Quantum resource distillation is a fundamental task in quantum information science and technology. Minimizing the overhead of distillation is crucial for the realization of quantum computation and other technologies. Here we explicitly demonstrate how, for general quantum resources, suitably designed quantum catalysts (i.e., auxiliary systems that remain unchanged before and after the process) enable distillation with constant overhead in the practical one-shot setting, thereby overcoming the established logarithmic lower bound for one-shot distillation overhead. In particular, for magic state distillation, our catalysis method paves a path for tackling the diverging batch size problem associated with code-based low-overhead protocols by enabling arbitrary reduction of the protocol size for any desired accuracy. Notably, this first yields constant-overhead magic state distillation methods with controllable protocol size. Furthermore, we demonstrate a tunable spacetime trade-off between overhead and success probability enabled by catalysts which offers significant versatility for practical implementation. Finally, we extend catalysis techniques to dynamical quantum resources and show that channel mutual information determines one-shot catalytic channel transformation, thereby advancing our understanding for both dynamical catalysis and information theory.

翻译：量子资源蒸馏是量子信息科学与技术中的一项基本任务。最小化蒸馏开销对于实现量子计算及其他技术至关重要。本文明确展示了对于一般量子资源，如何通过适当设计的量子催化剂（即在过程前后保持不变的辅助系统）在实际单次设置中实现恒定开销的蒸馏，从而克服了已建立的单次蒸馏开销对数下界。特别地，对于魔术态蒸馏，我们的催化方法为解决基于编码的低开销协议中存在的批处理规模发散问题开辟了路径，因为它能够为任意期望精度任意减小协议规模。值得注意的是，这首次产生了具有可控协议规模的恒定开销魔术态蒸馏方法。此外，我们展示了催化剂所实现的开销与成功概率之间可调谐的时空权衡，这为实际应用提供了显著的灵活性。最后，我们将催化技术推广至动态量子资源，并证明信道互信息决定了单次催化信道变换，从而增进了我们对动态催化和信息论的理解。