unitarity

Unitarity is the principle that the natural evolution of an isolated quantum system conserves total probability. Start with a state whose probabilities for all possible outcomes add up to one, let it evolve, and the probabilities still add up to one — never more, never less. Probability is neither manufactured nor destroyed as the system changes; it merely flows around among the possibilities.

The name comes from the fact that this evolution is carried out by unitary operators, which preserve the lengths of state vectors. Keeping a state's length fixed at one is the same as keeping its total probability at one, so unitarity and the use of unitary operators are two faces of a single idea. It also implies that quantum evolution is reversible: in principle the past state can always be reconstructed from the present one.

Unitarity is a deep and jealously guarded principle. Much of the puzzlement around quantum measurement comes from the fact that an ideal measurement seems to break it, collapsing a spread-out state to one outcome and apparently discarding the others. And the long debate over whether information is lost in black holes is, at bottom, a worry about whether unitarity survives there. Physicists treat any apparent loss of unitarity as a red flag demanding explanation.