Quantum Inf Process (2017) 16:202
Unitary reconstruction of secret for stabilizer-based
quantum secret sharing
Received: 5 April 2017 / Accepted: 4 July 2017
© The Author(s) 2017. This article is an open access publication
Abstract We propose a unitary procedure to reconstruct quantum secret for a quantum
secret sharing scheme constructed from stabilizer quantum error-correcting codes.
Erasure correcting procedures for stabilizer codes need to add missing shares for
reconstruction of quantum secret, while unitary reconstruction procedures for certain
class of quantum secret sharing are known to work without adding missing shares.
The proposed procedure also works without adding missing shares.
Keywords Quantum secret sharing · Quantum error correction · Stabilizer code
Mathematics Subject Classiﬁcation 81P94 · 94A62
Secret sharing (SS)  is a cryptographic scheme to encode a secret to multiple
shares being distributed to participants, so that only qualiﬁed sets of participants can
reconstruct the original secret from their shares. Traditionally both secret and shares
were classical information (bits). Several authors [4,6,8,17] extended the traditional
SS to quantum one so that a quantum secret can be encoded to quantum shares.
There was a difference between early pioneering works [4,6,8,17] of quantum SS.
The ﬁrst quantum SS  was based on the controlled teleportation [9,20], whose recon-
struction of quantum secret involved classical communication among participants. On
the other hand, the others works [4,6,17] related reconstruction to quantum error cor-
Department of Information and Communication Engineering, Nagoya University,
Nagoya 464-8603, Japan