Additivity violation for the explicit CHLMW pair in the middle-order regime

Investigate whether the explicit pair of trace-preserving quantum channels obtained from the CHLMW subspaces R and the entrywise conjugate subspace \bar S violates minimum output Rényi entropy additivity for any Rényi order p in the interval [1/4,3/4].

Background

The paper constructs a trace-preserving normalization of the explicit CHLMW channel pair associated with six-dimensional subspaces R and \bar S of \mathbb{C}^4\otimes\mathbb{C}^3, and rigorously proves a positive-order additivity violation for every 0<p\leq 1/22. It also summarizes known results establishing violations outside portions of the middle-order range, including results for all 0\leq p\<1/4 and all p\>3/4 using non-explicit constructions, and for all p>1 using explicit constructions.

The unresolved issue identified by the paper is whether this particular explicit CHLMW pair exhibits any minimum output Rényi entropy additivity violation in the middle-order interval [1/4,3/4]. The question concerns the existence of a violation for that explicit pair, rather than the general existence of violations for quantum channels.