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arXiv · 2610.06702

Optimal compression with quantum retrieval

Shyam Dhamapurkar·Mohit Garg·Manaswi Paraashar·Jaikumar Radhakrishnan
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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 $n$.

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Shyam Dhamapurkar, Mohit Garg, Manaswi Paraashar, Jaikumar Radhakrishnan. 2026-10-05. Optimal compression with quantum retrieval. https://arxiv.org/abs/2610.06702

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