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Conjecture 5: Superactivation of Measurement-Free Modular Capacity

Big Picture

Conjecture 5 asks whether two individually useless inter-module links can jointly transmit logical quantum information once local nonunital refresh resources are included.

Current Status

No conjecture-local research nodes exist yet. The first pass should select a minimal one-module-pair model and determine whether ordinary superactivation constructions survive the measurement-free resource constraints.

Minimal Theorem Targets

  1. Start with memoryless links and one module-qubit pair.
  2. Look for a one-shot or finite-blocklength advantage before proving positive asymptotic rate.
  3. Test one explicit zero-capacity channel family, such as symmetric, erasure-assisted, or amplitude-damping-derived links.

Technical Tools

The first research pass should expect to use Smith-Yard superactivation, coherent-information nonadditivity, memory-channel coding, entanglement distillation, and one-shot decoupling.

Next Actions

  1. Create the first theorem/gap nodes under research/ using the bounded graph workflow.
  2. Add Zotero source checks only after a concrete target theorem is selected.
  3. Keep learning and manuscript material as stubs until a durable research spine exists.

Local Files