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 $$k+|J|$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>+</mml:mo> <mml:mo>|</mml:mo> <mml:mi>J</mml:mi> <mml:mo>|</mml:mo> </mml:mrow> </mml:math> and consists of O ( k | J |) one- or two-qudit unitary gates when | J | participants reconstruct k -qudit quantum secrets.