Quantitative Nonclassicality of Mediated Interactions

Authors:
raw_author_name: Ray Ganardi
raw_affiliation_string: Centre for Quantum Optical Technologies, Centre of New Technologies, University of Warsaw, Warsaw 02-097, Poland; Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk 80-308, Poland
raw_author_name: Ekta Panwar
raw_affiliation_string: Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk 80-308, Poland
raw_author_name: Mahasweta Pandit
raw_affiliation_string: Departamento de Física, Universidad de Murcia, Murcia E-30071, Spain; Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk 80-308, Poland
raw_author_name: Bianka Woloncewicz
raw_affiliation_string: Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk 80-308, Poland; Quantum Research Center, Technology Innovation Institute, Masdar City, Abu Dhabi, United Arab Emirates
raw_author_name: Tomasz Paterek
raw_affiliation_string: Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk 80-308, Poland; School of Mathematics and Physics, Xiamen University Malaysia, Sepang 43900, Malaysia

Abstract: In a plethora of physical situations, one can distinguish a mediator—a system that couples other, noninteracting, systems. Often, the mediator itself is not directly accessible to experimentation, yet it is interesting and sometimes crucial to understand if it admits nonclassical properties. An example of this sort that has recently been enjoying considerable attention is that of two quantum masses coupled via a gravitational field. It has been argued that the gain of quantum entanglement between the masses indicates nonclassicality of the states of the whole tripartite system. Here, we focus on the nonclassical properties of the involved interactions rather than the states. We derive inequalities the violation of which indicates noncommutativity and nondecomposability (open-system generalization of noncommuting unitaries) of interactions through the mediators. The derivations are based on properties of general quantum formalism and make minimalistic assumptions about the studied systems; in particular, the interactions can remain uncharacterized throughout the assessment. Furthermore, we also present conditions that solely use correlations between the coupled systems, excluding the need to measure the mediator. Next, we show that the amount of violation places a lower bound on suitably defined degree of nondecomposability. This makes the methods quantitative and at the same time experiment ready. We give applications of these techniques in two different fields: for detecting the nonclassicality of gravitational interaction and in bounding the Trotter error in quantum simulations.Received 24 March 2023Accepted 30 November 2023DOI:https://doi.org/10.1103/PRXQuantum.5.010318Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum correlations, foundations & formalismQuantum foundationsQuantum information theoryQuantum Information, Science & Technology