On Nonlocality and Incompatibility Breaking Channels

Swati Kumari^1*, Javid Naikoo², Sibashish Ghosh³, A. K. Pan⁴

¹Department of Physics and QFort, National Cheng Kung University, Tainan, Taiwan, Tainan City, Taiwan
²Center for Quantum optical Technologies, Center of New Technologies, University of Warsav, Warsav, Poland
³Departmant of mathematical Sciences, The Institute of Mathematical Sciences, Chennai, India
⁴Department of Physics, National Institute of Technology, Patna, India

* Presenter:Swati Kumari, email:swatipandey10@gs.ncku.edu.tw

Incompatibility and nonlocality are not only of foundational interest but also acts as a potential resource in quantum information theory. The equivalency for a pair of dichotomic incompatible observables and Bell nonlocality is already known. Here, we investigate these notions in the context of quantum channels, the completely positive and trace preserving maps. In this direction, we prove that in Bell CHSH scenario, the conjugate channels corresponding to the incompatibility breaking channels are themselves nonlocality breaking and vice versa. Further, we investigate this relation in tripartite scenario, where some well-known three qubits states viz., GHZ and maximally slice states are used to illustrate this equivalence by studying Svetlichny nonlocality and identifying the range of state and channel parameters for which incompatibility does coexist with nonlocality. We thus establish an equivalency between CHSH nonlocality and incompatibility breaking channel, which also follows from some states in tripartite scenario within certain range of state parameter.

Keywords: Bell Inequality, Quantum Channel, Incompatibility Breaking Channel, Nonlocality Breaking Channel