LinearKV is a training-free hybrid-PIC framework. Its key insight is a decoupled initialization: each linear layer maps its $K$ matched local states to a single initial state, while full-attention layers concatenate their KV as before. LinearKV is therefore compatible with existing PIC methods, reusing their token selection and recomputation as-is. We compare LinearKV with another method, HYPIC, which attempts to compose all $K$ cached states into the exact full-prefix state. Our experiments on three hybrid models and three PIC selectors show that LinearKV ties with HYPIC on two GDN models, recovering most of full quality (up to $92%$); on the Mamba-2 model, exact composition instead collapses under every selector---for instance, under EPIC, it recovers only $46.6%$ of full quality, versus $86.8%$ for a single cached block initializer. Furthermore, a single state initializer is also cheaper, cutting time-to-first-token to $0.46 imes$ full prefill, while exact composition incurs a further $5$--$17%$ overhead; results hold across LongBench QA and RULER at 8K--32K. Blogger's Review: LinearKV provides a efficient position-independent caching framework for hybrid LLMs, with its single cached state initialization method not only recovering most of full quality but also having lower computational cost and faster time-to-first-token. This makes LinearKV a promising solution for hybrid LLMs.