Physical origins of ruled surfaces on the reduced density matrices geometry

Joint product numerical range and geometry of reduced density matrices

The reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection $Θ$ is convex in $\mathbb{R}^3$. The boundary $\partialΘ$ of $Θ$ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti's theorem. This allows us to iden…

Geometry of reduced density matrices for symmetry-protected topological phases

In this paper, we study the geometry of reduced density matrices for states with symmetry-protected topological (SPT) order. We observe ruled surface structures on the boundary of the convex set of low dimension projections of the reduced density matrices. In order to signal the SPT order using ruled surfaces, it is important that we add a symmetry-breaking term to the boundary of the system---no ruled surface emerges in systems without boundary or when we add a symmetry-breaking term representing a thermodynamic quantity. Although the ruled surfaces only appear in the thermodynamic limit wher…

Factorization of unitary matrices induced by 3D anisotropic Ising interaction

Quantum computation is a continuously growing research area which is based on nature and resources of quantum mechanics, as superposition and entanglement. In its quantum circuits version, the use of convenient and appropriate gates is essential. But while those gates adopt convenient forms for computational algorithms, their design depends on specific quantum systems and stu? being used. These gates need manage quantum systems based on physical interactions ruled by quantum Hamiltonians. With this, gates design is restricted to properties and limitations of interactions and physical elements …

Appearance of causality in process matrices when performing fixed-basis measurements for two parties

The recently developed framework for quantum theory with no global causal order allows for quantum processes in which operations in local laboratories are neither causally ordered nor in a probabilistic mixture of definite causal orders. The causal relation between the laboratories is described by the process matrix. We show that, if the inputs of the laboratories are measured in a fixed basis, one can introduce an effective process matrix which is operationally indistinguishable from the original one. This effective process matrix can be obtained by applying the von Neumann- Luders update rul…

Limit distribution with a combination of density functions for a 2-state quantum walk

We consider 2-state quantum walks (QWs) on the line, which are defined by two matrices. One of the matrices operates the walk in certain intervals. In the usual QWs starting from the origin, localization does not occur at all. However, our walk can be localized around the origin. In this paper, we present some limit distributions for the walk.

通过高斯积分推导任意对称矩阵的环哈夫尼安生成函数

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration

本文通过仅依赖高斯积分的证明，将环哈夫尼安生成函数的适用范围从量子光学方法所限定的特殊矩阵推广到任意对称矩阵。