Verifiable hybrid secret sharing in the presence of noise

Abstract

Verifiable quantum secret sharing (VQSS) is the task of sharing a secret quantum state among the n nodes of a quantum network, in a way that it is possible to verify that the secret has been correctly distributed. A number of protocols that perform this task have been proposed. In particular, the verifiable hybrid secret sharing (VHSS) scheme proposed by Lipinska et al. (2019) realizes this task while reducing the number of required qubits, as compared to other existing protocols. The VHSS scheme was proven secure for noiseless quantum networks. In this work, we analyze its performance in the presence of noise. To do that, we first define different noise models in which qubits can be randomly erased or depolarized. Then, we propose several modifications for the protocol that allow us to run it more efficiently on quantum networks described by such noise models. Additionally, we explore a new approach to the VQSS task using approximate quantum error correction. We propose the verifiable trap secret sharing (VTSS) protocol, which combines the scheme by Lipinska et al. (2019) and the trap code by Broadbent et al. (2013). Our protocol achieves the same functionalities as the VHSS protocol and only requires that a strict majority of the nodes follows the protocol honestly, raising the maximum number of nodes that can cheat from ⌊(n-1)/4⌋ to ⌊(n-1)/2⌋. We can do this at the cost of increasing the probability of error in the protocol.