Algebraic structures of multipartite quantum systems

نویسنده

  • Hoshang Heydari
چکیده

We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically well-defined manner.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Complex projective scheme approach to the geometrical structures of multipartite quantum systems

We investigate the geometrical structures of multipartite quantum systems using the language of complex projective schemes, which are fundamental objects in algebraic geometry. In particular, we will explicitly construct multi-qubit states in terms of these schemes and also discuss separability and entanglement of bipartite and multipartite quantum states.

متن کامل

Bipartite Quantum Systems as an Algebraic-geometric Invariant

In [1] and [2] we defined new invariants of both bipartite and multipartite quantum systems under local unitary transformations via algebraic-geometry of determinantal varieties, and gave a new separability criterion based on our new invariants. The purpose of this note is to show how Schmidt numbers of pure states in bipartite systems, a classical invariant, can be read out from our invariants...

متن کامل

New Invariants and Separability Criterion of the Mixed States: Multipartite Case

We introduce algebraic sets in the complex linear space (or projective complex space) for the mixed states in a multipartite quantum systems as their invariants under local operations. The algebraic set has to be the union of the linear subspaces if the mixed state is separable, and thus we give a new criterion of separability of the mixed states in multipartite quantum systems. Some examples a...

متن کامل

Multipartite entanglement witnesses.

We derive a set of algebraic equations, the so-called multipartite separability eigenvalue equations. Based on their solutions, we introduce a universal method for the construction of multipartite entanglement witnesses. We witness multipartite entanglement of 10(3) coupled quantum oscillators, by solving our basic equations analytically. This clearly demonstrates the feasibility of our method ...

متن کامل

Quantum entanglement without eigenvalue spectra: multipartite case

We introduce algebraic sets in the products of the complex projective spaces for the mixed states in multipartite quantum systems, which are independent of their eigenvalues and only measure the “position” of their eigenvectors, as their non-local invariants (ie., remaining invariant after local unitary transformation). The algebraic sets have to be the union of linear subspaces if the multipar...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008