Measurement-device-independent quantum private queries by rotation-invariant twisted photons

Quantum private query is an important cryptography protocol aiming to protect both user’s and database’s privacy. However, to execute even the simplest quantum private queries, one must establish and maintain a shared reference frame. Here we propose a rotation-invariant Measurement-device-independent quantum private queries with hybrid encoding approach, combined polarization and transverse spatial modes to overcome the polarization misalignment associated with random rotations in long-distance transmission. The initial encoding and final decoding of information in our protocol can be conveniently performed in the polarization space. Furthermore, our hybrid encoding approach only needs to insert four q-plates in practical experiment and to overcome the polarization misalignment problem.