Fig. 8
Convergence of quantum memory for delayed Poisson process. a The classical memory requirement C μ for the delayed Poisson process diverges logarithmically with finer discretisation (N + 1 states), while the quantum memory C q appears to converge to a finite value. b Inspection of the eigenvalues of increasingly finer discretisation of the q-machine for the delayed Poisson process shows that the eigenvalues appear to fall off with a 1/n2 dependence. Plots shown for τ R /τ L = 1, and β is a normalisation constant chosen such that \(\mathop {\sum}\nolimits_{n = 101}^\infty {\kern 1pt} \beta {\mathrm{/}}n^2 = \mathop {\sum}\nolimits_{n = 101}^{N + 1} {\kern 1pt} \lambda _n\) for the N = 215 case (eigenvalues ranked largest to smallest)
