The
mathematical descriptions of joint probability distributions
of measure-
ment
outcomes occurring in quantum mechanics are very different.
Two local
measurements
on different subsystems are described by observables of
tensor
product
form on a common tensor Hilbert space (two-systems
correlations).
Two
measurements on the same system with an intermediate
dynamical evolu-
tion are
described by a state update rule, trace-preserving
completely positive
maps and
observables without a tensor product form (two-times
correlations).
Two-systems
correlations are restricted by Tsirelson’s bound. One might
ask if
Tsirelson’s
bound can also be used to find restrictions on two-times
correlations.
This
thesis partially answers this question. Tsirelson’s bound is
combined
with an
extended version of the Choi-Jamiolkowski Isomorphism, the
Leifer
Isomorphism,
which shows an equivalence between two-systems and two-times
correlations.
It is shown that Tsirelson’s bound, together with the Leifer
Iso-
morphism,
implies a tight bound on the average success probability of
a special
type of
(2, 1, p)-Random
Access Codings (RACs). RACs can be realised using
two-systems
correlations as well as two-times correlations, which allows
a com-
parison of
the two cases. An attempt to interpret the analogue of the
locality
condition
in the case of two-times correlations is made. It is found
that two-
times
correlations used to realise this special type of (2, 1, p)-RAC
cannot be
used to
communicate, as is the case for two-systems correlations.
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