Kronecker product/Direct product/Tensor product in Quantum Information theory

Application of the Kronecker product to simple spin systems

We show that the well known Kronecker product is a suitable tool for the construction of matrix representations of widely used spin Hamiltonians. In this way we avoid the explicit use of basis sets for the construction of the matrix elements. As illustrative examples we discuss two isotropic models and an anisotropic one.

Coherent States for Kronecker Products of Non-Compact Groups: Formulation and Applications

We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete series representations of SU(1,1). These are the generalization of the `Barut Girardello' coherent states to the Kronecker Product of two non-compact groups.The resolution of the identity and the analytic phase space representation of these states is presented. This phase space representation is based on the basis of products of `pair coherent states' rather tha…

Kronecker态：量子信息中多部分最大纠缠态的强有力来源

Kronecker states: a powerful source of multipartite maximally entangled states in quantum information

本文提出W态拼接方法，将多量子比特纠缠态表示为张量网络，通过等型分解构造Kronecker态，可生成任意Kronecker子空间，为多部分纠缠资源理论提供新工具。

通过克罗内克积实现前缀和

Prefix Sums via Kronecker Products

本文通过克罗内克积方法设计了具有零缺陷、恒定扇出度和更小深度的递归前缀和电路，并应用于改进量子加法器的Toffoli深度和规模。

Kronecker product in terms of Hubbard operators and the Clebsch-Gordan decomposition of SU(2)xSU(2)

We review the properties of the Kronecker (direct, or tensor) product of square matrices $A \otimes B \otimes C \cdots$ in terms of Hubbard operators. In its simplest form, a Hubbard operator $X_n^{i,j}$ can be expressed as the $n$-square matrix which has entry 1 in position $(i,j)$ and zero in all other entries. The algebra and group properties of the observables that define a multipartite quantum system are notably straightforward in such a framework. In particular, we use the Kronecker product in Hubbard notation to get the Clebsch-Gordan decomposition of the product group $SU(2) \times SU(…

Kronecker products of projective representations of translation groups

Projective irreps of (Z_N)^2 can be labelled by divisors n of N. A product of two irreps, labelled by n and n', can be decomposed into projective irreps labelled by M, where M strongly depends on the arithmetic structure of N, n, n' and their relations (gcd, lcm etc.). Such decompostion describes two important physical effects: (i) changes of a magnetic period of the crystal lattice (with unchaged crystal period N); (2) each representation can be related with a charged particle moving in an external magnetic field and a periodic potential --- a product of (projective) irreps corresponds to int…