TY - JOUR
T1 - Complementary contributions of indeterminism and signaling to quantum correlations
AU - Hall, Michael J.W.
PY - 2010/12/28
Y1 - 2010/12/28
N2 - Simple quantitative measures of indeterminism and signaling, I and S, are defined for models of statistical correlations. It is shown that any such model satisfies a generalized Bell-type inequality, with tight upper bound B(I,S). This upper bound explicitly quantifies the complementary contributions required from indeterminism and signaling, for modeling any given violation of the standard Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. For example, all models of the maximum quantum violation must either assign no more than 80% probability of occurrence to some underlying event, and/or allow a nonlocal change of at least 60% in an underlying marginal probability of one observer in response to a change in measurement setting by a distant observer. The results yield a corresponding complementarity relation between the numbers of local random bits and nonlocal signaling bits required to model a given violation. A stronger relation is conjectured for simulations of singlet states. Signaling appears to be a useful resource only if a "gap" condition is satisfied, corresponding to being able to nonlocally flip some underlying marginal probability p to its complementary value 1-p.
AB - Simple quantitative measures of indeterminism and signaling, I and S, are defined for models of statistical correlations. It is shown that any such model satisfies a generalized Bell-type inequality, with tight upper bound B(I,S). This upper bound explicitly quantifies the complementary contributions required from indeterminism and signaling, for modeling any given violation of the standard Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. For example, all models of the maximum quantum violation must either assign no more than 80% probability of occurrence to some underlying event, and/or allow a nonlocal change of at least 60% in an underlying marginal probability of one observer in response to a change in measurement setting by a distant observer. The results yield a corresponding complementarity relation between the numbers of local random bits and nonlocal signaling bits required to model a given violation. A stronger relation is conjectured for simulations of singlet states. Signaling appears to be a useful resource only if a "gap" condition is satisfied, corresponding to being able to nonlocally flip some underlying marginal probability p to its complementary value 1-p.
UR - http://www.scopus.com/inward/record.url?scp=78650985686&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.82.062117
DO - 10.1103/PhysRevA.82.062117
M3 - Article
SN - 1050-2947
VL - 82
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 6
M1 - 062117
ER -