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Article overview
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Near-Optimal and Explicit Bell Inequality Violations | | Harry Buhrman
; Oded Regev
; Giannicola Scarpa
; Ronald de Wolf
; | | Date: |
22 Dec 2010 | | Abstract: | Bell inequality violations correspond to behavior of entangled quantum
systems that cannot be simulated classically. We give two new two-player games
with Bell inequality violations that are stronger, fully explicit, and arguably
simpler than earlier work.
The first game is based on the Hidden Matching problem of quantum
communication complexity, introduced by Bar-Yossef, Jayram, and Kerenidis. This
game can be won with probability~1 by a quantum strategy using a maximally
entangled state with local dimension $n$ (e.g., $log n$ EPR-pairs), while we
show that the winning probability of any classical strategy differs from 1/2 by
at most $O(log n/sqrt{n})$.
The second game is based on the integrality gap for Unique Games by Khot and
Vishnoi and the quantum rounding procedure of Kempe, Regev, and Toner. Here
$n$-dimensional entanglement allows to win the game with probability $1/(log
n)^2$, while the best winning probability without entanglement is $1/n$. This
near-linear ratio ("Bell inequality violation") is near-optimal, both in terms
of the local dimension of the entangled state, and in terms of the number of
possible outputs of the two players. | | Source: | arXiv, 1012.5043 | | Services: | Forum | Review | PDF | Favorites | |
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