Quantum state reconstruction and stabilization

Stefan Weigert

Ryutaroh Matsumoto

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.

Shogo Chiwaki, Ryutaroh Matsumoto

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.

Péter Udvarhelyi

Bond reconstruction in vacancy-related structures affects their formation energies, symmetries, and electronic and optical properties. Using density functional theory, we investigate bond reconstruction mechanisms of monovacancies and vacancy aggregates in monolayer silicon carbide. Multiple bond descriptors reveal that isolated monovacancies undergo both in-plane reconstruction and out-of-plane distortion, which together shape their stability and electronic structure. For compact vacancy aggregates, we show that bond reconstruction acts as a key stabilization mechanism. However, in carbon monovacancy, reconstruction suppresses optical activity. In contrast, a highly stable aggregate composed of three carbon vacancies surrounding a silicon vacancy emerges as a promising infrared color-center candidate, combining a triplet ground state with a favorable Debye-Waller factor of the emission. These results highlight the role of bond reconstruction in defining the quantum properties of vacancy defects in two-dimensional silicon carbide.

Peter Mittelstaedt

Peter Mittelstaedt