A Cryptographic approach to Quantum Metrology.

Summary We derive a general framework for a quantum metrology scheme where the quantum probes are exchanged via an unsecured quantum channel. We construct two protocols for this task which offer a trade-off between difficulty of implementation and efficiency. We show that, for both protocols, a malicious eavesdropper cannot access any information regarding the unknown parameter. We further derive general inequalities regarding how the uncertainty in a resource state for quantum metrology can bias the estimate and the precision. From this, we link the effectiveness of the cryptographic part of the protocol to the effectiveness of the metrology scheme with a (potentially) malicious probe resource state.