Quantum networks self-test all entangled states

Certifying quantum properties with minimal assumptions is a fundamental problem in quantum information science. Self-testing is a method to infer the underlying physics of a quantum experiment only from the measured statistics 1 , 2 . Although all bipartite pure entangled states can be self-tested 3 , little is known about how to self-test quantum states of an arbitrary number of systems. Here we introduce a framework of network-assisted self-testing and use it to self-test any pure entangled quantum state of an arbitrary number of systems. The scheme requires the preparation of a number of singlets that scales linearly with the number of systems, and the implementation of standard projective and Bell measurements, all feasible with current technology 4 . When all the network constraints are exploited, the obtained self-testing certification is stronger than what is achievable in any Bell-type scenario. Our work shows how properly designed networks offer new opportunities for the certification of quantum phenomena.