Manuscript Hawk04-B@2 · Hawk04-B.tex · section · ba3b0713

The corrected destination ledger

The corrected destination ledger · lines 2077–2169

The word “bin” denotes a declared residual subsystem. It does not denote a physical deletion mechanism. The table concerns unknown quantum codes, not only classical labels.

Condition or interface	Complete-channel conclusion	Recovery task
Condition or interface	Complete-channel conclusion	Recovery task
Complete coherent body	The code is preserved in $R B$ . The program returns both quantum outputs; it contains no $Enter$ .	Global restore (eq:restore); complete access is sufficient.
Constant complete complement	Radiation has the syndrome form $A (X \otimes σ_{K}) A^{†}$ . The residual is logical-input independent.	Local quantum decoder (eq:decoder), followed by quantum return.
Constant radiation channel	No-hiding places a recoverable copy of the whole code in the complete residual.	Quantum recovery from $B$ ; classical readout of $B$ is not generally that recovery.
Merely nonconstant complement	Some logical information is distinguished by $B$ . Residual-only recovery of the entire code does not follow.	A local decoder requires a separate proof; joint recovery exists for the complete isometry.
Four-Majorana control	Radiation is measure-and-prepare. For $0 < c_{R} < 1$ , both individual recovery errors are positive, while $R B$ is reversible.	$ε_{rec}^{R} = (3 - 1 - c_{R}^{2}) /4 \geq 1/2$ ; $ε_{rec}^{B} = (1 - c_{R}) /2$ .
Residual readout with record retained	Observable access is $R K$ , with unnormalized conditional quantum branches. The complete apparatus also retains $E$ .	An assisted quantum decoder may use $R K$ . Bits alone do not replace the diary.
Residual readout with record dropped	The observable output is exactly the original channel $N$ , not a newly erased radiation channel.	Exactly the pre-existing radiation-only recovery task.
All retained outputs converted to classical data	The observable channel is measure-and-prepare after any classical-to-quantum reconstruction.	Error at least $1 - 1/ d$ .
All observable outputs dropped	The retained algebra is scalar. Any newly allocated fixed quantum output is a replacement channel.	Optimal deterministic reconstruction error $a_{d} = 1 - d^{- 2}$ ; the complete unitary dilation still has a global inverse.
Vanishing source energy alone	It constrains a selected energy expectation, not the complete complementary channel.	No radiation recovery certificate follows without a channel comparison.
Selected radiation entropy alone	An entropy of selected inputs does not identify the destination of all logical matrix units and reference correlations.	No decoder or residual-independence conclusion follows.

The corrected destination ledger

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