Assessment and reproducibility boundary

A laboratory or simulated verification of a specified decoder can use independent preparations of the Bell input and the success variable

With $n$ independent complete attempts, ${\hat{F}}_e=n^{-1}{\sum }_i{Y}_i$, Hoeffding's inequality gives

This certifies a Bell-input diagnostic. A worst-case channel claim additionally uses (eq:Bellconversion), full process data, or another uniform channel certificate.

For complete-record tomography with a finite alphabet of size $K$, coordinatewise Hoeffding and a union bound give, with probability at least $1-\alpha$,

Complete-record laws and their residual instruments remain distinct, as emphasized in En03-A and Psy02-B CheungEn03A,CheungPsy02B. Repeated records inside one correlated attempt do not increase $n$.

If normalized Choi states have a certified trace-distance discrepancy at most $a_J$, then (eq:Choiconversion) supplies channel discrepancy at most $d{a}_J$, and Proposition prop:robustness propagates that allowance to the recovery optimum.

Repeated injections into one evolving source are not automatically independent. Shared residual memory, changing energy, and overlapping radiation require a history-conditional assessment model. Simulation of independent initial preparations is not observation of an astrophysical black hole.

Passive source observation also does not ordinarily supply a prepared logical input, its reference, or a controlled channel-tomography interface. Replacing a classical observation device by a quantum one does not create those absent access channels CheungPsy03D. The task-specific numerical bounds of that manuscript are not imported here.

A reproducibility record for any extension of the model should include:

1. code dimension, conserved sector, and allowed input states;

2. all initially fixed states and their purifiers;

3. every transition map, Hamiltonian, and charge operator;

4. radiation mode and occupation regulators;

5. pending, completed, vacuum, loss, and endpoint branches;

6. the complete observer channel and its excluded environment;

7. decoder and quantum/classical storage requirements;

8. exact or certified numerical norm and entropy errors;

9. the endpoint resource ledger;

10. sampling independence and validation-selection assumptions.