  In quantum theory, a quantum state on a composite system of two parties
realizes a non-negative probability with any measurement element with a tensor
product form. However, there also exist non-quantum states which satisfy the
above condition. Such states are called beyond-quantum states, and cannot be
detected by standard Bell tests. To distinguish a beyond-quantum state from
quantum states, we propose a measurement-device-independent (MDI) test for
beyond-quantum state detection, which is composed of quantum input states on
respective parties and quantum measurements across the input system and the
target system on respective parties. The performance of our protocol is
independent of the forms of the tested states and the measurement operators,
which provides an advantage in practical scenarios. We also discuss the
importance of tomographic completeness of the input sets to the detection.
