Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Lovitz, Benjamin"'
Autor:
Lovitz, Benjamin, Lowe, Angus
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 tree-like e
Externí odkaz:
http://arxiv.org/abs/2410.21417
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 relevant. Example
Externí odkaz:
http://arxiv.org/abs/2409.18948
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 introduce a number of techniques built on different geometric properties of th
Externí odkaz:
http://arxiv.org/abs/2407.16767
We introduce a convergent hierarchy of lower bounds on the minimum value of a real homogeneous polynomial over the sphere. The main practical advantage of our hierarchy over the sum-of-squares (SOS) hierarchy is that the lower bound at each level of
Externí odkaz:
http://arxiv.org/abs/2310.17827
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 algorithmic proble
Externí odkaz:
http://arxiv.org/abs/2212.03851
Publikováno v:
Physical Review A, 106:062443, 2022
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 the sense
Externí odkaz:
http://arxiv.org/abs/2210.16389
Autor:
Lovitz, Benjamin, Steffan, Vincent
Publikováno v:
Quantum 6, 692 (2022)
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 Moulton to exhibit an explicit sequence of product states with exponential
Externí odkaz:
http://arxiv.org/abs/2110.07781
Autor:
Lovitz, Benjamin, Petrov, Fedor
Publikováno v:
Forum of Mathematics, Sigma, Volume 11, 2023, e27
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-rank condition
Externí odkaz:
http://arxiv.org/abs/2103.15633
Autor:
Lovitz, Benjamin, Johnston, Nathaniel
Publikováno v:
Quantum 6, 760 (2022)
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: Mathematical and Theoretical, 41:375305, 08 2008]. In this work, we determine th
Externí odkaz:
http://arxiv.org/abs/2010.02876
Publikováno v:
Quantum 3, 172 (2019)
We introduce a property of a matrix-valued linear map $\Phi$ that we call its "non-m-positive dimension" (or "non-mP dimension" for short), which measures how large a subspace can be if every quantum state supported on the subspace is non-positive un
Externí odkaz:
http://arxiv.org/abs/1906.04517