Confident entanglement detection via separable numerical range
- URL: http://arxiv.org/abs/2107.04365v1
- Date: Fri, 9 Jul 2021 11:14:45 GMT
- Title: Confident entanglement detection via separable numerical range
- Authors: Timo Simnacher, Jakub Czartowski, Konrad Szyma\'nski and Karol
\.Zyczkowski
- Abstract summary: We investigate the joint (separable) numerical range of multiple measurements.
In an experiment, if the confidence region for the obtained data and the separable numerical range are disjoint, entanglement is reliably detected.
We explicitly compute the volume of separable and standard numerical range for two locally traceless two-qubit product observables.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We investigate the joint (separable) numerical range of multiple
measurements, i.e., the regions of expectation values accessible with
(separable) quantum states for given observables. This not only enables
efficient entanglement detection, but also sheds light on the geometry of the
set of quantum states. More precisely, in an experiment, if the confidence
region for the obtained data and the separable numerical range are disjoint,
entanglement is reliably detected. Generically, the success of such an
experiment is more likely the smaller the separable numerical range is compared
to the standard numerical range of the observables measured. We quantify this
relation using the ratio between these two volumes and show that it cannot be
arbitrarily small, giving analytical bounds for any number of particles, local
dimensions as well as number of measurements. Moreover, we explicitly compute
the volume of separable and standard numerical range for two locally traceless
two-qubit product observables, which are of particular interest as they are
easier to measure in practice. Furthermore, we consider typical volume ratios
for generic observables and extreme instances.
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