Entangled games do not require much entanglement (withdrawn)

TL;DR

This paper establishes a tight upper bound on the entanglement needed for strategies in two-player games with classical questions and quantum answers, showing that such strategies require only a linear amount of entanglement, which simplifies their analysis.

Contribution

It provides the first explicit upper bound on the entanglement needed for strategies in these games, demonstrating that the required entanglement is linear in the question size and making the problem computationally more tractable.

Findings

Entanglement needed is at most 5n qubits for n-bit questions.

The bound is optimal within a factor of 5/2.

Computing the game value is in NP due to the entanglement bound.

Abstract

We prove an explicit upper bound on the amount of entanglement required by any strategy in a two-player cooperative game with classical questions and quantum answers. Specifically, we show that every strategy for a game with n-bit questions and n-qubit answers can be implemented exactly by players who share an entangled state of no more than 5n qubits--a bound which is optimal to within a factor of 5/2. Previously, no upper bound at all was known on the amount of entanglement required even to approximate such a strategy. It follows that the problem of computing the value of these games is in NP, whereas previously this problem was not known to be computable.