Measurement-free reconstruction circuit of quantum secrets in quantum secret sharing
Shogo Chiwaki, Ryutaroh Matsumoto · Quantum Information Processing · 2025
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 $$k+|J|$$ k + | J | and consists of O ( k | J |) one- or two-qudit unitary gates when | J | participants reconstruct k -qudit quantum secrets.