Controlled quantum secure remote sensing

Abstract: Quantum resources enable secure quantum sensing (SQS) of remote systems, offering significant advantages in precision and security. However, decoherence in the quantum communication channel and during the evolution of quantum states can erode these advantages. In this work, we first propose a general $N-$particle scheme that achieves Heisenberg-limited (HL) scaling for single-parameter estimation in the presence of an ideal quantum communication channel and encoding scenario. For non-ideal dynamics, we introduce a modified protocol incorporating local quantum optimal control (QOC) operations to address noise in SQS under generalized Pauli dephasing and parallel dephasing noise. We analyze two distinct scenarios: a noiseless communication channel with noisy evolution, and a noisy communication channel with noisy evolution. For the noisy channel, we model the link between the communicating parties as a depolarizing channel. The protocol leverages QOC operations to actively mitigate noise, enhancing the achievable quantum Fisher information (QFI) and the classical Fisher information (CFI) based on the chosen measurement strategy.