Single-qubit loss-tolerant quantum position verification protocol secure against entangled attackers

TL;DR

This paper analyzes the loss-tolerance of quantum position verification protocols based on BB84 states, providing tight bounds and demonstrating security against entangled attackers even with realistic photon loss and slow transmission.

Contribution

It introduces a method using semidefinite programming to establish tight loss-error bounds for QPV protocols, enhancing their practical security and extending analysis to multiple bases and device-independent QKD.

Findings

Protocols remain secure with moderate photon loss

Tight bounds enable realistic experimental implementation

Security extends to multiple bases and slow photon transmission

Abstract

Protocols for quantum position verification (QPV) which combine classical and quantum information are insecure in the presence of loss. We study the exact loss-tolerance of the most popular protocol for QPV, which is based on BB84 states, and generalizations of this protocol. By bounding the winning probabilities of a variant of the monogamy-of-entanglement game using semidefinite programming (SDP), we find tight bounds for the relation between loss and error for these extended non-local games. These new bounds enable the usage of QPV protocols using more-realistic experimental parameters. We show how these results transfer to the variant protocol which combines $n$ bits of classical information with a single qubit, thereby exhibiting a protocol secure against a linear amount of entanglement (in the classical information $n$) even in the presence of a moderate amount of photon loss. Moreover, this protocol stays secure even if the photon encoding the qubit travels arbitrarily slow in an optical fiber. We also extend this analysis to the case of more than two bases, showing even stronger loss-tolerance for that case. Finally, since our semi-definite program bounds a monogamy-of-entanglement game, we describe how they can also be applied to improve the analysis of one-sided device-independent QKD protocols.