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关于温度变化可解决多伊奇 - 约扎问题:热力学查询复杂度的探索

Comment on Temperature change can solve the Deutsch-Jozsa problem: An exploration of thermodynamic query complexity

Ridha Horchani

arXiv 2607.11911首次发表:更新:

AI 中文总结

探讨温度变化解决多伊奇 - 约扎问题中的热力学查询复杂度,指出相关读出分析有误,CNOT扇出产生相关寄存器,样本下限不源于平斯克不等式,热反冲机制相关的单查询读出声明及样本必要性需修正。

AI 中文摘要

我们表明,《物理评论A》第113卷,012420(2026年)中的读出分析并未确立所声称的一个热查询后跟多个统计上有用的探测样本的资源计算。对角查询后探测的CNOT扇出会广播其一量子比特边缘,但产生的是完全相关的寄存器而非独立副本。因此,平衡假设和常数假设之间的迹距离及相对熵都不会增加,对辅助位的重复测量仅提供一次伯努利观测。独立样本则需要重复制备和热交换,这在原文采用的定义下属于重复查询。我们还表明,那里所述的样本下限并非源自平斯克不等式:该不等式对倒数相对熵给出了相反的排序。热反冲机制可能仍会在探测温度中编码决策,但单查询读出声明及所引用的约116个样本的必要性需要修正。

英文摘要

We show that the readout analysis in Phys. Rev. A 113, 012420 (2026) does not establish the claimed resource accounting of one thermal query followed by many statistically useful probe samples. A CNOT fanout of a diagonal post-query probe broadcasts its one-qubit marginal but produces perfectly correlated registers rather than independent copies. Consequently, neither the trace distance nor the relative entropy between the balanced and constant hypotheses increases, and repeated measurements of the ancillas provide only one Bernoulli observation. Independent samples instead require repeated preparation and heat exchange, which are repeated queries under the definition adopted in the original paper. We also show that the sample lower bound stated there does not follow from Pinsker's inequality: the inequality gives the opposite ordering for the reciprocal relative entropy. The thermal-kickback mechanism may still encode the decision in the probe temperature, but the one-query readout claim and the quoted necessity of approximately 116 samples require correction.

CommentsComment on https://doi.org/10.1103/qky6-2bfs (arXiv:2505.15887)

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