Random coding for sharing bosonic quantum secrets

TL;DR

This paper introduces a probabilistic continuous-variable quantum secret sharing protocol using bosonic modes and passive interferometers, demonstrating its near-universal applicability and efficient decoding with Gaussian unitaries.

Contribution

It presents a new secret sharing scheme for bosonic quantum states with simple conditions on the interferometer, showing that almost any interferometer can implement the protocol.

Findings

Almost any random interferometer can implement the secret sharing protocol.

Decoding can be efficiently performed with Gaussian unitaries and a limited number of squeezers.

Fidelity of reconstructed state depends on input squeezing levels.

Abstract

We consider a protocol for sharing quantum states using continuous variable systems. Specifically we introduce an encoding procedure where bosonic modes in arbitrary secret states are mixed with several ancillary squeezed modes through a passive interferometer. We derive simple conditions on the interferometer for this encoding to define a secret sharing protocol and we prove that they are satisfied by almost any interferometer. This implies that, if the interferometer is chosen uniformly at random, the probability that it may not be used to implement a quantum secret sharing protocol is zero. Furthermore, we show that the decoding operation can be obtained and implemented efficiently with a Gaussian unitary using a number of single-mode squeezers that is at most twice the number of modes of the secret, regardless of the number of players. We benchmark the quality of the reconstructed state by computing the fidelity with the secret state as a function of the input squeezing.