Two of the fundamental no-go theorems of quantum information are the no-cloning theorem (that it is impossible to make copies of general quantum states) and the no-teleportation theorem (the prohibition on sending quantum states over classical channels without pre-shared entanglement). They are known to be equivalent, in the sense that a collection of quantum states is clonable if and only if it is teleportable. Our main result suggests that this is not the case when computational efficiency is considered. We give a collection of quantum states and oracles relative to which these states are efficiently clonable but not efficiently teleportable. Given that the opposite scenario is impossible (states that can be teleported can always trivially be cloned), this gives the most complete oracle separation possible between these two important no-go properties. In doing so, we introduce a related quantum no-go property, reconstructibility, which refers to the ability to construct a quantum state from a uniquely identifying classical description. We show the stronger result of a collection of quantum states that are efficiently clonable but not efficiently reconstructible. This novel no-go property only exists in relation to computational efficiency, as it is trivial for unbounded computation. It thus opens up the possibility of further computational no-go properties that have not yet been studied because they do not exist outside the computational context.

翻译：量子信息的两大基本禁戒定理是量子不可克隆定理（无法复制一般量子态）和量子不可传输定理（禁止在没有预共享纠缠的情况下通过经典信道传输量子态）。已知这两个定理等价，即一组量子态可克隆当且仅当可传输。我们的主要结果表明，当考虑计算效率时，情况并非如此。我们构造了一组量子态及相应的预言机，使得这些量子态可高效克隆但无法高效传输。鉴于反之情形不可能成立（可传输的量子态总可以平凡地克隆），这给出了这两个重要禁戒性质间最完备的预言机分离结果。在此过程中，我们引入了相关的量子禁戒性质——可重构性，指通过唯一辨识的经典描述重构量子态的能力。我们证明了更强的结果：存在一组量子态可高效克隆但无法高效重构。这一新型禁戒性质仅存在于计算效率语境中，在无界计算条件下平凡成立。因此，它揭示了可能存在尚未被研究的其他计算禁戒性质，这些性质在计算语境之外并不存在。