Device-Independent Bit Commitment based on the CHSH Inequality

Abstract

Bit commitment and coin flipping occupy a unique place in the device-independent landscape, as the only device-independent protocols thus far suggested for these tasks are reliant on tripartite GHZ correlations. Indeed, we know of no other bipartite tasks, which admit a device-independent formulation, but which are not known to be implementable using only bipartite nonlocality. Another interesting feature of these protocols is that the pseudo-telepathic nature of GHZ correlations -- in contrast to the generally statistical character of nonlocal correlations, such as those arising in the violation of the CHSH inequality -- is essential to their formulation and analysis. In this work, we present a device-independent bit commitment protocol based on CHSH testing, which achieves the same security as the optimal GHZ-based protocol. The protocol is analyzed in the most general settings, where the devices are used repeatedly and may have long-term quantum memory. We also recast the protocol in a post-quantum setting where both honest and dishonest parties are restricted only by the impossibility of signaling, and find that overall the supra-quantum structure allows for greater security.

15 pages, 3 figures

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• Local Randomness: Examples and Application
• Quantum cryptography beyond key distribution: theory and experiment
• High fidelity GHZ generation within nearby nodes
• Device-Independent Oblivious Transfer from the Bounded-Quantum-Storage-Model and Computational Assumptions
• Composably secure device-independent encryption with certified deletion
• Device-independent quantum authorization based on the Clauser-Horne-Shimony-Holt game
• Bright-light detector control emulates the local bounds of Bell-type inequalities
• Simulating nonlocal no-signaling boxes
• Breaking barriers in two-party quantum cryptography via stochastic semidefinite programming
• Device-independent quantum state discrimination