Quantum

Integral zeros of Krawtchouk polynomials and quantum entanglements

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 09/11/2026, 05:13:24 UTC.

Briefings

A 2026 paper resolves integral zeros of Krawtchouk polynomials for three asymmetric families of parameters, linking these mathematical properties to quantum information theory. The study settled the symmetric case previously raised by Heo and Kiem (2019) and extended the solution to specific asymmetric configurations involving quadratic and linear functions of a variable t or s. The remaining cases for higher m values are identified as sporadic zeros with finite counts.

Key points

• The paper solves the integral zeros problem for three asymmetric families of Krawtchouk polynomials parametrized by quadruples (m,n,k,l) where m<=n and k<=l, extending previous work by Heo and Kiem (2019).
• Specific families solved include (m,n,k,l)=(3,t^2-1,t(t-1)/2,t(t+1)/2) for t>=2, (m,n,k,l)=(4,3t^2+2t-1,(3t^2-t)/2,(3t^2+5t+2)/2) for t>=2, and (m,n,k,l)=(4,3s^2+4s,(3s^2+s)/2,(3s^2+7s+4)/2) for s>=1.

Context

This research connects discrete mathematics with quantum information theory by determining conditions for integral zeros of Krawtchouk polynomials, which relate to subspaces satisfying range criteria. The findings provide a complete classification for specific parameter families previously raised as open problems.

Limitations

The study covers only three specific asymmetric families of Krawtchouk polynomial zeros; remaining cases for m>=5 are identified as sporadic zeros with finite counts. The paper is a preprint (arXiv:2611.08518v1) from November 2026, and the specific numerical values for the sporadic zeros are not fully enumerated in the provided evidence.

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