Quantum-Kaniadakis entropy as a measure of quantum correlations through implicit bounds

• URL: http://arxiv.org/abs/2510.07241v1
• Date: Wed, 08 Oct 2025 17:07:12 GMT
• Title: Quantum-Kaniadakis entropy as a measure of quantum correlations through implicit bounds
• Authors: Narayan S Iyer, Shraddha Sharma,
• Abstract summary: We examine the relationship of negative conditional quantum Kaniadakis entropy ($alpha-$CQKE) with the fully entangled fraction (FEF)<n>FEF is a substantial yardstick for quantum information processing protocols including teleportation, and quantum steerability.<n>We formulate propositions linking negative $alpha-$CQKE to the k-copy steerability of isotropic states for projective measurements.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the present article, we examine the relationship of negative conditional quantum Kaniadakis entropy ($\alpha-$CQKE) with the fully entangled fraction (FEF) which is a substantial yardstick for quantum information processing protocols including teleportation, and quantum steerability, executed over four vital quantum states with maximally mixed marginals, the 2-qubit Werner state, the 2-qubit Weyl state, the 2-qudit Werner state and the isotropic state. We initiate our analysis in 2$\otimes$2 systems where we derive implicit bounds on FEF when the $\alpha-$CQKE takes negative values, i.e. when $\alpha-$CQKE $\in$ $R^{-}$ for 2-qubit Werner state. Consequently, we derive the sufficient implicit bounds for a definitive claim on the non-usefulness of Werner state for quantum teleportation provided its visibility parameter succeeds to elude a critical region, the exception region 1, where the situation becomes inconclusive. Subsequently, we replicate the same for the 2-qubit Weyl state with some constraints augmented by an analogous exception region 2 and the correlation tensor matrix elements. Furthermore, we extend our investigation to d $\otimes$ d states, commencing our analysis with the Isotropic state. We derive implicit bounds on FEF of the Isotropic state and the 2-qudit Werner state resembling the ones in the 2$\otimes$2 analysis. Additionally, we utilize the convoluted relationship between the FEF and quantum steerability to formulate propositions linking negative $\alpha-$CQKE to the k-copy steerability of isotropic states for projective measurements, thereby reducing the intricacy of the study of k-copy steerability directly via FEF. In the appendix section of the article, we provide corroborative calculations and supplementary materials to the theorems presented in the main sections.

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