Another dual formulation of the separability problem

Combinatorial approach to multipartite quantum systems:basic formulation

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of pure and mixed states, Von-Neumann entropy, separability of multipartite quantum states and quantum operations in terms of the graphs associated with quantum states. In order to address the separability and entanglement questions using graphs, we introduce a modified tensor product of weighted graphs, and establish its algebraic properties. In particular, we s…

Separability conditions based on local fine-grained uncertainty relations

Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using fine-grained uncertainty relations. Fine-grained uncertainty relations can be obtained by consideration of the spectral norms of certain positive matrices. One of possible approaches to separability conditions is connected with upper bounds on the sum of maximal probabilities. Separability conditions are often formulated for measurements that have a special structu…

On the tensor convolution and the quantum separability problem

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product is separable or entangled. We show that the tensor convolution defined for certain mappings on an almost arbitrary locally compact abelian group, give rise to formulation of an equivalent problem to the separability one.

Computational complexity of the quantum separability problem

Ever since entanglement was identified as a computational and cryptographic resource, researchers have sought efficient ways to tell whether a given density matrix represents an unentangled, or separable, state. This paper gives the first systematic and comprehensive treatment of this (bipartite) quantum separability problem, focusing on its deterministic (as opposed to randomized) computational complexity. First, I review the one-sided tests for separability, paying particular attention to the semidefinite programming methods. Then, I discuss various ways of formulating the quantum separabili…

作为量子信道的 Wilsonian 重整化与不动点处的可分性

Wilsonian Renormalization as a Quantum Channel and the Separability of Fixed Points

将 Wilsonian 重整化表述为量子信道作用于动量空间密度矩阵，证明不动点处理论真空在动量尺度间无纠缠，结果源于尺度对称性并约束基态与期望值。

Another Formulation of the Wick's Theorem. Farewell, Pairing?

The algebraic formulation of Wick's theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed. Each element of the matrix is the average of the chronological product of only two operators. This formulation is extremely convenient for practical calculations in quantum field theory and statistical physics by the methods of symbolic mathematics using computers.

探究问题难度与QUBO性质之间的关系

Investigating the Relation Between Problem Hardness and QUBO Properties

本文通过分析聚类和SVM训练的QUBO谱隙，揭示了问题难度与QUBO性质的关系，发现聚类谱隙与数据可分性正相关，而SVM相反。