束缚纠缠不足以实现指数级量子学习优势
Bound Entanglement Is Insufficient for an Exponential Quantum Learning Advantage
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中文总结 AI 辅助
研究纠缠资源属性与量子学习样本复杂度提升的关系，通过归约准则探讨其作用，发现在n量子比特泡利信道学习等中，违反该准则会排除指数优势，其是实现指数优势的必要条件。
中文摘要 AI 辅助
虽然已知纠缠能使量子学习的样本复杂度实现指数级提升，但尚不清楚纠缠资源的哪些属性导致了这种提升。我们通过归约准则来解决这个问题，所有束缚纠缠态都满足该条件。在n量子比特泡利信道学习中，我们表明限制输入态或测量效应以满足此准则会排除非相干自适应协议的指数优势。对于这里考虑的单边相干自适应协议，即使不受限制的一方在信道使用中保留量子关联，指数下界仍然存在。使用条件最小熵，我们进一步量化了随着对归约准则的更大违反被允许，样本复杂度下界如何减弱。最后，我们表明在共轭态学习中也出现了同样的阻碍：受限联合测量无法重现对ρ⊗ρ*进行无限制联合测量的对数样本优势。这些结果表明违反归约准则是在此处考虑的学习任务中实现指数优势的必要条件。
英文摘要
While entanglement is known to enable exponential improvements in the sample complexity of quantum learning, it remains unclear which properties of entangled resources are responsible for such improvements. We address this question through the reduction criterion, a condition obeyed by all bound-entangled states. In $n$-qubit Pauli-channel learning, we show that restricting either the input states or the measurement effects to satisfy this criterion rules out an exponential advantage for incoherent adaptive protocols. An exponential lower bound persists for the one-sided coherent adaptive protocols considered here, even when the unrestricted side retains quantum correlations across channel uses. Using conditional min-entropy, we further quantify how the sample-complexity lower bounds weaken as larger violations of the reduction criterion are allowed. Finally, we show that the same obstruction appears in conjugate-state learning: restricted joint measurements cannot reproduce the logarithmic-sample advantage of unrestricted joint measurements on $ρ\otimesρ^*$. These results identify violation of the reduction criterion as a necessary condition for an exponential advantage in the learning tasks considered here.
