  The non-Hermitian skin effect (NHSE) refers to that an extensive number of
eigenstates of a non-Hermitian system are localized in open boundaries. Here we
predict a universal phenomenon that with local particle-hole(-like) symmetry
(PHS) the skin modes must be equally distributed on different boundaries,
manifesting a novel nonlocalization of the local PHS, which is unique to
non-Hermitian systems. We develop a generic theory for the emergent nonlocal
symmetry-protected NHSE by connecting the non-Hermitian system to an extended
Hermitian Hamiltonian in a quadruplicate Hilbert space, which maps the skin
modes to the topological zero modes and the PHS to an emergent nonlocal
symmetry in the perspective of many body physics. The predicted NHSE is robust
against perturbations. We propose optical Raman lattice models to observe the
predicted phenomena in all physical dimensions, which are accessible with
cold-atom experiments.
