Deterministic quantum one-time pad via Fibonacci anyons

Anyonic states, which are topologically robust because of their peculiar structure of Hilbert space, have important applications in quantum computing and quantum communication. Here we investigate the capacity of the deterministic quantum one-time pad (DQOTP) that uses Fibonacci anyons as an information carrier. We find that the Fibonacci particle-antiparticle pair produced from vacuum can be used to asymptotically send $2{log}_2{d}_{\tau }$ bits of classical information ($d_{\tau }$ is the quantum dimension of a Fibonacci anyon $\tau$), which equals anyonic mutual information of the pair. Furthermore, by studying the DQOTP via a parameterized state of six Fibonacci anyons with trivial total charge, we give the analytical results of the maximum number of messages that can be sent for different parameters, which is a step function with every step corresponding to a regular simplex from the viewpoint of geometry. The results for the maximum number of messages sent by the DQOTP can be explained by anyonic accessible information.

Figure 1

The maximum amount of information $N_m(|\mathcal{G}\left(p\right)\rangle )$ transmitted deterministically from Alice to Bob through the state $\left|\mathcal{G}\right(p)\rangle$ for different $p$.

Figure 2

The graph of three functions of $p$: anyonic mutual information $\tilde{I}\left({\tilde{\rho }}^{AB}\right)$ (black solid line), $\tilde{I}\left({\tilde{\sigma }}^{AB}\right)$ (black dotted line), and the Holevo bound $\mathcal{X}\left({\tilde{\rho }}^{AB}\right)$ (red dashed line), which is the difference between $\tilde{I}\left({\tilde{\rho }}^{AB}\right)$ and $\tilde{I}\left({\tilde{\sigma }}^{AB}\right)$. $\tilde{I}\left({\tilde{\sigma }}^{AB}\right)$ and $\mathcal{X}\left({\tilde{\rho }}^{AB}\right)$ are step functions; both are left continuous at points with $p$ coordinates: $1/5, 1/4, 1/3$, and $1/2$. $P$ ($Q$) is the extreme point of function $\tilde{I}\left({\tilde{\rho }}^{AB}\right) \left[\mathcal{X}\left({\tilde{\rho }}^{AB}\right)\right]$, whose $p$ coordinate is $1/d_{\tau }^3$ ($1/5$).