Parameter-Free Lower Bounds on Concurrence and Convex-Roof Extended Negativity from Centered Realignment

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.