In this note, we observe that quantum logspace computations are verifiable by classical logspace algorithms, with unconditional security. More precisely, every language in BQL has an (information-theoretically secure) streaming proof with a quantum logspace prover and a classical logspace verifier. The prover provides a polynomial-length proof that is streamed to the verifier. The verifier has a read-once one-way access to that proof and is able to verify that the computation was performed correctly. That is, if the input is in the language and the prover is honest, the verifier accepts with high probability, and, if the input is not in the language, the verifier rejects with high probability even if the prover is adversarial. Moreover, the verifier uses only $O(\log n)$ random bits.

翻译：本文指出，量子对数空间计算可被经典对数空间算法以无条件安全性验证。具体而言，BQL中的每种语言均存在（信息论意义上安全的）流式证明，其证明者为量子对数空间，验证者为经典对数空间。证明者提供多项式长度的证明，该证明以流式方式传输给验证者。验证者对该证明具有一次读取单向访问权限，并能验证计算是否正确执行。即：若输入属于该语言且证明者诚实，验证者将以高概率接受；若输入不属于该语言，即使证明者存在恶意行为，验证者仍将以高概率拒绝。此外，验证者仅使用$O(\log n)$个随机比特。