[quantum-info] Colloquium Institute for Quantum Computing Monday, 9 June 2014 at 2:30PM QNC 1506

[Matthew Fries]

Colloquium

Institute for Quantum Computing

Monday, 9 June 2014 at 2:30PM

QNC 1506

Unbounded entanglement can be needed to achieve the optimal success probability

Laura Mancinska

Centre for Quantum Technologies, Singapore

Quantum entanglement is known to provide a strong advantage in many two-party distributed tasks. We investigate the question of how much entanglement is needed to reach optimal performance. For the first time we show that there exists a purely classical scenario for which no finite amount of entanglement suffices. To this end we introduce a simple two-party nonlocal game $H$, inspired by Hardy's paradox. In our game each player has only two possible questions and can provide bit strings of any finite length as answer. We exhibit a sequence of strategies which use entangled states in increasing dimension $d$ and succeed with probability $1-O(d^{-c})$ for some $c\geq 0.13$. On the other hand, we show that any strategy using an entangled state of local dimension $d$ has success probability at most $1-\Omega(d^{-2})$. In addition, we show that any strategy restricted to producing answers in a set of cardinality at most $d$ has success probability at most $1-\Omega(d^{-2})$. (This is joint work with Thomas Vidick.)