# Semi-device-independent bounds on entanglement

@article{Liang2011SemideviceindependentBO, title={Semi-device-independent bounds on entanglement}, author={Yeong-Cherng Liang and Tam{\'a}s V{\'e}rtesi and Nicolas Brunner}, journal={Physical Review A}, year={2011}, volume={83}, pages={022108} }

Detection and quantification of entanglement in quantum resources are two key steps in the implementation of various quantum-information processing tasks. Here, we show that Bell-type inequalities are not only useful in verifying the presence of entanglement but can also be used to bound the entanglement of the underlying physical system. Our main tool consists of a family of Clauser-Horne-like Bell inequalities that cannot be violated maximally by any finite-dimensional maximally entangled…

## 53 Citations

Device-independent entanglement quantification and related applications.

- Computer SciencePhysical review letters
- 2013

It is shown that the method presented provides a rigorous way to construct dimension witnesses, gives new insights into the question whether bound entangled states can violate a Bell inequality, and can be used to construct device-independent entanglement witnesses involving an arbitrary number of parties.

Semi-device-independent characterization of multipartite entanglement of states and measurements

- PhysicsPhysical Review A
- 2018

The semi-device-independent framework allows one to draw conclusions about properties of an unknown quantum system under weak assumptions. Here we present a semi-device-independent scheme for the…

Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth.

- Computer SciencePhysical review letters
- 2015

We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities…

Linking entanglement detection and state tomography via quantum 2-designs

- PhysicsNew Journal of Physics
- 2019

An experimentally feasible and efficient method for detecting entangled states with measurements that extend naturally to a tomographically complete set, and is twice as effective as standard witnesses in the sense that both upper and lower bounds can be derived.

Geometrical self-testing of partially entangled two-qubit states

- MathematicsNew Journal of Physics
- 2020

It is shown that, when a set of correlators in the simplest Bell scenario satisfies a condition, the geometry of the state vectors is uniquely determined, and a geometrical scheme for self-testing is superior in that a realization with an arbitrary number of measurements can be self-tested.

Entanglement estimation from Bell inequality violation

- Physics
- 2013

It is well known that the violation of Bell’s inequality in the form given by Clauser, Horne, Shimony, and Holt (CHSH) in two-qubit systems requires entanglement, but not vice versa, i.e., there are…

Characterization of quantum correlations with local dimension constraints and its device-independent applications

- Mathematics, Computer Science
- 2013

This work characterize quantum nonlocality under local dimension constraints via a complete hierarchy of semidefinite programming relaxations and derives a Bell-type inequality that can only be violated when each of the three parties has local dimension greater than two.

Bell scenarios in which nonlocality and entanglement are inversely related

- Mathematics
- 2014

We show that for two-qubit chained Bell inequalities with an arbitrary number of measurement settings, nonlocality and entanglement are not only different properties but are inversely related.…

The Essence of More Nonlocality with Less Entanglement in Bell Tests

- Physics
- 2014

In this paper, we will explore the essence of the phenomenon that state with less entanglement may generate greater Bell violation in the two-qubit Bell tests with CH-type inequalities, i.e., more…

Optimization of device-independent witnesses of entanglement depth from two-body correlators

- Computer SciencePhysical Review A
- 2019

The problem of finding the $k$-producible bounds of such DIWEDs under different assumptions is considered, not surprisingly, with the weakest assumptions, only for a relatively small number of parties; however, one can still learn interesting features from these solutions that motivate the search on larger systems under the assumption that these features persist.

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