The memory cost of sequential quantum state preparation

arXiv:2611.14652v1 Announce Type: new Abstract: How much memory does a quantum device need to prepare systems one at a time? We address this question through the lens of quantum resource theories, which formalize physical restrictions on how the memory may interact with the stream of systems it processes. By comparing sequential with collective preparation, we show that under general assumptions both have the same asymptotic memory cost per output. Still, sequential preparation can require an unboundedly larger memory than collective one, and we investigate how this gap depends on the physical restrictions on the allowed interactions.