Majority-Agreed Key Distribution using Absolutely Maximally Entangled Stabilizer States

TL;DR

This paper explores the use of absolutely maximally entangled stabilizer and graph states for secure quantum key distribution, establishing conditions for cooperation among parties and extending results to qudit systems.

Contribution

It proves that a majority of parties is necessary and sufficient for QKD with AME stabilizer states and extends this to qudit cases, also generalizing to non-AME graph states.

Findings

Majority cooperation is necessary and sufficient for QKD with AME stabilizer states.

Stabilizer structure enables QKD across any bipartition in graph states.

Protocols for conference and multiple keys are feasible with current graph state technology.

Abstract

In [Phys. Rev. A 77, 060304(R),(2008)], Facchi et al. introduced absolutely maximally entangled (AME) states and also suggested ``majority-agreed key distribution"(MAKD) as a possible application for such states. In MAKD, the qubits of an AME state are distributed one each to many spatially separated parties. AME property makes it necessary that quantum key distribution(QKD) between any two parties can only be performed with the cooperation of a majority of parties. Our contributions to MAKD are, $(1)$ We recognize that stabilizer structure of the shared state is a useful addition to MAKD and prove that the cooperation of any majority of parties(including the two communicants) is necessary and sufficient for QKD between any two parties sharing AME stabilizer states. Considering the rarity of qubit AME states, we extended this result to the qudit case. $(2)$ We generalize to shared graph states that are not necessarily AME. We show that the stabilizer structure of graph states allows for QKD between any inseparable bipartition of qubits. Inseparability in graph states is visually apparent in the connectivity of its underlying mathematical graph. We exploit this connectivity to demonstrate conference keys and multiple independent keys per shared state. Recent experimental and theoretical progress in graph state preparation and self-testing make these protocols feasible in the near future.