Álvaro Gómez Iñesta

Verifiable hybrid secret sharing (VHSS) is a task in which a secret quantum state must be split among n parties, such that they can only recover the secret if a sufficient number of parties cooperate, while small coalitions of parties learn nothing. Each party may hold classical and/or quantum shares, and the parties must be able to collectively verify that their shares can later be used to reconstruct a valid quantum state. Here, we explore the resource efficiency of VHSS protocols, critical for implementation in near-term quantum networks. Lipinska et al. [PRA 102(2):022405, 2020] recently introduced a protocol that required a reduced number of qubits per party. Building on this, we further optimize their protocol and reduce the quantum communication overhead. While the scaling with the number of parties remains unchanged, our improvements yield orders-of-magnitude reductions in the time required to successfully distribute and verify a quantum secret.