A Computational Separation Between Quantum No-cloning and No-teleportation

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.