Abstract
Inferring the underlying physical state of a system from measurement results is a fundamental task in physics. Remarkably, quantum mechanics enables the strongest form of inference: there exist states known to be fully characterized (up to local transformations) by their measurement statistics alone. This is known as self-testing. Self-testing was first demonstrated for the EPR pair and was more recently extended to all two-particle states. However, the question of whether an arbitrary quantum state can be self-tested, and up to which transformations, is a long-standing open question. In this letter, we answer it affirmatively by providing explicit self-testing correlations for all quantum states. Doing so, we show that local unitary transformations and global complex conjugation are the unique unobservable transformations in the device-independent setting of quantum information. Our protocol requires the preparation of a number of distributed EPR pairs that scales linearly with the number of particles, and the implementation of standard projective and Bell state measurements. Our work thus marks the first experimentally feasible protocol for arbitrary state certification in the future quantum internet.
