  Local simultaneous state discrimination (LSSD) is a recently introduced
problem in quantum information processing. Its classical version is a non-local
game played by non-communicating players against a referee. Based on a known
probability distribution, the referee generates one input for each of the
players and keeps one secret value. The players have to guess the referee's
value and win if they all do so. For this game, we investigate the advantage of
no-signalling strategies over classical ones. We show numerically that for
three players and binary values, no-signalling strategies cannot provide any
improvement over classical ones. For a certain LSSD game based on a binary
symmetric channel, we show that no-signalling strategies are strictly better
when multiple simultaneous instances of the game are played. Good classical
strategies for this game can be defined by codes, and good no-signalling
strategies by list-decoding schemes. We expand this example game to a class of
games defined by an arbitrary channel, and extend the idea of using codes and
list decoding to define strategies for multiple simultaneous instances of these
games. Finally, we give an expression for the limit of the exponent of the
classical winning probability, and show that no-signalling strategies based on
list-decoding schemes achieve this limit.

Quantum Physics