  The low-temperature physics of quantum many-body systems is largely governed
by the structure of their ground states. Minimizing the energy of local
interactions, ground states often reflect strong properties of locality such as
the area law for entanglement entropy and the exponential decay of correlations
between spatially separated observables. In this letter we present a novel
characterization of locality in quantum states, which we call `local
reversibility'. It characterizes the type of operations that are needed to
reverse the action of a general disturbance on the state. We prove that unique
ground states of gapped local Hamiltonian are locally reversible. This way, we
identify new fundamental features of many-body ground states, which cannot be
derived from the aforementioned properties. We use local reversibility to
distinguish between states enjoying microscopic and macroscopic quantum
phenomena. To demonstrate the potential of our approach, we prove specific
properties of ground states, which are relevant both to critical and
non-critical theories.
