Multi-agent techniques such as role playing or multi-turn debates have been shown to be effective in improving the performance of large language models (LLMs) in downstream tasks. Despite their differences in workflows, existing multi-agent systems constructed from a single base LLM mostly use natural language for agent communication. While this is appealing for its simplicity and interpretability, it also introduces inevitable information loss as one model must down sample its continuous state vectors to discrete tokens before transferring them to the other model. Such losses are particularly significant when the information to transfer is not simple facts, but reasoning logics or abstractive thoughts. To tackle this problem, we propose a new communication protocol that transfers both natural language tokens and token-wise state transition trajectory from one agent to another. Particularly, compared to the actual state value, we find that the sequence of state changes in LLMs after generating each token can better reflect the information hidden behind the inference process. We propose a State Delta Encoding (SDE) method to represent state transition trajectories. The experimental results show that multi-agent systems with SDE achieve SOTA performance compared to other communication protocols, particularly in tasks that involve complex reasoning.