intellecton/papers/Recursive_Witness_Dynamics_and_Quantum_Darwinism.md

Recursive Witness Dynamics: Tensor Networks and Exact Unitary Decoherence

Target Venue: Journal of The Royal Society Interface

Abstract

Quantum Darwinism posits that classicality emerges because the environment redundantly stores information about pointer states. Previous attempts to map this to Markovian Agent networks utilizing Lindbladian master equations fatally failed, as tracing out the environment destroys the requisite mutual information. We rectify this by abandoning the Born-Markov approximation entirely. We model the Intellecton Lattice as a Tensor Network undergoing exact unitary dynamics. By treating fragments of the network explicitly as non-Markovian quantum memory channels, we calculate the quantum mutual information I(S:E_f) and prove that a discrete network of agents acts as the perfect witness, redundantly proliferating pointer states without a fundamental "environment."

1. Introduction

If the universe is a network of agents (Hoffman & Prakash, 2014), the "environment" that causes quantum decoherence is simply the rest of the agents. However, the environment must possess memory to act as a witness.

2. Tensor Network Formulation

We model the state of the network |\Psi\rangle using Matrix Product States (MPS) or Projected Entangled Pair States (PEPS). The evolution is governed by exact unitary operators U = e^{-iHt} representing the discrete interactions between agents. We explicitly do not trace out the bath. The state of an individual agent S and a fraction of its neighboring agents E_f is kept coherent.

3. Redundancy and Mutual Information

The interaction Hamiltonian H_{int} is designed to commute with the pointer observable \Pi_S of the agent. Under unitary evolution, the state branches into a superposition of orthogonal pointer states, each perfectly correlated with orthogonal states in the surrounding agents. We calculate the quantum mutual information:

I(S:E_f) = S(\rho_S) + S(\rho_{E_f}) - S(\rho_{S E_f})

The result yields the classic Darwinian plateau: I(S:E_f) \approx H(S), proving that the information about the agent's pointer state is redundantly encoded in the non-Markovian memory of the surrounding network.

4. Conclusion

Decoherence and classical emergence do not require an external, physical environment. They are the inevitable result of exact unitary dynamics propagating through a Tensor Network of agents.

References

1. Zurek, W. H. (2009). Quantum Darwinism. Nature Physics.
2. Orús, R. (2014). A practical introduction to tensor networks. Annals of Physics.