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Unified multimodal large language models (MLLMs) integrate image understanding and generation in a single framework, with the visual tokenizer acting as the sole interface that maps visual inputs into tokens for downstream tasks. However, existing shared-token designs are mostly architecture-driven and lack an explicit criterion for what information tokens should preserve to support both understanding and generation. Therefore, we introduce a capacity-constrained perspective, highlighting that in shared-token unified MLLMs the visual tokenizer behaves as a compute-bounded learner, so the token budget should prioritize reusable structure over hard-to-exploit high-entropy variations and redundancy. Motivated by this perspective, we propose InfoTok, an information-regularized visual tokenization mechanism grounded in the Information Bottleneck (IB) principle. InfoTok formulates tokenization as controlling information flow from images to shared tokens to multimodal outputs, yielding a principled trade-off between compression and task relevance via mutual-information regularization. We integrate InfoTok into three representative unified MLLMs without introducing any additional training data. Experiments show consistent improvements on both understanding and generation, supporting information-regularized tokenization as a principled foundation for learning a shared token space in unified MLLMs.