Random coding for sharing bosonic quantum secrets
arXiv:1808.06870 · doi:10.1103/PhysRevA.100.022303
The paper proposes a continuous‑variable quantum secret sharing protocol where arbitrary bosonic secret states are mixed with squeezed ancillas via a randomly chosen passive interferometer, and shows that decoding can be done efficiently with Gaussian unitaries while analyzing reconstruction fidelity.
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.
Updated figure 1, added figure 2, closer to published version