The Rényi coherent information is a family of computable quantities frequently used as stand-ins for the von Neumann coherent information when studying mixed-state phases of matter and error-correction thresholds in noisy quantum codes. Because it is defined as a difference of two Rényi entropies rather than a direct generalization of a single quantity, it has lacked a guarantee of monotonicity in the Rényi index and has carried no clear operational interpretation. This unreviewed arXiv preprint, not yet peer-reviewed, addresses both gaps specifically for stabilizer codes.
On the monotonicity side, the authors prove that for Pauli noise arising from independent Bernoulli processes, the Rényi-n coherent information is nondecreasing in the positive-integer index n. The result follows from a general combinatorial theorem: when independent random bits are mapped linearly to a fine label and a coarse label, the corresponding Rényi entropy difference is nondecreasing in n. The stabilizer-code case maps naturally onto this structure via the syndrome and the joint syndrome–logical class, and the theorem extends to classical linear codes and detector error models as well.
On the operational side, for arbitrary stochastic Pauli noise the authors show that the Rényi-n coherent information acquires a concrete meaning through postselection: one requires syndrome agreement across a data block and n−1 auxiliary blocks. They characterize precisely when this postselection defines a valid quantum channel, establish that saturation of the Rényi-n coherent information is equivalent to asymptotically perfect recovery of the postselected channel, and prove that it upper-bounds the ordinary coherent information achievable by any syndrome-conditioned recovery. These results, if confirmed, would place the use of Rényi coherent information as a diagnostic for decodability transitions on firmer theoretical footing.