Separability, entanglement, and full families of commuting normal matrices

Separability and entanglement of quantum states based on covariance matrices

commuting and non -commuting graphs of finit groups

فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...

Matrices commuting with a given normal tropical matrix

Consider the space M n of square normal matrices X = (xij) over R ∪ {−∞}, i.e., −∞ ≤ xij ≤ 0 and xii = 0. Endow M n with the tropical sum ⊕ and multiplication ⊙. Fix a real matrix A ∈ M n and consider the set Ω(A) of matrices in M n which commute with A. We prove that Ω(A) is a finite union of alcoved polytopes; in particular, Ω(A) is a finite union of convex sets. The set Ω(A) of X such that A...

Commuting triples of matrices

The variety C(3, n) of commuting triples of n × n matrices over C is shown to be irreducible for n = 7. It had been proved that C(3, n) is reducible for n ≥ 30, but irreducible for n ≤ 6. Guralnick and Omladič have conjectured that it is reducible for n > 7.

Entanglement and Non-Separability of CAR Systems

We study quantum entanglement of bipartite CAR systems. We show that triangle inequality of von Neumann entropy does not hold in these systems. Meanwhile, we show non-separability in the sense of Florig-Summers for our CAR systems. Entanglement degrees by Narnhofer are generalized to an arbitrary, that is, not-necessarily commuting pair of general C∗-systems. These new entanglement degrees are ...