Quantum Darwinism Survival
Common Pointer Conservation over Superposed Interaction Structures
Generalizes the two-body Hamiltonian classification of Doucet and Deffner to indefinite, superposed, or fluctuating interaction structures. Tracing out an inaccessible orthogonal control register reduces accessible dynamics to an incoherent mixture, establishing exact algebraic survival criteria.
Claim Boundary & Exclusions Audit
What Is Claimed (Within Scope)
- •Channelwise exact nondemolition requires a common conserved rank-one pointer decomposition across all nonzero channels.
- •Redundant classical objectivity requires that pointer values generate distinguishable records in many disjoint environmental fragments.
- •Commutation makes a record distinction survivable; conditional-record distinguishability makes it broadcast.
What Is NOT Claimed (Prohibited Inferences)
- •Does not derive the Born rule, wave-function collapse, or definite-event generation.
Technical Exposition & Formulation
When an inaccessible control register T carries the channel label in state |tau> = sum_a c_a |a>, the restricted density operator on system and accessible environment is rho'_SE = sum_a |c_a|^2 U(a) rho_SE U(a)^dag. Common-pointer preservation requires [A^(a)_{alpha k}, P_s] = 0 for all active channels a and fragments k.
Assumptions & Input Data
- Initially uncorrelated orthogonal control register.
- Block-controlled unitary evolution.
Declared Complete Carrier (K3)
System S, fragments E_k, control register T, and pointer P_s.
Source Provenance & Verification Hashes
Quantum_Darwinism_Survival_Theorem_Revised2...
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