Entropy bounds for multiparty device-independent cryptography

Abstract

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.

Added discussion on the tightness of the entropy bounds, with comparison between analytical bounds and numerical estimations. Added explicit proof of the necessity of genuine multipartite entanglement for the secrecy of a party's outcome

References in corpus (50)

• The Security of Practical Quantum Key Distribution
• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• Secure Quantum Key Distribution
• Optimal eavesdropping in quantum cryptography with six states
• Satellite-relayed intercontinental quantum network
• Quantum Random Number Generators
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Practical challenges in quantum key distribution
• From Bell's Theorem to Secure Quantum Key Distribution
• Device-independent quantum key distribution secure against collective attacks
• Bounding the set of quantum correlations
• All multipartite Bell correlation inequalities for two dichotomic observables per site
• Fully device independent quantum key distribution
• Quantum random number generation
• Bell's theorem for general N-qubit states
• Secure device-independent quantum key distribution with causally independent measurement devices
• Private Randomness Expansion With Untrusted Devices
• Bell-type inequalities to detect true n-body non-separability
• A Fully Quantum Asymptotic Equipartition Property
• Entanglement Detection in the Stabilizer Formalism
• Quantum Communication between N partners and Bell's inequalities
• Multi-partite entanglement speeds up quantum key distribution in networks
• Security of practical private randomness generation
• More Randomness from the Same Data
• Light-matter entanglement over 50 km of optical fibre
• Asymptotic violation of Bell inequalities and distillability
• Using complete measurement statistics for optimal device-independent randomness evaluation
• Entanglement between a diamond spin qubit and a photonic time-bin qubit at telecom wavelength
• Modular architectures for quantum networks
• Quantum network routing and local complementation
• Security and Composability of Randomness Expansion from Bell Inequalities
• Fully device independent Conference Key Agreement
• Continuous-variable measurement-device-independent multipartite quantum communication
• Tight multipartite Bell's inequalities involving many measurement settings
• Entropy accumulation with improved second-order term
• Conference key agreement with single-photon interference
• Finite-key effects in multi-partite quantum key distribution protocols
• Quantum Key Distribution between N partners: optimal eavesdropping and Bell's inequalities
• Bounds on Quantum Correlations in Bell Inequality Experiments
• Device-independent quantum key distribution secure against adversaries with no long-term quantum memory
• A two-qubit Bell inequality for which POVM measurements are relevant
• Large-scale quantum networks based on graphs
• A framework for quantum-secure device-independent randomness expansion
• Quantum Router with Network Coding
• Randomness versus nonlocality in the Mermin-Bell experiment with three parties
• Bell inequalities for multipartite qubit quantum systems and their maximal violation
• Comment on "Fully device-independent conference key agreement" [Phys. Rev. A 97, 022307 (2018)]
• Tight upper bound for the maximal expectation value of the Mermin operators
• Device-independent secret-key-rate analysis for quantum repeaters

Cited by in corpus (15)

• Security of device-independent quantum key distribution protocols: a review
• Device-independent quantum key distribution with asymmetric CHSH inequalities
• Device-independent lower bounds on the conditional von Neumann entropy
• Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints
• An elegant proof of self-testing for multipartite Bell inequalities
• Boosting device-independent cryptography with tripartite nonlocality
• Universal construction of genuinely entangled subspaces of any size
• The future of secure communications: device independence in quantum key distribution
• Tight upper bound for the maximal expectation value of the $N$-partite generalized Svetlichny operator
• Mermin and Svetlichny inequalities for non-projective measurement observables
• Device-Independent Certification of Multipartite Distillable Entanglement
• Expanding bipartite Bell inequalities for maximum multi-partite randomness
• Genuine multipartite entanglement is not necessary for standard device-independent conference key agreement
• Tight analytic bound on the trade-off between device-independent randomness and nonlocality
• Nonlocality in Continuous-Variable Quantum Networks