Anyonic states, which are topologically robust because of their peculiar structure Hilbert space, have important applications in quantum computing and communication. Here we investigate the capacity deterministic one-time pad (DQOTP) that uses Fibonacci anyons as an information carrier. We find particle-antiparticle pair produced from vacuum can be used to asymptotically send $2{log}_{2}{d}_{\e...

As a consequence of Algorithm 1 below, there always exist integers x, y ∈ Z such that ax+by = gcd(a, b). We say that a and b are co-prime (or relatively prime) if gcd(a, b) = 1, i.e., ax = 1 mod b. From this, x is the multiplicative inverse of a modulo b, and likewise y is the multiplicative inverse of b modulo a. The following deterministic algorithm shows that gcd(a, b) (and additionally, the...

Hittmeir recently presented a deterministic algorithm that provably computes the prime factorisation of positive integer $N$ in $N^{2/9+o(1)}$ bit operations. Prior to this breakthrough, best known complexity bound for problem was $N^{1/4+o(1)}$, result going back 1970s. In paper we push Hittmeir's techniques further, obtaining rigorous, factoring with $N^{1/5+o(1)}$.