Effects of reduced measurements independence on self-testing

Self-testing, which refers to device independent characterization of the state and the measurement, has been intensively studied in quantum information theory. One of the implicit assumptions in self-testing theorem is, measurement settings should be chosen randomly and independently by each party. The relaxation of this assumption potentially gives untrusted device providers the power to control the device with no quantum feature, even fake the quantum behavior by using the classical strategies within the device. In this paper, we analyze the effects of the reduced measurements independence on self-testing two-qubit entangled states based on the violation of Bell inequalities. By assuming adversary's capabilities, we show to achieve the maximum CHSH violation in this case, four different state-measurements preparations should be provided. Without run information one could not really self-test the underlying system in each run anymore, but it must be equal with one of four entangled systems up to local unitaries.

Automated summary

This paper investigates the effects of reduced measurements independence on self-testing, and finds that it allows device providers to control the device and fake quantum behavior.