Minimum
entangled state dimension required for pseudo-telepathy
(pp275-284)
Gilles Brassard, Andre A. Methot and
Alain Tapp
doi:
https://doi.org/10.26421/QIC5.45-2
Abstracts:
Pseudo-telepathy provides an intuitive way of looking at Bell's
inequalities, in
which it is often obvious that feats achievable by use of quantum
entanglement would be classically impossible. A~two-player
pseudo-telepathy game proceeds as follows: Alice
and Bob are individually asked a question and
they must provide an answer. They
are \emph{not} allowed any form of communication
once the questions are asked, but they may have
agreed on a common strategy prior to the execution of the game. We~say
that they \emph{win} the game if the questions and answers fulfil
a specific relation. A~game exhibits \emph{pseudo-telepathy} if
there is a quantum strategy that makes Alice and Bob
win the game for all possible questions, provided they
share prior entanglement, whereas it would be impossible to win this
game systematically in a classical setting. In~this
paper, we show that any two-player pseudo-telepathy
game requires the quantum players to share an
entangled quantum system of dimension at least~\mbox{$3 \times 3$}. This
is optimal for two-player games, but the most efficient pseudo-telepathy
game possible, in terms of total dimension, involves \emph{three}
players who share a quantum system of dimension~\mbox{$2
\times 2 \times 2$}.
Key words:
Pseudo-telepathy, entanglement, nonlocality,
Bell's inequaliteis, POV Ms. |