Quantum secret sharing using squeezing and almost any passive interferometer.
Francesco Arzani, Giulia Ferrini, Frédéric Grosshans, Damian Markham · arXiv (Cornell University) · 2018
We consider the sharing of quantum secret states using continuous variable systems. Specifically we introduce an encoding procedure where we mix the secret mode with several ancillary squeezed modes through a passive interferometer. We derive simple conditions on the interferometer for this encoding scheme to give a secret sharing protocol and we prove that they are satisfied by almost any interferometer with respect to the Haar measure. 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 in linear optics with an additional squeezer per access party. We analyze the quality of the reconstructed state as a function of the input squeezing.