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Measurement-Device-Independent Detection of Beyond-Quantum State

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.