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 teleportable without entanglement if and only if it is clonable. Our main result suggests that this is not the case when computational efficiency is considered. We give a collection of quantum states and quantum oracles relative to which these states are efficiently clonable but not efficiently teleportable without entanglement. Given that the opposite scenario is impossible (states that can be teleported without entanglement can always trivially be cloned), this gives the most complete quantum oracle separation possible between these two important no-go properties. We additionally study the complexity class $\mathsf{clonableQMA}$, a subset of $\mathsf{QMA}$ whose witnesses are efficiently clonable. As a consequence of our main result, we give a quantum oracle separation between $\mathsf{clonableQMA}$ and the class $\mathsf{QCMA}$, whose witnesses are restricted to classical strings. We also propose a candidate oracle-free promise problem separating these classes. We finally demonstrate an application of clonable-but-not-teleportable states to cryptography, by showing how such states can be used to protect against key exfiltration.

翻译：量子信息中两个基本的不可行定理是不可克隆定理（无法复制一般量子态）和不可隐形传输定理（禁止在没有预共享纠缠的情况下通过经典信道发送量子态）。已知这两者在如下意义上是等价的：一组量子态无需纠缠即可隐形传输当且仅当其可被克隆。我们的主要结果表明，在考虑计算效率时，情况并非如此。我们给出了一组量子态及相对该组态的量子预言机，使得这些态可被高效克隆，但在没有纠缠的情况下无法高效隐形传输。鉴于相反情形不可能存在（无需纠缠即可隐形传输的态总是可以被平凡地克隆），这给出了这两个重要不可行性质之间最完备的量子预言机分离。此外，我们研究了复杂度类$\mathsf{clonableQMA}$，它是$\mathsf{QMA}$的一个子类，其证明子可被高效克隆。作为主要结果的推论，我们给出了$\mathsf{clonableQMA}$与类$\mathsf{QCMA}$（其证明子限制为经典字符串）之间的量子预言机分离。我们还提出了一个候选的无预言机承诺问题来分离这些类。最后，我们展示了可克隆但不可隐形传输的态在密码学中的应用，通过说明此类态如何用于防止密钥泄露。