Postselection Tradeoffs
A Universal Information Budget for Conditional Records
Proves that postselection cannot generate objective information from nothing. While selecting a specific measurement outcome can increase fragment information, the probability-weighted average gain is strictly bounded by the control conditional mutual information.
Claim Boundary & Exclusions Audit
What Is Claimed (Within Scope)
- •Average Postselection Identity: sum_y p_y chi_y - chi = I(Lambda : Y | F) - I(Lambda : Y).
- •Universal Control Budget: sum_y p_y (chi_y - chi) <= I(Lambda : T | F).
- •Outcome-Resolved Tradeoff: p_y [chi_y - chi] <= I(Lambda : T | F) + (1 - p_y) chi.
- •Coherent postselection redistributes existing correlation; it does not amplify classical pointer information beyond the control budget.
What Is NOT Claimed (Prohibited Inferences)
- •Does not create free information. If I(Lambda : T | F) = 0, average postselection gain is nonpositive.
Technical Exposition & Formulation
Applies the chain rule of quantum mutual information to a classical pointer Lambda, environmental fragment F, and quantum control T subject to an arbitrary instrument with outcome Y.
Theorems & Mathematical Propositions
Universal Average Postselection Bound
[EXA]Exact result- Finite-dimensional Hilbert spaces.
- Y is generated from T via a local quantum channel.
From the chain rule, average gain equals I(Lambda : Y | F) - I(Lambda : Y) <= I(Lambda : Y | F). Data processing on local channel T -> Y gives I(Lambda : Y | F) <= I(Lambda : T | F).
Assumptions & Input Data
- Finite-dimensional cq states; trace-preserving instruments.
Declared Complete Carrier (K3)
Pointer Lambda, fragment F, control T, and instrument register Y.
Source Provenance & Verification Hashes
QD_Postselection_Tradeoff_Theorem_Report_2...
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