All Unitaries Having Operator Schmidt Rank 2 are Controlled Unitaries

نویسندگان

  • Scott M. Cohen
  • Li Yu
چکیده

برای دانلود 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

nt - p h / 03 06 14 4 v 1 2 2 Ju n 20 03 Operator - Schmidt decompositions and the Fourier transform , with applications to the operator - Schmidt numbers of unitaries

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C ⊗ C whose operatorSchmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C ⊗ C with operatorSchmidt number S for every S ∈ {1, ..., 9}. This corollary...

متن کامل

Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries

The operator-Schmidt decomposition is useful in quantum information theory for quantifying the nonlocality of bipartite unitary operations. We construct a family of unitary operators on C ⊗ C whose operatorSchmidt decompositions are computed using the discrete Fourier transform. As a corollary, we produce unitaries on C ⊗ C with operatorSchmidt number S for every S ∈ {1, ..., 9}. This corollary...

متن کامل

Unitaries in a Simple C-algebra of Tracial Rank One

Let A be a unital separable simple infinite dimensional C∗-algebra with tracial rank no more than one and with the tracial state space T (A) and let U(A) be the unitary group of A. Suppose that u ∈ U0(A), the connected component of U(A) containing the identity. We show that, for any ǫ > 0, there exists a selfadjoint element h ∈ As.a such that ‖u− exp(ih)‖ < ǫ. We also study the problem when u c...

متن کامل

Homotopy of unitaries in simple C∗-algebras with tracial rank one

Let ǫ > 0 be a positive number. Is there a number δ > 0 satisfying the following? Given any pair of unitaries u and v in a unital simple C∗-algebra A with [v] = 0 in K1(A) for which ‖uv − vu‖ < δ, there is a continuous path of unitaries {v(t) : t ∈ [0, 1]} ⊂ A such that v(0) = v, v(1) = 1 and ‖uv(t)− v(t)u‖ < ǫ for all t ∈ [0, 1]. An answer is given to this question when A is assumed to be a un...

متن کامل

Unitary local invariance

We address unitary local invariance of bipartite pure states. Given a bipartite state |Ψ〉〉 = ∑ ij ψij |i〉1⊗|j〉2 the complete characterization of the class of local unitaries U1 ⊗ U2 for which U1 ⊗ U2|Ψ〉〉 = |Ψ〉〉 is obtained in terms of the singular values of the matrix Ψ = [ψ]ij . Suppose you are given a bipartite pure state |Ψ〉〉 ∈ H1 ⊗H2 and asked for which (pairs of) unitaries the state is loc...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2016