A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations
A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations
We describe a two-player non-local game, with a fixed small number of questions and answers, such that an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ϵ</mml:mi></mml:math>-close to optimal strategy requires an entangled state of dimension <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mn>2</mml:mn><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>ϵ</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>/</mml:mo></mml:mrow><mml:mn>8</mml:mn></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:math>. Our non-local game is inspired by the three-player non-local game of Ji, Leung …