In particular, optimal quantum strategies for XOR games are completely determined by the uncertainty principle alone. This breakthrough result has yielded the fundamental open question whether optimal quantum strategies are always restricted by local uncertainty principles, with entanglement-based steering playing no role. In a work published in Nature communication, we provide a negative answer to the question, showing that both steering and uncertainty relations play a fundamental role in determining optimal quantum strategies for non-local games. Our theoretical findings are confirmed by an experimental implementation with entangled photons.
Quantum non-locality, precisely the lack of a local realistic description of nature, can be understood as the advantage that a set of parties have when executing common tasks (Bell Inequalities) and using resources from quantum mechanics instead of classical mechanics. It has been recently proven that the optimal strategies for any non-local task are a consequence of two effects: the ability of parties to steer quantum states at a distance and the strength of local uncertainty relations. Quite surprisingly, the complete dominance of the uncertainty relation in determining the optimal strategy has been observed for a large class of non-local tasks.
A breakthrough result in [Science, vol. 330, no. 6007, 1072 (2010)] paraphrased in the title of that paper as "The uncertainty principle determines the non-locality of quantum mechanics". In that paper a fundamental question whether the two foundational pillars of quantum mechanics, namely its non-local correlations and local uncertainty principle, are always in such inextricable quantitative correspondence with each other. In this paper, we provide - both theoretically and experimentally - an answer to this question. We show a non-local task, for which the full dominance of the uncertainty relation in determining the optimal quantum strategy would lead to the violation of the Einstein rule of no superluminal signaling. We prove that this task has the so called self-testing property (a unique quantum state and measurements up to unitaries are necessary for its optimal violation) which allows us to test the claim experimentally. The corresponding quantum optical experiment performed using entangled quantum photons rules out the uncertainty relation supremacy in determining the optimal quantum strategy for the task.
The experimental work was implemented by Sadiq Muhammad, Marcus Grünfeld, and Mohamed Bourennane at Fysikum, Stockholm University. The theoretical part was performed by Ravishankar Ramanathan, Dardo Goyeneche, Piotr Mironowicz , and Paweł Horodecki from National Quantum Information Centre, Gdasnk, Poland.
This work has been published in:R. Ramanathan, D. Goyeneche , S. Muhammad, P. Mironowicz, M. Grünfeld, M. Bourennane, and P. Horodecki, Steering is an essential feature of non-locality in quantum theory, DOI: 10.1038/s41467-018-06255-5
