Lossy-and-Constrained Extended Non-Local Games with Applications to Quantum Cryptography

TL;DR

This paper extends the framework of non-local games to include constraints and loss, demonstrating that SDP hierarchies still converge and applying this to improve security bounds in quantum cryptography protocols.

Contribution

It introduces a generalized model of non-local games with constraints and loss, proving the convergence of SDP hierarchies in this setting and applying it to quantum cryptography.

Findings

SDP hierarchies converge even with constraints and loss

Tighter security bounds for quantum cryptography protocols

Applications to relativistic bit commitment, QKD, and position verification

Abstract

Extended non-local games are a generalization of monogamy-of-entanglement games, played by two quantum parties and a quantum referee that performs a measurement on their local quantum system. Along the lines of the NPA hierarchy, the optimal winning probability of those games can be upper bounded by a hierarchy of semidefinite programs (SDPs) converging to the optimal value. Here, we show that if one extends such games by considering constraints and loss, motivated by experimental errors and loss through quantum communication, the convergence of the SDPs to the optimal value still holds. We give applications of this result, and we compute SDPs that show tighter security of protocols for relativistic bit commitment, quantum key distribution, and quantum position verification.