Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing

Abstract

For a quantum secret sharing scheme built from a general quantum stabilizer code, no measurement-free circuit has been known for reconstructing its quantum secrets, except particular classes, such as one proposed by Cleve, Gottesman and Lo. We propose a measurement-free reconstruction circuit of quantum secrets in quantum secret sharing based on stabilizer codes. Our reconstruction circuit has width \(k+|J|\) and consists of O(k|J|) one- or two-qudit unitary gates when |J| participants reconstruct k-qudit quantum secrets.