Resource-constrained reconstruction regions

Proposition prop:B2 gives monotonicity in budget, error tolerance, and library inclusion.

For the single-block target and authorized triple:

The first statement is a genuine lower bound from Theorem thm:B5, not the failure of one proposed decoder.

For batch access:

For the second equality, destructively consume qubit 4 without reporting its outcome, then apply the triple decoder. The resulting unconditioned channel is the partial trace over 4 followed by $\mathcal{D}$. The initial occupancy proves the lower bound.

The code-theoretic price of a logical algebra concerns the smallest physical support for its representatives PastawskiPreskill. For this block the full logical-qubit price is three. Our execution cost additionally specifies delivery, output, workspace, schedule, and operations. The streaming optimum two therefore does not change the algebraic price or contradict its support bound.