Random coding for sharing bosonic quantum secrets

Arzani, FrancescoUniversite de Lorraine,Sorbonne Université,Sorbonne University (author)

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.

Ferrini, Giulia,1984Chalmers tekniska högskola,Chalmers University of Technology(Swepub:cth)ferrini (author)
Grosshans, FredericSorbonne Université,Sorbonne University,Université Paris-Saclay,University Paris-Saclay,Centre national de la recherche scientifique (CNRS) (author)
Markham, DamianCentre national de la recherche scientifique (CNRS),Sorbonne Université,Sorbonne University (author)
Universite de LorraineSorbonne Université (creator_code:org_t)

By the author/editor: Arzani, Francesc ...; Ferrini, Giulia, ...; Grosshans, Frede ...; Markham, Damian

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