Unbounded violation of quantum steering inequality

Quantum steering is a relatively simple test for proving that the values of quantum-mechanical measurement outcomes come into being only in the act of measurement. By exploiting quantum correlations, Alice can influence ( steer ) Bob’s physical system in a way that is impossible in classical mechanics, as shown by the violation of steering inequalities. Demonstrating this and similar quantum effects for systems of increasing size, approaching even the classical limit, is a long-standing challenging problem. Here, we prove an experimentally feasible unbounded violation of a steering inequality. We derive its universal form where tolerance for measurement-setting errors is explicitly built in by means of the Deutsch–Maassen–Uffink entropic uncertainty relation. The method is general and opens the possibility of employing bipartite steering for randomness certification and development of quantum technologies, e.g., random access codes.