Benjamin Lovitz
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View article: Constructive counterexamples to the additivity of minimum output Rényi entropy of quantum channels for all $p>1$
Constructive counterexamples to the additivity of minimum output Rényi entropy of quantum channels for all $p>1$ Open
We present explicit quantum channels with strictly sub-additive minimum output Rényi entropy for all $p>1$, improving upon prior constructions which handled $p>2$. Our example is provided by explicit constructions of linear subspaces with …
View article: A linear-time algorithm for Chow decompositions
A linear-time algorithm for Chow decompositions Open
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 is pencil based, hence it relies on generalized eigenvalue c…
View article: A hierarchy of eigencomputations for polynomial optimization on the sphere
A hierarchy of eigencomputations for polynomial optimization on the sphere Open
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-squares (RSOS) hierarchy is that the lower bound at each level…
View article: Nearly tight bounds for testing tree tensor network states
Nearly tight bounds for testing tree tensor network states Open
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 succinct representations of quantum many-body systems with a …
View article: X-arability of mixed quantum states
X-arability of mixed quantum states Open
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, different notions of entanglement (or lack thereof) become releva…
View article: A hierarchy of eigencomputations for polynomial optimization on the sphere
A hierarchy of eigencomputations for polynomial optimization on the sphere Open
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-squares (RSOS) hierarchy is that the lower bound at each level…
View article: A generalization of Kruskal’s theorem on tensor decomposition
A generalization of Kruskal’s theorem on tensor decomposition Open
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 ‘splitting theorem’ for sets of product tensors, in which the k-ran…
View article: Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond
Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond Open
We study the problem of finding elements in the intersection of an arbitrary conic variety in $\mathbb{F}^n$ with a given linear subspace (where $\mathbb{F}$ can be the real or complex field). This problem captures a rich family of algorit…
View article: A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces Open
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 known methods already at the first level, and it is complete in…
View article: A generalization of Kruskal's theorem on tensor decomposition
A generalization of Kruskal's theorem on tensor decomposition Open
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 "splitting theorem" for sets of product tensors, in which the k-ran…
View article: On decomposable correlation matrices
On decomposable correlation matrices Open
Correlation matrices (positive semidefinite matrices with ones on the\ndiagonal) are of fundamental interest in quantum information theory. In this\nwork we introduce and study the set of $r$-decomposable correlation matrices:\nthose that …
View article: Toward a generalization of Kruskal's theorem on tensor decomposition
Toward a generalization of Kruskal's theorem on tensor decomposition Open
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 propose a conjecture in which the k-rank condition of Kruskal…
View article: Practical quantum appointment scheduling
Practical quantum appointment scheduling Open
We propose a protocol based on coherent states and linear optics operations\nfor solving the appointment-scheduling problem. Our main protocol leaks\nstrictly less information about each party's input than the optimal classical\nprotocol, …
View article: Families of quantum fingerprinting protocols
Families of quantum fingerprinting protocols Open
We introduce several families of quantum fingerprinting protocols to evaluate\nthe equality function on two $n$-bit strings in the simultaneous message\npassing model. The original quantum fingerprinting protocol uses a tensor\nproduct of …