Entanglement of approximate quantum strategies in XOR games
Dimiter Ostrev, Thomas Vidick

TL;DR
This paper constructs specific XOR games demonstrating that achieving near-optimal bias requires a large amount of entanglement, significantly improving previous bounds on entanglement and noise tolerance in quantum self-tests.
Contribution
It introduces XOR games with minimal inputs that require substantial entanglement for near-optimal strategies, advancing understanding of entanglement complexity in quantum games.
Findings
Exponential improvement in input size and noise tolerance over previous self-tests.
Near-optimal strategies require entanglement scaling as \\varepsilon^{-1/5} in the constructed XOR games.
Tight bounds on entanglement needed for \\varepsilon$-optimal strategies in XOR games.
Abstract
We show that for any there is an XOR game with inputs for one player and inputs for the other player such that ebits are required for any strategy achieving bias that is at least a multiplicative factor from optimal. This gives an exponential improvement in both the number of inputs or outputs and the noise tolerance of any previously-known self-test for highly entangled states. Up to the exponent the scaling of our bound with is tight: for any XOR game there is an -optimal strategy using ebits, irrespective of the number of questions in the game.
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