Matrix product state representations
نویسندگان
چکیده
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.
منابع مشابه
On minimal degrees of faithful quasi-permutation representations of nilpotent groups
By a quasi-permutation matrix, we mean a square non-singular matrix over the complex field with non-negative integral trace....
متن کاملar X iv : q ua nt - p h / 06 08 19 7 v 2 1 4 M ay 2 00 7 MATRIX PRODUCT STATE REPRESENTATIONS
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-r...
متن کاملHidden Symmetries of Stochastic Models
In the matrix product states approach to n species diffusion processes the stationary probability distribution is expressed as a matrix product state with respect to a quadratic algebra determined by the dynamics of the process. The quadratic algebra defines a noncommutative space with a SUq(n) quantum group action as its symmetry. Boundary processes amount to the appearance of parameter depend...
متن کاملIrreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$
We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$. We specialize the indeterminates used in defining these representations to non zero complex numbers. We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$. We then determine necessary and sufficient conditions that guarantee the irreducibility of th...
متن کاملExplicit product ensembles for separable quantum states
We present a general method for constructing pure-product-state representations for density operators of N quantum bits. If such a representation has nonnegative expansion coefficients, it provides an explicit separable ensemble for the density operator. We derive the condition for separability of a mixture of the GreenbergerHorne-Zeilinger state with the maximally mixed state.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Quantum Information & Computation
دوره 7 شماره
صفحات -
تاریخ انتشار 2007