  Barycentric and pairwise quantum Renyi leakages are proposed as two measures
of information leakage for privacy and security analysis in quantum computing
and communication systems. These quantities both require minimal assumptions on
the eavesdropper, i.e., they do not make any assumptions on the eavesdropper's
attack strategy or the statistical prior on the secret or private classical
data encoded in the quantum system. They also satisfy important properties of
positivity, independence, post-processing inequality, and unitary invariance.
The barycentric quantum Renyi leakage can be computed by solving a
semi-definite program and the pairwise quantum Renyi leakage possesses an
explicit formula. The barycentric and pairwise quantum Renyi leakages form
upper bounds on the maximal quantum leakage, the sandwiched quantum
$\alpha$-mutual information, the accessible information, and the Holevo's
information. Furthermore, differentially-private quantum channels are shown to
bound these measures of information leakage. Global and local depolarizing
channels, that are common models of noise in quantum computing and
communication, restrict private or secure information leakage. Finally, a
privacy-utility trade-off formula in quantum machine learning using variational
circuits is developed. The privacy guarantees can only be strengthened, i.e.,
information leakage can only be reduced, if the performance degradation grows
larger and vice versa.
