Destructive partial readout

This is the local restatement of Hawk04-B's partial-trace and apparatus results CheungHawk04B (thm:drop, prop:measurement-dilation).

The physical carrier $K$ in (eq:read-dilation) is quantum. It becomes a commutative observable interface after the omitted factor $E$ is traced out. The omitted information is preserved in the complete coherent output; it is not claimed to be independently recoverable from $E$ alone.

For example,

Neither marginal generally retains the unknown phase. Joint $KE$ access does. Neither marginal channel is constant on the entire qubit code, so this is not a counterexample to Corollary cor:nohiding.