocol parameters with an asymptotically vanishing fraction of rounds and, as a consequence, achieves the optimal rate of one key bit per singlet. Notably, we prove this result using seedless extractors that can be implemented efficiently.
As our foundational understanding of quantum information theory broadens, it remains to be seen whether novel foundational developments will lead to corresponding applications. Promising branches are quantum networks and quantum cryptography, which are more intertwined by the day. In particular, a fascinating phenomena is that in networks with independent sources, Bell nonlocality can take place without the need for measurement settings for the parties, i.e. in each round, each source is asked to produce the same state and each party measures the same measurement. This is in stark contrast to standard Bell nonlocality, where seed randomness is necessary to certify nonlocality and through it, randomness of the outcomes. Building on nonlocality without seed randomness in networks, we propose a device-independent quantum key distribution protocol (which can be extended to quantum conference key agreement if it involves more than 2 parties) which allows for the generation of shared secret keys without the need for input randomness. We rely on recent results on nonlocality in networks and its robustness, showing how in a ring network with N bipartite sources, one must only make standard assumptions in order to run the protocol, while no trust is required from the devices themselves. We thus give a device-independent proof of security under this network assumption in the IID setting. In summary, we propose a first-of-a-kind protocol for Device-Independent Quantum Key Distribution which is native to the network setting, and which does not demand input randomness from the parties in order to produce output randomness.
Multiparty quantum cryptography based on distributed entanglement will find its natural application in the upcoming quantum networks.The security of many multipartite device-independent (DI) protocols, such as DI conference-key agreement, relies on bounding the von Neumann entropy of the parties' outcomes conditioned on the eavesdropper's information, given the violation of a multipartite Bell inequality.We consider three parties testing the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality and certify the privacy of their outcomes by bounding the conditional entropy of a single party's outcome and the joint conditional entropy of two parties' outcomes.From the former bound, we show that genuine multipartite entanglement is necessary to certify the privacy of a party's outcome, while the latter significantly improves previous results.We obtain the entropy bounds thanks to two general results of independent interest.The first one drastically simplifies the quantum setup of an N -partite Bell scenario.The second one provides an upper bound on the violation of the MABK inequality by an arbitrary N -qubit state, as a function of the state's parameters.
The rates of several device-independent (DI) protocols, including quantum key-distribution (QKD) and randomness expansion (RE), can be computed via an optimization of the conditional von Neumann entropy over a particular class of quantum states. In this work we introduce a numerical method to compute lower bounds on such rates. We derive a sequence of optimization problems that converge to the conditional von Neumann entropy of systems defined on general separable Hilbert spaces. Using the Navascués-Pironio-Acín hierarchy we can then relax these problems to semidefinite programs, giving a computationally tractable method to compute lower bounds on the rates of DI protocols. Applying our method to compute the rates of DI-RE and DI-QKD protocols we find substantial improvements over all previous numerical techniques, demonstrating significantly higher rates for both DI-RE and DI-QKD. In particular, for DI-QKD we show a minimal detection efficiency threshold which is within the realm of current capabilities. Moreover, we demonstrate that our method is capable of converging rapidly by recovering all known tight analytical bounds up to several decimal places. Finally, we note that our method is compatible with the entropy accumulation theorem and can thus be used to compute rates of finite round protocols and subsequently prove their security.