Abstract:
Classical probabilistic models of (noisy) quantum systems are not only
relevant for understanding the non-classical features of quantum mechanics, but
they are also useful for determining the possible advantage of using quantum
resources for information processing tasks. A common feature of these models is
the presence of inaccessible information, as captured by the concept of
preparation contextuality: There are ensembles of quantum states described by
the same density operator, and hence operationally indistinguishable, and yet
in any probabilistic (ontological) model, they should be described by distinct
probability distributions. In this work, we quantify the inaccessible
information of a model in terms of the maximum distinguishability of
probability distributions associated to any pair of ensembles with identical
density operators, as quantified by the total variation distance of the
distributions. We obtain a family of lower bounds on this maximum
distinguishability in terms of experimentally measurable quantities. In the
case of an ideal qubit this leads to a lower bound of, approximately, 0.07.
These bounds can also be interpreted as a new class of robust preparation
non-contextuality inequalities. Our non-contextuality inequalities are phrased
in terms of generalizations of max-relative entropy and trace distance for
general operational theories, which could be of independent interest.
Under sufficiently strong noise any quantum system becomes preparation
non-contextual, i.e., can be described by models with zero inaccessible
information. Using our non-contextuality inequalities, we show that this can
happen only if the noise channel has the average gate fidelity less than or
equal to 1/D(1+1/2+...+1/D), where D is the dimension of the Hilbert space.
Duke University * Arts & Sciences * Physics * Faculty * Staff * Grad * Researchers * Reload * Login
Copyright (c) 2001-2002 by Duke University Physics.