Author

B. Lovitz

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Preprint Sep 2026

PPT states of almost maximal Schmidt number

We construct PPT states on $\mathbb{C}^m \otimes\mathbb{C}^n$ that have Schmidt number asymptotically approaching the smaller local dimension. More specifically, we construct a PPT state with Schmidt number at least $$ \left\lceil \frac{m + n - ((m - n)^2 + 4(m + n - 1))^{1/2}}{2} \right\rceil. $$ In the case of equal...

Nathaniel Johnston, B. Lovitz · 1 citation

Preprint Aug 2026

Superadditivity of classical communication over quantum channels via random and deterministic permutations

The main observation of this work is that Haar randomness can be replaced by random permutations without changing the limiting geometry responsible for nonadditivity, and this replacement turns a continuous problem over unitary matrices into a discrete combinatorial problem over zero--one permutation matrices, and ther...

B. Lovitz, Peixue Wu · 2 citations