A Classical RAM Design That Mimics Quantum Collapse and Entanglement"

Summary

At the core of the Triangle Symbolic Processing Framework (TSPF) lies a family of symbolic primitives that simulate quantum‑like behaviors in classical environments. These primitives do not use quantum hardware, but they offer a deterministic approximation of key quantum phenomena such as ambiguity, collapse, entanglement, basis sensitivity, and symbolic no‑cloning. Together, they form the foundation for a logic architecture that mimics quantum gates using classical symbolic representations. 1. Ambiguity State (Δ) The ambiguity symbol Δ represents a symbolic register in an unresolved state. It is not a classical 0 or 1, nor a probabilistic superposition, but rather an epistemic uncertainty—a logical symbol that signifies an unresolved bit. Registers in the Δ state cannot be copied or duplicated because their value is undefined. Any attempt to clone or inspect Δ prematurely forces collapse, irreversibly resolving it. This enforces the symbolic no‑cloning principle, mirroring the spirit of the quantum no‑cloning theorem. 2. Collapse Operator Collapse is defined using the operator COL_Δ(R, B), which takes a symbolic register R (in state Δ) and a basis B (usually X or Z). If B matches the initialization basis, collapse is deterministic, yielding the correct bit. If B differs, collapse still resolves Δ but outputs a random bit, injecting symbolic entropy. Once collapsed, R becomes fixed (0 or 1) and Δ is destroyed. This operation satisfies three key constraints: Irreversibility Symbolic no‑cloning Basis sensitivity 3. Basis Tagging Each Δ register is initialized with a hidden basis (X or Z). During collapse, only if the chosen basis matches this tag will collapse be coherent. This tagging is essential for BB84-style protocols, ensuring alignment is only determined post-collision. 4. Entanglement Primitive The primitive ENT(R₁, R₂) symbolically links two Δ registers across agents. Collapsing one leads to the correlated collapse of the other: If bases match, both parties r...