13 citations · 66 across the 21 of their papers we have counts for
8 papers · 1 filter
Explicit tensors beyond the linear flattening barrier
Benjamin Lovitz
We construct explicit n x n x n tensors of border rank at least 3n-o(n), improving the previous record of (2 + )n due to (Landsberg and Michalek 2025). We also prove t…
Improved bounds on stabilizer extent and Clifford rank
Pulkit Sinha, Benjamin Lovitz
We prove that every pure state of stabilizer rank at most has stabilizer extent at most , and establish the analogous bound for the squared Clifford c…
A 27 x 27 x 27 counterexample to Comon's conjecture
Benjamin Lovitz
We report an explicit construction of a 27 x 27 x 27 symmetric tensor with rational entries that has tensor rank 55 over the rational numbers and symmetric tensor rank 56 over the…
Sharp bounds for perfect quantum state classification beyond antidistinguishability
Nathaniel Johnston, Benjamin Lovitz, Vincent Russo +1
A multiset of pure quantum states is said to be k-learnable if there is a measurement strategy that always narrows an unknown sample drawn from the list down to one of at most k ca…
PPT states of almost maximal Schmidt number
Nathaniel Johnston, Benjamin Lovitz
We construct PPT states on that have Schmidt number asymptotically approaching the smaller local dimension. More specifically, we construct a PPT…
Superadditivity of classical communication over quantum channels via random and deterministic permutations
Benjamin Lovitz, Peixue Wu
Since Hastings' proof of superadditivity of classical communication over quantum channels, considerable effort has been devoted to finding a structural explanation of this phenomen…
Border rank=rank for Kruskal tensors and a Kruskal's theorem for skew decompositions
Alexander Taveira Blomenhofer, Benjamin Lovitz
We show that border rank is equal to rank for Kruskal tensors. We also give an analogous Kruskal condition for alternating tensors, which certifies uniqueness of skew rank decompos…
Counterexamples to additivity of minimum output -Rényi entropy of quantum channels for all
Debbie Leung, Benjamin Lovitz, Ion Nechita +1
The additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every Rényi order , at the von Neumann point , a…