  We investigate quantum dynamics of a quantum walker on a finite bipartite
non-Hermitian lattice, in which the particle can leak out with certain rate
whenever it visits one of the two sublattices. Quantum walker initially located
on one of the non-leaky sites will finally totally disappear after a length of
evolution time and the distribution of decay probability on each unit cell is
obtained. In one regime, the resultant distribution shows an expected
decreasing behavior as the distance from the initial site increases. However,
in the other regime, we find that the resultant distribution of local decay
probability is very counterintuitive, in which a relatively high population of
decay probability appears on the edge unit cell which is the farthest from the
starting point of the quantum walker. We then analyze the energy spectrum of
the non-Hermitian lattice with pure loss, and find that the intriguing behavior
of the resultant decay probability distribution is intimately related to the
existence and specific property of edge states, which are topologically
protected and can be well predicted by the non-Bloch winding number. The exotic
dynamics may be observed experimentally with arrays of coupled resonator
optical waveguides.
