We consider the asymptotic key rates achieved in the simplest quantum key distribution protocols, namely, the BB84 and the six-state protocols when nonuniform noise is present in the system. We first observe that higher qubit error rates do not necessarily imply lower key rates. Second, we consider protocols with advantage distillation and show that it can be advantageous to use the basis with higher quantum bit error rate for the key generation. We then discuss the relation between advantage distillation and entanglement distillation protocols. We show that applying advantage distillation to a string of bits formed by the outcomes of measurements in the basis with a higher quantum bit error rate is closely connected to the two-to-one entanglement distillation protocol of Deutsch-Ekert-Jozsa-Macchiavello-Popescu-Sanpera [Phys. Rev. Lett. 77, 2818 (1996)PRLTAO0031-900710.1103/PhysRevLett.77.2818]. Finally, we discuss the implications of these results for implementations of quantum key distribution.

We consider the task of sharing a secret quantum state in a quantum network in a verifiable way. We propose a protocol that achieves this task, while reducing the number of required qubits, as compared to the existing protocols. To achieve this, we combine classical encryption of the quantum secret with an existing verifiable quantum secret sharing scheme based on Calderbank-Shor-Steane quantum error correcting codes. In this way we obtain a verifiable hybrid secret sharing scheme for sharing qubits, which combines the benefits of quantum and classical schemes. Our scheme does not reveal any information to any group of less than half of the n nodes participating in the protocol. Moreover, for sharing a one-qubit state each node needs a quantum memory to store n single-qubit shares, and requires a workspace of at most 3n qubits in total to verify the quantum secret. Importantly, in our scheme an individual share is encoded in a single qubit, as opposed to previous schemes requiring ω(logn) qubits per share. Furthermore, we define a ramp verifiable hybrid scheme. We give explicit examples of various verifiable hybrid schemes based on existing quantum error correcting codes.

In this Reply we correct a mistake that we made in the correctness proofs of our protocol. Specifically, the Bell inequality we used ensures security but does not allow us to produce a key. In this Reply we explain and correct this mistake by adjusting the Bell inequality we used in the proof. Incidentally, this correction leads to slightly better asymptotic key rates. Importantly, none of the conclusions of the article are affected.

In the implementation of device-independent (DI) quantum key distribution (QKD) we are interested in maximizing the key rate, i.e. the number of key bits that can be obtained per signal, for a fixed security parameter. In the finite size regime, we furthermore also care about the minimum number of signals required before key can be obtained at all. Here, we perform a fully finite size analysis of device independent protocols using the CHSH inequality both for collective and coherent attacks. For coherent attacks, we sharpen the results recently derived in Arnon-Friedman et al (2018 Nat. Commun. 9 459), to reduce the minimum number of signals before key can be obtained. In the regime of collective attacks, where the devices are restricted to have no memory, we employ two different techniques that exploit this restriction to further reduce the number of signals. We then discuss experimental platforms in which DIQKD may be implemented. We analyse Bell violations and expected QBER achieved in previous Bell tests with distant setups and situate these parameters in the security analysis. Moreover, focusing on one of the experimental platforms, namely nitrogen-vacancy based systems, we describe experimental improvements that can lead to a DI QKD implementation in the near future.

We present a security analysis of conference key agreement (CKA) in the most adversarial model of device independence (DI). Our protocol can be implemented by any experimental setup that is capable of performing Bell tests [specifically, the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality], and security can in principle be obtained for any violation of the MABK inequality that detects genuine multipartite entanglement among the N parties involved in the protocol. As our main tool, we derive a direct physical connection between the N-partite MABK inequality and the Clauser-Horne-Shimony-Holt (CHSH) inequality, showing that certain violations of the MABK inequality correspond to a violation of the CHSH inequality between one of the parties and the other N-1. We compare the asymptotic key rate for device-independent conference key agreement (DICKA) to the case where the parties use N-1 device-independent quantum key distribution protocols in order to generate a common key. We show that for some regime of noise the DICKA protocol leads to better rates.

We consider the task of anonymously transmitting a quantum message in a network. We present a protocol that accomplishes this task using the W state and we analyze its performance in a quantum network where some form of noise is present. We then compare the performance of our protocol with some of the existing protocols developed for the task of anonymous transmission. We show that, in many regimes, our protocol tolerates more noise and achieves higher fidelities of the transmitted quantum message than the other ones. Furthermore, we demonstrate that our protocol tolerates one nonresponsive node. We prove the security of our protocol in a semiactive adversary scenario, meaning that we consider an active adversary and a trusted source.

Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot distinguish if a state is genuinely multipartite entangled or just entangled across some bipartition.We thus generalise this bipartite concept to the multipartite setting by introducing non-positive maps that are positive on the subset of biseparable states but can map to a non-positive element if applied to a genuine multipartite entangled state. We explicitly construct examples of multipartite non-positive maps, obtained from positive maps via a lifting procedure, that in this fashion can reveal genuine multipartite entanglement in a robust way.