Optimal compression with quantum retrieval

Abstract:We consider the following data compression problem. Given a string $x \in \{0,1\}^m$ of Hamming weight at most $n$, compress it into a shorter string $y \in \{0,1\}^s$ so that any bit $x_i$ of $x$ can be retrieved without any error using at most $t$ quantum queries to the standard oracle encoding of $y$. If queries are allowed to be adaptive we show how optimal compression up to a logarithmic factor can be achieved. If the queries are required to be made non-adaptively, we show schemes whose space is optimal in its dependence on $m$ except for a logarithmic factor, and is at most quadratically worse when compared to the optimum in its dependence on $n$.

Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS); Information Retrieval (cs.IR); Information Theory (cs.IT)

arXiv:2610.06702 [quant-ph]

(or arXiv:2610.06702v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.06702 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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