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We propose a definition of wavefunction "branchings": quantum superpositions
which can't be feasibly distinguished from the corresponding mixed state, even
under time evolution. Our definition is largely independent of interpretations,
requiring only that it takes many more local gates to swap branches than to
distinguish them. We give several examples of states admitting such branch
decompositions. Under our definition, we show that attempts to get
relative-phase information between branches will fail without frequent active
error correction, that branches are effectively the opposite of good
error-correcting codes, that branches effectively only grow further apart in
time under natural evolution, that branches tend to absorb spatial
entanglement, that branching is stronger in the presence of conserved
quantities, and that branching implies effective irreversibility. Identifying
these branch decompositions in many-body quantum states could shed light on the
emergence of classicality, provide a metric for experimental tests at the
quantum/ classical boundary, and allow for longer numerical time evolution
simulations. We see this work as a generalization of the basic ideas of
environmentally-induced decoherence to situations with no clear system/
environment split.
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