93 research outputs found
Sequential random access codes and self-testing of quantum measurement instruments
Quantum Random Access Codes (QRACs) are key tools for a variety of protocols
in quantum information theory. These are commonly studied in
prepare-and-measure scenarios in which a sender prepares states and a receiver
measures them. Here, we consider a three-party prepare-transform-measure
scenario in which the simplest QRAC is implemented twice in sequence based on
the same physical system. We derive optimal trade-off relations between the two
QRACs. We apply our results to construct semi-device independent self-tests of
quantum instruments, i.e. measurement channels with both a classical and
quantum output. Finally, we show how sequential QRACs enable inference of upper
and lower bounds on the sharpness parameter of a quantum instrument
Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
We present a technique for reducing the computational requirements by several
orders of magnitude in the evaluation of semidefinite relaxations for bounding
the set of quantum correlations arising from finite-dimensional Hilbert spaces.
The technique, which we make publicly available through a user-friendly
software package, relies on the exploitation of symmetries present in the
optimisation problem to reduce the number of variables and the block sizes in
semidefinite relaxations. It is widely applicable in problems encountered in
quantum information theory and enables computations that were previously too
demanding. We demonstrate its advantages and general applicability in several
physical problems. In particular, we use it to robustly certify the
non-projectiveness of high-dimensional measurements in a black-box scenario
based on self-tests of -dimensional symmetric informationally complete
POVMs.Comment: A. T. and D. R. contributed equally for this projec
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