A Monogamy-of-Entanglement Game With Applications to Device-Independent Quantum Cryptography

TL;DR

This paper analyzes a quantum game based on entanglement monogamy, demonstrating that optimal success probabilities are achievable without entanglement and applying this to quantum cryptography security proofs.

Contribution

It proves that strategies maximizing individual game success are optimal in parallel, leading to new security guarantees for BB84 and position-verification protocols.

Findings

Optimal parallel success probability matches individual game success

BB84 remains secure with untrusted measurement devices

Extended uncertainty relation for quantum side information

Abstract

We consider a game in which two separate laboratories collaborate to prepare a quantum system and are then asked to guess the outcome of a measurement performed by a third party in a random basis on that system. Intuitively, by the uncertainty principle and the monogamy of entanglement, the probability that both players simultaneously succeed in guessing the outcome correctly is bounded. We are interested in the question of how the success probability scales when many such games are performed in parallel. We show that any strategy that maximizes the probability to win every game individually is also optimal for the parallel repetition of the game. Our result implies that the optimal guessing probability can be achieved without the use of entanglement. We explore several applications of this result. First, we show that it implies security for standard BB84 quantum key distribution when the receiving party uses fully untrusted measurement devices, i.e. we show that BB84 is one-sided device independent. Second, we show how our result can be used to prove security of a one-round position-verification scheme. Finally, we generalize a well-known uncertainty relation for the guessing probability to quantum side information.