Kaiyan Shi

Quantum sensing is a promising technology capable of demonstrating clear advantage over comparable classical techniques for precise measurement. One application of quantum sensing is in function estimation, which can be done using a network of entangled quantum sensors, allowing for measurements with greater optimal sensitivity than unentangled sensing protocols. Since quantum sensor networks will likely be used to measure data that should remain private (e.g., biomedical data), it is imperative that these protocols include a cryptographic mechanism to hide sensitive information. In this work, we show that entangled sensor networks are vulnerable to differential attacks. To mitigate these attacks, we introduce secure sensing protocols based on differential privacy. We reconcile Heisenberg-limited scaling and differential privacy and introduce several protocols achieving varying balances between the two. We show that our protocols are resilient to attacks by quantum adversaries and we find advantages in the privacy-utility trade-off when using quantum resources.

In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This is a fundamental problem in query complexity, and appears in many contexts, particularly cryptography. In this work, we examine the setting in which the oracle allows for quantum queries to both the forward and the inverse direction of the permutation—except that the challenge value cannot be submitted to the latter. Within that setting, we consider two options for the inversion algorithm: whether it can get quantum advice about the permutation, and whether it must produce the entire preimage (search) or only the first bit (decision). We prove several theorems connecting the hardness of the resulting variations of the inversion problem, and establish lower bounds for them. Our results indicate that, perhaps surprisingly, the inversion problem does not become significantly easier when the adversary is granted oracle access to the inverse, provided it cannot query the challenge itself.