The structure of quantum mechanics forbids a bipartite scenario for masking quantum information, however, it allows multipartite maskers. The Latin squares are found to be closely related to a series of tripartite maskers. This adds another item, significantly different from the original no-cloning theorem, to the no-go theorems. On the other hand, anyonic excitations in two dimensions exhibit exotic collective behaviors of quantum physics, and open the avenue of fault-tolerant topological quantum computing. Here, we give the Latin-square construction of Abelian and Ising anyons in the Kitaev model and study the maskable space configuration in anyonic space. The circling and braiding of Kitaev anyons are masking operations on extended hyperdisks in anyonic space. We also realize quantum information masking in a teleportation way in the Kitaev Ising anyon model.The structure of quantum mechanics forbids a bipartite scenario for masking quantum information, however, it allows multipartite maskers. The Latin squares are found to be closely related to a series of tripartite maskers. This adds another item, significantly different from the original no-cloning theorem, to the no-go theorems. On the other hand, anyonic excitations in two dimensions exhibit exotic collective behaviors of quantum physics, and open the avenue of fault-tolerant topological quantum computing. Here, we give the Latin-square construction of Abelian and Ising anyons in the Kitaev model and study the maskable space configuration in anyonic space. The circling and braiding of Kitaev anyons are masking operations on extended hyperdisks in anyonic space. We also realize quantum information masking in a teleportation way in the Kitaev Ising anyon model.

arXiv:2404.02814Physical Review AMar 20, 20244 citations

Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state

Daichi Takikawa, Satoshi Fujimoto

We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with ${Z}_{2}$ gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the ${\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}1$ to an Abelian phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}2$, in which the ${Z}_{2}$ vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\mathrm{\ensuremath{\Gamma}}$ term only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with ${Z}_{2}$ gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the ${\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}1$ to an Abelian phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}2$, in which the ${Z}_{2}$ vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\mathrm{\ensuremath{\Gamma}}$ term only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.

arXiv:2003.05645Physical review. B./Physical review. BNov 9, 202017 citations

We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with

{Z}_{2}

gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the ${\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}1$ to an Abelian phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}2$, in which the

{Z}_{2}

vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\mathrm{\ensuremath{\Gamma}}$ term only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.