No-deleting theorem

In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary quantum state, it is impossible to delete one of the copies. It is a time-reversed dual to the no-cloning theorem,^[1][2] which states that arbitrary states cannot be copied. It was proved by Arun K. Pati and Samuel L. Braunstein.^[3] Intuitively, it is because information is conserved under unitary evolution.^[4]

This theorem seems remarkable, because, in many senses, quantum states are fragile; the theorem asserts that, in a particular case, they are also robust.

The no-deleting theorem, together with the no-cloning theorem, underpin the interpretation of quantum mechanics in terms of category theory, and, in particular, as a dagger symmetric monoidal category.^[5][6] This formulation, known as categorical quantum mechanics, in turn allows a connection to be made from quantum mechanics to linear logic as the logic of quantum information theory (in exact analogy to classical logic being founded on Cartesian closed categories).