张量积随机子空间的集中性估计及其在量子信息论中的应用

Local extrema of entropy functions under tensor products

We show that under a certain condition of local commutativity the minimum von-Neumann entropy output of a quantum channel is locally additive. We also show that local minima of the 2-norm entropy functions are closed under tensor products if one of the subspaces has dimension 2.

具有大非耦合子空间的非马尔可夫开放量子系统的过程张量模拟

Process tensor simulations of non-Markovian open quantum systems with large uncoupled subspaces

本文提出结合泰勒展开的PT-MPO方法，将非马尔可夫开放量子系统模拟复杂度从$O(d^6)$降至$O(d^3)$，支持数百态的高效模拟，适用于多模腔QED系统。

Bipartite subspaces having no LOCC-distinguishable bases

It is proved that there exist subspaces of bipartite tensor product spaces that have no orthonormal bases that can be perfectly distinguished by means of LOCC protocols. A corollary of this fact is that there exist quantum channels having sub-optimal classical capacity even when the receiver may communicate classically with a third party that represents the channel's environment.

贫瘠高原的统计模型与 Pauli 可观测量的反集中

Statistical models of barren plateaus and anti-concentration of Pauli observables

针对可观测量非定域性、初始态纠缠和电路表达能力三类贫瘠高原来源提出统计模型，并证明任意两个 Pauli 可观测量在贫瘠高原区域以高概率反集中，为量子景观优化与热启动提供新认识。

对称分解的Krylov复杂度与无色张量模型

Symmetry-resolved Krylov Complexity and the Uncoloured Tensor Model

研究对称分解的Krylov复杂度在特定子空间与全空间中的关系，以及无色张量模型中复杂度的分布特性。

The Church of the Symmetric Subspace

The symmetric subpace has many applications in quantum information theory. This review article begins by explaining key background facts about the symmetric subspace from a quantum information perspective. Then we review, and in some places extend, work of Werner and Chiribella that connects the symmetric subspace to state estimation, optimal cloning, the de Finetti theorem and other topics. In the third and final section, we discuss how the symmetric subspace can yield concentration-of-measure results via the calculation of higher moments of random quantum states. There are no new results in …

Geometric properties of SIC-POVM tensor square

It's known that if $d^2$ vectors from $d$-dimensional Hilbert space $H$ form a SIC-POVM (SIC for short) then tensor square of those vectors form an equiangular tight frame on the symmetric subspace of $H\otimes H$. We prove that for any SIC of WH-type (Weyl-Heisenberg group covariant) this squared frame can be obtained as a projection of WH-type basis of $H\otimes H$ onto the symmetric subspace. We give a full description of the set of all WH-type bases, so this set could be used as a search space for SIC solutions. Also we show that a particular element of this set is close to a SIC solution …

A completely entangled subspace of maximal dimension

A completely entangled subspace of a tensor product of Hilbert spaces is a subspace with no non-trivial product vector. K. R. Parthasarathy determined the maximum dimension possible for such a subspace. Here we present a simple explicit example of one such space. We determine the set of product vectors in its orthogonal complement and see that it spans whole of the orthogonal complement. This way we are able to determine the minimum dimension possible for an unextendible product basis (UPB) consisting of product vectors which are linearly independent but not necessarily mutually orthogonal.

计算代数簇的线性截面：量子纠缠、张量分解及其他问题

Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond

针对二次代数簇与线性子空间求交这一最坏情况NP难的问题，提出一种可高效求解泛型子空间实例的算法，并给出其在量子纠缠判定、低秩分解等问题中的多项式时间算法与唯一性结果。