Monogamy relations of entropic non-contextual inequalities and their experimental demonstration

¹ Department of Physical Sciences, Indian Institute of Science Education & Research Mohali, Sector 81 SAS Nagar Manauli PO 140306, Punjab, India
² Departamento de Física Aplicada II, Universidad de Sevilla - E-41012, Sevilla, Spain
³ Vice Chancellor, Punjabi University Patiala - 147002, Punjab, India

^(a) E-mail: dileepsingh@iisermohali.ac.in
^(b) E-mail: jaskaran@us.es (corresponding author)
^(c) E-mail: kavita@iisermohali.ac.in
^(d) E-mail: arvind@iisermohali.ac.in

Received: 13 January 2023
Accepted: 26 May 2023

Abstract

We analyze monogamous relationships of abritrary entropic non-contextuality (ENC) inequalities via a graph theoretic approach. While ENC inequalities are important in quantum information theory, a theoretical and experimental understanding of their monogamous nature is still elusive. We analyze conditions for ENC inequalities to exhibit a monogamous relationship and derive the same explicitly for an entropic version of the Bell-CHSH scenario. Next, we consider two different sets of three qubit states and experimentally show that they exhibit monogamy of entropic Bell-CHSH inequality. The monogamous relationship of these inequalities is theoretically exhibited via an insightful proof and is experimentally demonstrated on an NMR quantum information processor. We also develop a novel and easy-to-implement experimental method to evaluate entropies on an NMR quantum information processor using only the information about expectation values of the observables.