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We propose a definition of wavefunction "branchings": quantum superpositionswhich can't be feasibly distinguished from the corresponding mixed state, evenunder time evolution. Our definition is largely independent of interpretations,requiring only that it takes many more local gates to swap branches than todistinguish them. We give several examples of states admitting such branchdecompositions. Under our definition, we show that attempts to getrelative-phase information between branches will fail without frequent activeerror correction, that branches are effectively the opposite of gooderror-correcting codes, that branches effectively only grow further apart intime under natural evolution, that branches tend to absorb spatialentanglement, that branching is stronger in the presence of conservedquantities, and that branching implies effective irreversibility. Identifyingthese branch decompositions in many-body quantum states could shed light on theemergence of classicality, provide a metric for experimental tests at thequantum/ classical boundary, and allow for longer numerical time evolutionsimulations. We see this work as a generalization of the basic ideas ofenvironmentally-induced decoherence to situations with no clear system/environment split.

Wavefunction branching: when you can't tell pure states from mixed states