Boosting device-independent cryptography with tripartite nonlocality

Abstract

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.

arXiv comment12 pages main text, 36 pages in total. 5 figures, 3 tables

References in corpus (44)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Bell nonlocality
• Advances in Quantum Cryptography
• Device-independent security of quantum cryptography against collective attacks
• Secure quantum key distribution with realistic devices
• Significant-loophole-free test of Bell's theorem with entangled photons
• Random Numbers Certified by Bell's Theorem
• Hacking commercial quantum cryptography systems by tailored bright illumination
• The Uncertainty Principle in the Presence of Quantum Memory
• From Bell's Theorem to Secure Quantum Key Distribution
• Device-independent quantum key distribution secure against collective attacks
• Full-field implementation of a perfect eavesdropper on a quantum cryptography system
• Fully device independent quantum key distribution
• Secure device-independent quantum key distribution with causally independent measurement devices
• Private Randomness Expansion With Untrusted Devices
• Randomness vs Non Locality and Entanglement
• Experimental device-independent quantum key distribution between distant users
• Quantum Communication between N partners and Bell's inequalities
• Maximally Non-Local and Monogamous Quantum Correlations
• Multi-partite entanglement speeds up quantum key distribution in networks
• Memory Attacks on Device-Independent Quantum Cryptography
• Security of practical private randomness generation
• Quantum Conference Key Agreement: A Review
• Device-independent randomness expansion against quantum side information
• Photonic verification of device-independent quantum key distribution against collective attacks
• Asymptotic violation of Bell inequalities and distillability
• Device-independent Randomness Expansion with Entangled Photons
• Security and Composability of Randomness Expansion from Bell Inequalities
• Fully device independent Conference Key Agreement
• Entropy accumulation with improved second-order term
• Device-independent quantum key distribution with asymmetric CHSH inequalities
• Quantum Key Distribution between N partners: optimal eavesdropping and Bell's inequalities
• Towards a realization of device-independent quantum key distribution
• Computing conditional entropies for quantum correlations
• Computing secure key rates for quantum key distribution with untrusted devices
• Improved DIQKD protocols with finite-size analysis
• Device-independent quantum key distribution from generalized CHSH inequalities
• A Genuine Multipartite Bell Inequality for Device-independent Conference Key Agreement
• Randomness versus nonlocality in the Mermin-Bell experiment with three parties
• Simple and practical DIQKD security analysis via BB84-type uncertainty relations and Pauli correlation constraints
• Entropy bounds for multiparty device-independent cryptography
• Genuine multipartite entanglement is not a precondition for secure conference key agreement
• Comment on "Fully device-independent conference key agreement" [Phys. Rev. A 97, 022307 (2018)]
• Quantifying necessary quantum resources for nonlocality

Cited by in corpus (8)

• Device-independent lower bounds on the conditional von Neumann entropy
• An elegant proof of self-testing for multipartite Bell inequalities
• 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
• Genuine multipartite entanglement is not necessary for standard device-independent conference key agreement
• Expanding bipartite Bell inequalities for maximum multi-partite randomness
• Long-Distance Device-Independent Conference Key Agreement
• A Classification Program for Nonlocality Paradoxes of Three Qubits