Absorption at boundaries in discrete-time quantum walks yields complementary classical Fisher information on the coin state, so two binary readouts generically give a full-rank Fisher matrix and tight Cramér-Rao bounds without mode-resolved tomography.
Absorption Probabilities for the Two-Barrier Quantum Walk
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abstract
Let p_j^(n) be the probability that a Hadamard quantum walk, started at site j on the integer lattice {0,...,n}, is absorbed at 0. We give an explicit formula for p_j^(n). Our formula proves a conjecture of John Watrous, concerning an empirically observed linear fractional recurrence relation for the numbers p_1^(n).
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Absorption-based qubit estimation in discrete-time quantum walks
Absorption at boundaries in discrete-time quantum walks yields complementary classical Fisher information on the coin state, so two binary readouts generically give a full-rank Fisher matrix and tight Cramér-Rao bounds without mode-resolved tomography.