In this work, we study a particular class of Bell inequalities involving only direct equality-comparisons of outcomes. In the bipartite case, the scenario can be interpreted as a natural generalization of full-correlator in- equalities (XOR games) beyond binary outputs. We define the sub-polytope of the local polytope corresponding to this scenario and solve it for several bipartite and multipartite scenarios by leveraging some structural prop- erties. In doing so, we obtain thousands of new tight inequalities, many of which are also facets of the standard local polytope. We also define unanimous Bell inequalities, a particular case of the previous class applied to the multipartite setting in which only full-equality events (all outcomes equal) are considered. We show that such inequalities can always be written as deterministic nonlocal games, and we give a simple multipartite unanimous family and prove its local bound. We show that most of these inequalities admit quantum violations, and we also display aspects of their importance for nonlocality. For instance, we identify examples where such inequalities can act as dimension witnesses, outcome witnesses, witnesses of genuine multipartite nonlocality, as well as being relevant to CHSH. These results show that these simple and elegant inequalities by themselves provide a powerful tool for discovering new Bell inequalities and device-independent witnesses.In this work, we study a particular class of Bell inequalities involving only direct equality-comparisons of outcomes. In the bipartite case, the scenario can be interpreted as a natural generalization of full-correlator in- equalities (XOR games) beyond binary outputs. We define the sub-polytope of the local polytope corresponding to this scenario and solve it for several bipartite and multipartite scenarios by leveraging some structural prop- erties. In doing so, we obtain thousands of new tight inequalities, many of which are also facets of the standard local polytope. We also define unanimous Bell inequalities, a particular case of the previous class applied to the multipartite setting in which only full-equality events (all outcomes equal) are considered. We show that such inequalities can always be written as deterministic nonlocal games, and we give a simple multipartite unanimous family and prove its local bound. We show that most of these inequalities admit quantum violations, and we also display aspects of their importance for nonlocality. For instance, we identify examples where such inequalities can act as dimension witnesses, outcome witnesses, witnesses of genuine multipartite nonlocality, as well as being relevant to CHSH. These results show that these simple and elegant inequalities by themselves provide a powerful tool for discovering new Bell inequalities and device-independent witnesses.

quant-pharXiv:2603.17030Physical Review AMar 19, 20260 citations

Witnessing Genuine Multipartite Entanglement with Positive Maps

Marcus Huber, Ritabrata Sengupta

We derive a general framework that lifts any set of bipartite to multipartite entanglement witnesses and we show how positive maps can naturally be incorporated into this framework. We show that some previous approaches for multipartite entanglement detection are intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by nondecomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.We derive a general framework that lifts any set of bipartite to multipartite entanglement witnesses and we show how positive maps can naturally be incorporated into this framework. We show that some previous approaches for multipartite entanglement detection are intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by nondecomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.

arXiv:1404.7449Physical Review LettersSep 2, 2014105 citations

Universal methods for extending any entanglement witness from the bipartite to the multipartite case

Bang-Hai Wang, Hai-Ru Xu, Simone Severini B

Any bipartite entanglement witness $W$ can be written as $W={c}_{\ensuremath{\sigma}}I\ensuremath{-}\ensuremath{\sigma}$, where $\ensuremath{\sigma}$ is a quantum state, $I$ is the identity matrix, and ${c}_{\ensuremath{\sigma}}$ is a non-negative number. We present a general method to extend the given entanglement witness to multipartite cases via purification, partial purification, and direct tensor of the quantum state $\ensuremath{\sigma}$. Our methods extend $\ensuremath{\sigma}$ but leave the parameter ${c}_{\ensuremath{\sigma}}$ untouched. This is very valuable since the parameter is generally not easy to compute.Any bipartite entanglement witness $W$ can be written as $W={c}_{\ensuremath{\sigma}}I\ensuremath{-}\ensuremath{\sigma}$, where $\ensuremath{\sigma}$ is a quantum state, $I$ is the identity matrix, and ${c}_{\ensuremath{\sigma}}$ is a non-negative number. We present a general method to extend the given entanglement witness to multipartite cases via purification, partial purification, and direct tensor of the quantum state $\ensuremath{\sigma}$. Our methods extend $\ensuremath{\sigma}$ but leave the parameter ${c}_{\ensuremath{\sigma}}$ untouched. This is very valuable since the parameter is generally not easy to compute.

arXiv:1405.2021Physical Review AAug 13, 20143 citations

Any bipartite entanglement witness

W

can be written as $W={c}_{\ensuremath{\sigma}}I\ensuremath{-}\ensuremath{\sigma}$, where $\ensuremath{\sigma}$ is a quantum state,

I

is the identity matrix, and ${c}_{\ensuremath{\sigma}}$ is a non-negative number. We present a general method to extend the given entanglement witness to multipartite cases via purification, partial purification, and direct tensor of the quantum state $\ensuremath{\sigma}$. Our methods extend $\ensuremath{\sigma}$ but leave the parameter ${c}_{\ensuremath{\sigma}}$ untouched. This is very valuable since the parameter is generally not easy to compute.