We construct a quantum oracle relative to which $\mathsf{BQP} = \mathsf{QMA}$ but cryptographic pseudorandom quantum states and pseudorandom unitary transformations exist, a counterintuitive result in light of the fact that pseudorandom states can be "broken" by quantum Merlin-Arthur adversaries. We explain how this nuance arises as the result of a distinction between algorithms that operate on quantum and classical inputs. On the other hand, we show that some computational complexity assumption is needed to construct pseudorandom states, by proving that pseudorandom states do not exist if $\mathsf{BQP} = \mathsf{PP}$. We discuss implications of these results for cryptography, complexity theory, and quantum tomography.

翻译：我们构造了一个量子谕示，在该谕示下$\mathsf{BQP} = \mathsf{QMA}$，但密码学意义上的伪随机量子态和伪随机酉变换仍然存在，这一反直觉的结果源于伪随机态可被量子梅林-亚瑟对手"破解"这一事实。我们阐释了这种微妙性源于对量子输入和经典输入进行操作的算法之间的差异。另一方面，我们通过证明若$\mathsf{BQP} = \mathsf{PP}$则伪随机态不存在，表明构造伪随机态需要某种计算复杂性假设。我们讨论了这些结果对密码学、复杂性理论及量子层析成像的启示意义。