Interplay of nonlocality and incompatibility breaking qubit channels

Abstract

Incompatibility and nonlocality are not only of foundational interest but also act as important resources for quantum information theory. In the Clauser-Horne-Shimony-Holt (CHSH) scenario, the incompatibility of a pair of observables is known to be equivalent to Bell nonlocality. Here, we investigate these notions in the context of qubit channels. The Bell-CHSH inequality has a greater perspective--compared to any genuine tripartite nonlocality scenario--while determining the interplay between nonlocality breaking qubit channels and incompatibility breaking qubit channels. In the Bell-CHSH scenario, we prove that if the conjugate of a channel is incompatibility breaking, then the channel is itself nonlocality breaking and vice versa. However, this equivalence is not straightforwardly generalized to multipartite systems, due to the absence of an equivalence relation between incompatibility and nonlocality in the multipartite scenario. We investigate this relation in the tripartite scenario by considering some well-known states like Greenberger-Horne-Zeilinger and $W$ states and using the notion of Mermin and Svetlichny nonlocality. By subjecting the parties in question to unital qubit channels, we identify the range of state and channel parameters for which incompatibility coexists with nonlocality. Further, we identify the set of unital qubit channels that is Mermin or Svetlichny nonlocality breaking irrespective of the input state.

References in corpus (4)

• Tripartite entanglement versus tripartite nonlocality in 3-qubit GHZ-class states
• Incompatibility of quantum channels
• Complete classification of steerability under local filters and its relation with measurement incompatibility
• Tight upper bound for the maximal quantum value of the Svetlichny operators

Cited by in corpus (3)

• Tight upper bound for the maximal expectation value of the $N$-partite generalized Svetlichny operator
• The transfer of nonlocality between two- and three-qubit dissipative systems with counter-rotating-wave terms
• Quantum Zeno Effect on Genuine Tripartite Nonlocality and Entanglement in Quantum Dissipative System