Light cone tensor network and time evolution

Regularly Decomposable Tensors and Classical Spin States

A spin-$j$ state can be represented by a symmetric tensor of order $N=2j$ and dimension $4$. Here, $j$ can be a positive integer, which corresponds to a boson; $j$ can also be a positive half-integer, which corresponds to a fermion. In this paper, we introduce regularly decomposable tensors and show that a spin-$j$ state is classical if and only if its representing tensor is a regularly decomposable tensor. In the even-order case, a regularly decomposable tensor is a completely decomposable tensor but not vice versa; a completely decomposable tensors is a sum-of-squares (SOS) tensor but not vi…

Compositions and tensor products of linear maps between matrix algebras

In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement, Schmidt numbers of bi-partite states and block-positivity, together with various kinds of positive maps between matrix algebras like entanglement breaking maps, $k$-superpositive maps, completely positive maps, $k$-positive maps. We will begin with concrete examples of elementary positive maps given by $x\mapsto s^*xs$, and use Choi matrices and duality to explain all the notions mentioned above. We also show that …

长程相互作用自旋链中光锥的涌现源于相消干涉

Emergence of Light Cones in Long-range Interacting Spin Chains Is Due to Destructive Interference

本文研究长程相互作用自旋链中光锥涌现的机制，指出纠缠量子效应间的相消干涉会指数抑制光锥外的纠缠，是形成有效纠缠光锥的必要原因，并发现缩短相互作用范围反而会加快纠缠输运。

Toeplitz与Fejér-Riesz算子系统张量锥中的范畴关系与二分纠缠

Categorical relations and bipartite entanglement in tensor cones for Toeplitz and Fejér-Riesz operator systems

本文研究算子系统张量积基锥产生的张量锥中的可分性与纠缠，重点探讨Toeplitz与Fejér-Riesz算子系统的范畴关系，并给出后者线性映射完全正的单矩阵判据。

Entangleability of cones

We solve a long-standing conjecture by Barker, proving that the minimal and maximal tensor products of two finite-dimensional proper cones coincide if and only if one of the two cones is generated by a linearly independent set. Here, given two proper cones $C_1$, $C_2$, their minimal tensor product is the cone generated by products of the form $x_1 \otimes x_2$, where $x_1 \in C_1$ and $x_2 \in C_2$, while their maximal tensor product is the set of tensors that are positive under all product functionals $f_1 \otimes f_2$, where $f_1$ is positive on $C_1$ and $f_2$ is positive on $C_2$. Our pro…

Annihilating Entanglement Between Cones

Every multipartite entangled quantum state becomes fully separable after an entanglement breaking quantum channel acted locally on each of its subsystems. Whether there are other quantum channels with this property has been an open problem with important implications for entanglement theory (e.g., for the distillation problem and the PPT squared conjecture). We cast this problem in the general setting of proper convex cones in finite-dimensional vector spaces. The entanglement annihilating maps transform the $k$-fold maximal tensor product of a cone $C_1$ into the $k$-fold minimal tensor produ…