  We investigate the time evolution of the subsystem trace distance and
Schatten distances after local operator quenches in two-dimensional conformal
field theory (CFT) and in one-dimensional quantum spin chains. We focus on the
case of a subsystem being an interval embedded in the infinite line. The
initial state is prepared by inserting a local operator in the ground state of
the theory. We only consider the cases in which the inserted local operator is
a primary field or a sum of several primaries. While a nonchiral primary
operator can excite both left-moving and right-moving quasiparticles, a
holomorphic primary operator only excites a right-moving quasiparticle and an
anti-holomorphic primary operator only excites a left-moving one. The reduced
density matrix (RDM) of an interval hosting a quasiparticle is orthogonal to
the RDM of the interval without any quasiparticles. Moreover, the RDMs of two
intervals hosting quasiparticles at different positions are also orthogonal to
each other. We calculate numerically the entanglement entropy, R\'enyi entropy,
trace distance, and Schatten distances in time-dependent states excited by
different local operators in the critical Ising and XX spin chains. These
results match the CFT predictions in the proper limit.
