Parameter-Free Lower Bounds on Concurrence and Convex-Roof Extended Negativity from Centered Realignment
Year: 2026
Type: article
Abstract: Extended realignment matrices give computable lower bounds on bipartite entanglement measures, but introduce auxiliary parameters whose optimization is generally left numerical. We show that the supremum of the two-parameter realignment excess equals the centered realignment excess associated with the enhanced realignment criterion. Taking its nonnegative part yields parameter-free lower bounds on concurrence and normalized convex-roof extended negativity (CREN). The concurrence bound is exact for pure states with a qubit subsystem, and the CREN bound is exact for all bipartite pure states. Both bounds are tight on isotropic states; these tightness properties are shared with the uncentered realignment bounds rather than new advantages of centering. Mixed two-qubit examples demonstrate both a strict quantitative improvement and a positive centered bound when the uncentered realignment bound vanishes. We also prove that repeated-column, vector, and general auxiliary-block extensions have the same unrestricted optimum within the class considered. A corollary connects the centered excess to an established entanglement-of-formation construction, and its relation to memory-assisted entropic uncertainty methods is discussed. The optimization proof uses trace-norm compression and a matching large-parameter limit.
Source: Entropy
DOI: 10.3390/e28111238
Authors: Jian-Hua Guo, Xiao-Bin Liang
Institution: Shangrao Normal University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7225746051
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