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.
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.
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 improve 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.
Device-independent (DI) protocols, such as DI conference key agreement (DICKA) and DI randomness expansion (DIRE), certify private randomness by observing nonlocal correlations when two or more parties test a Bell inequality. While most DI protocols are restricted to bipartite Bell tests, harnessing multipartite nonlocal correlations may lead to better performance. Here, we consider tripartite DICKA and DIRE protocols based on testing multipartite Bell inequalities, specifically: the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality, and the Holz and the Parity-CHSH inequalities introduced in the context of DICKA protocols. We evaluate the asymptotic performance of the DICKA (DIRE) protocols in terms of their conference key rate (net randomness generation rate), by deriving lower bounds on the conditional von Neumann entropy of one party's outcome and two parties' outcomes. For the Holz inequality, we prove a tight analytical lower bound on the one-outcome entropy and conjecture a tight lower bound on the two-outcome entropy. We additionally re-derive the analytical one-outcome entropy bound for the MABK inequality with a much simpler method and obtain a numerical lower bound on the two-outcome entropy for the Parity-CHSH inequality. Our simulations show that DICKA and DIRE protocols employing tripartite Bell inequalities can significantly outperform their bipartite counterparts. Moreover, we establish that genuine multipartite entanglement is not a precondition for multipartite DIRE while its necessity for DICKA remains an open question.
We propose two semi-device-independent approaches that are able to quantify unknown multipartite quantum entanglement experimentally, where the only information that has to be known beforehand is quantum dimension, and the concept that plays a key role is nondegenerate Bell inequalities. Specifically, using the nondegeneracy of multipartite Bell inequalities, we obtain useful information on the purity of target quantum state. Combined with an estimate of the maximal overlap between the target state and pure product states, and a continuous property of the geometric measure of entanglement, we shall prove the information on purity allows us to give a lower bound for this entanglement measure. In addition, we show that a different combination of the above results also converts to a lower bound for the relative entropy of entanglement. As a demonstration, we apply our approach on 5-partite qubit systems with the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality, and show that useful lower bounds for the geometric measure of entanglement can be obtained if the Bell expression value is larger than 3.60, and those for the relative entropy of entanglement can be given if the Bell expression value is larger than 3.80, where the Tsirelson bound is 4.
Abstract Position-based cryptography allows a party to prove its geographic location by responding to challenges from verifiers. Classical position verification is impossible against entangled adversaries. Quantum position verification overcomes this but requires trusted measurement devices at the verifi cation locations. We introduce Device-Independent Position Verification using the Mermin-Ardehali Belinskii-Klyshko four-party Bell inequality. Our protocol uses four verifiers at the corners of a square and a single prover. The MABK inequality has classical bound BMABK ≤ 4, while quantum mechan ics achieves BMABK = 4√2 ≈ 5.657 using the four-qubit Greenberger-Horne-Zeilinger state. We prove security against general quantum adversaries using relativistic no-go theorems and the entropy accumulation theorem. Using realistic experimental parameters (four-photon GHZ state fidelity F = 0.85, detector efficiency η = 0.65), we predict a Bell violation BMABK = 4.25, exceeding the classical bound by 0.25. The protocol tolerates up to 15% noise and achieves verification distances up to 30 km with current technology. This work provides the first practical path to location verification on untrusted hardware.
Nonlocal tests on multi-partite quantum correlations form the basis of protocols that certify randomness in a device-independent (DI) way. Such correlations admit a rich structure, making the task of choosing an appropriate test difficult. For example, extremal Bell inequalities are tight witnesses of nonlocality, but achieving their maximum violation places constraints on the underlying quantum system, which can reduce the rate of randomness generation. As a result there is often a trade-off between maximum randomness and the amount of violation of a given Bell inequality. Here, we explore this trade-off for more than two parties. More precisely, we study the maximum amount of randomness that can be certified by correlations with a particular violation of the Mermin-Ardehali-Belinskii-Klyshko (MABK) inequality. For any even number of parties, we find that maximum randomness cannot occur beyond a threshold quantum violation, which increases with the number of parties, and we give a conjectured form of the maximum randomness in terms of the MABK value. We also show that maximum randomness can be obtained for any MABK violation for odd numbers of parties. To obtain our results, we derive new families of Bell inequalities certifying maximum randomness from a technique for randomness certification, which we call "expanding Bell inequalities''. Our technique allows a bipartite Bell expression to be used as a seed, and transformed into a multi-partite Bell inequality tailored for randomness certification, showing how intuition learned in the bipartite case can find use in more complex scenarios.
Device-independent (DI) quantum protocols use Bell inequality violations to ensure security or certify quantum properties without assumptions on the devices’ internal workings. In this work, we study the role of rank-one qubit positive operator-valued measures (POVMs) in DI scenarios. This class includes all qubit extremal POVMs, i.e., those measurements that cannot be realized as mixtures of others, as well as part of non-extremal POVMs, recently shown to be useful in sequential quantum protocols. We demonstrate that any rank-one POVM can generate correlations in bipartite scenarios that saturate a Tsirelson inequality when two parties share an arbitrary entangled two-qubit state and perform specific self-tested measurements. For extremal POVMs, such saturation enables explicit computation of guessing probability and worst-case conditional von Neumann entropy. From the Tsirelson inequality, we establish a randomness certification method that facilitates numerical simulations and we validate it through a proof-of-concept experiment with three-outcome POVMs and tilted entangled states.