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arXiv:2408.02258 · Quantum Information Processing

On fully entangled fraction and quantum conditional entropies for states with maximally mixed marginals

Komal Kumar, Indranil Chakrabarty, Nirman Ganguly

Published Mar 6, 2025• 2 citations
arXivHTMLPDF
DOI
10.1007/s11128-025-04695-9

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In this paper, we examine the relationship of negative conditional quantum Kaniadakis entropy ([Formula: see text]-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⊗2 systems, where we derive implicit bounds on FEF when the [Formula: see text]-CQKE takes negative values, i.e. when [Formula: see text]-CQKE [Formula: see text] for 2-qubit Werner state. Consequently, we derive the sufficient implicit bounds for a definitive claim on the nonusefulness 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 [Formula: see text] 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 [Formula: see text] analysis. Additionally, we utilize the convoluted relationship between the FEF and quantum steerability to formulate propositions linking negative [Formula: see text]-CQKE to the [Formula: see text]-copy steerability of isotropic states for projective measurements, thereby reducing the intricacy of the study of [Formula: see text]-copy steerability directly via FEF. In the appendix section of this paper, we provide corroborative calculations and supplementary materials to the theorems presented in the main sections.