Quantum steering ellipsoids and quantum obesity in critical systems

¹ Departamento de Física, Universidade Federal de São Carlos - Rodovia Washington Luís, km 235 - SP-310, 13565-905 São Carlos, SP, Brazil
² CESQ/ISIS (UMR 7006), CNRS and Université de Strasbourg - 67000, Strasbourg, France
³ Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas - Calle Serrano 113b, 28006 Madrid, Spain

Received: 23 September 2024
Accepted: 6 November 2024

Abstract

Quantum obesity (QO) is a novel function introduced to quantify quantum correlations that go beyond traditional measures like entanglement, while also functioning as an entanglement witness. One of the key strengths of QO lies in its analyticity for arbitrary states of bipartite systems, making it a more accessible and versatile tool compared to other measures of quantum correlations, such as quantum discord. In this work, we highlight the importance of QO as a fundamental quantity for identifying signatures of quantum phase transitions, which are critical changes in the ground state of quantum systems driven by quantum fluctuations. We introduce a mechanism based on local filtering operations designed to enhance the critical behavior of QO near phase transition points, providing a deeper understanding of these phenomena. Furthermore, we present a theorem that characterizes how QO transforms under local quantum operations and classical communications (LOCC), which broadens its applicability to a wider range of quantum systems. This opens new avenues for exploring quantum criticality and other novel quantum phenomena by leveraging the analytically computable, pairwise QO, thus offering both theoretical insights and practical applications in quantum information science.