English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

A quantum walker on a graph, prepared in the state $| \psi_{\rm in} \rangle$,e.g. initially localized at node $r_{\rm in}$, is repeatedly probed, with fixedfrequency $1/\tau$, to test its presence at some target node $r_{\rm d}$ untilthe first successful detection. This is a quantum version of the first-passageproblem. We investigate the total detection probability $P_{\rm det}$, i.e. theprobability to eventually detect the particle after an arbitrary number ofdetection attempts. It is demonstrated that this total detection probability isless than unity in symmetric systems, where it is possible to find initialstates which are shielded from the detector by destructive interference,so-called dark states. The identification of physically equivalent initialstates yields an upper bound for $P_{\rm det}$ in terms of the reciprocal ofthe number $\nu$ of physically equivalent states. The relevant subgroup of thesystem's symmetry operations is found to be the stabilizer of the detectionstate. Using this, we prove that all bright, i.e. surely detectable, states aresymmetric with respect to the stabilizer. This implies that $P_{\rm det}$ canbe obtained from a diagonalization of the "symmetrized" Hamiltonian, instead ofhaving to find all eigenstates of the Hamiltonian.

Quantum total detection probability from repeated measurements II. Exploiting symmetry