13 citations · 66 across the 21 of their papers we have counts for
26 papers
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…
The complexity of perfect quantum state classification
Nathaniel Johnston, Benjamin Lovitz, Vincent Russo +1
The problem of quantum state classification asks how accurately one can identify an unknown quantum state that is promised to be drawn from a known set of pure states. In this work…
Constructive counterexamples to the additivity of minimum output Rényi entropy of quantum channels for all
Harm Derksen, Benjamin Lovitz
We present explicit quantum channels with strictly sub-additive minimum output Rényi entropy for all , improving upon prior constructions which handled . Our example is p…
A linear-time algorithm for Chow decompositions
Alexander Taveira Blomenhofer, Benjamin Lovitz
We propose a linear-time algorithm to compute low-rank Chow decompositions. Our algorithm can decompose concise symmetric 3-tensors in n variables of Chow rank n/3. The algorithm i…
Nearly tight bounds for testing tree tensor network states
Benjamin Lovitz, Angus Lowe
Tree tensor network states (TTNS) generalize the notion of having low Schmidt-rank to multipartite quantum states, through a parameter known as the bond dimension. This leads to su…
X-arability of mixed quantum states
Harm Derksen, Nathaniel Johnston, Benjamin Lovitz
The problem of determining when entanglement is present in a quantum system is one of the most active areas of research in quantum physics. Depending on the setting at hand, differ…
Linear preservers of secant varieties and other varieties of tensors
Fulvio Gesmundo, Young In Han, Benjamin Lovitz
We study the problem of characterizing linear preserver subgroups of algebraic varieties, with a particular emphasis on secant varieties and other varieties of tensors. We introduc…
A hierarchy of eigencomputations for polynomial optimization on the sphere
Benjamin Lovitz, Nathaniel Johnston
We introduce a convergent hierarchy of lower bounds on the minimum value of a real form over the unit sphere. The main practical advantage of our hierarchy over the real sum-of-squ…
Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond
Nathaniel Johnston, Benjamin Lovitz, Aravindan Vijayaraghavan
We study the problem of finding elements in the intersection of an arbitrary conic variety in with a given linear subspace (where can be the real or com…
A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
Nathaniel Johnston, Benjamin Lovitz, Aravindan Vijayaraghavan
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms know…
New techniques for bounding stabilizer rank
Benjamin Lovitz, Vincent Steffan
In this work, we present number-theoretic and algebraic-geometric techniques for bounding the stabilizer rank of quantum states. First, we refine a number-theoretic theorem of Moul…
A generalization of Kruskal's theorem on tensor decomposition
Benjamin Lovitz, Fedor Petrov
Kruskal's theorem states that a sum of product tensors constitutes a unique tensor rank decomposition if the so-called k-ranks of the product tensors are large. We prove a "splitti…
Entangled subspaces and generic local state discrimination with pre-shared entanglement
Benjamin Lovitz, Nathaniel Johnston
Walgate and Scott have determined the maximum number of generic pure quantum states that can be unambiguously discriminated by an LOCC measurement [Journal of Physics A: Mathematic…
The Non-m-Positive Dimension of a Positive Linear Map
Nathaniel Johnston, Benjamin Lovitz, Daniel Puzzuoli
We introduce a property of a matrix-valued linear map that we call its "non-m-positive dimension" (or "non-mP dimension" for short), which measures how large a subspace can be…
On decomposable correlation matrices
Benjamin Lovitz
Correlation matrices (positive semidefinite matrices with ones on the diagonal) are of fundamental interest in quantum information theory. In this work we introduce and study the s…
Toward a generalization of Kruskal's theorem on tensor decomposition
Benjamin Lovitz
Kruskal's theorem states that a sum of product tensors constitutes a unique tensor rank decomposition if the so-called k-ranks of the product tensors are large. In this work, we pr…
Practical Quantum Appointment Scheduling
Dave Touchette, Benjamin Lovitz, Norbert Lütkenhaus
We propose a protocol based on coherent states and linear optics operations for solving the appointment-scheduling problem. Our main protocol leaks strictly less information about…