Unique decompositions, faces, and automorphisms of separable states

نویسندگان

  • Erik Alfsen
  • Fred Shultz
چکیده

Let Sk be the set of separable states on B(C ⊗ C) admitting a representation as a convex combination of k pure product states, or fewer. If m > 1, n > 1, and k ≤ max (m,n), we show that Sk admits a subset Vk such that Vk is dense and open in Sk, and such that each state in Vk has a unique decomposition as a convex combination of pure product states, and we describe all possible convex decompositions for a set of separable states that properly contains Vk. In both cases we describe the associated faces of the space of separable states, which in the first case are simplexes, and in the second case are direct convex sums of faces that are isomorphic to state spaces of full matrix algebras. As an application of these results, we characterize all affine automorphisms of the convex set of separable states, and all automorphisms of the state space of B(C⊗C) that preserve entanglement and separability.

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

Separability condition for composite systems of distinguishable fermions

We study characterization of separable (classically correlated) states for composite systems of distinguishable fermions. In the computation of entanglement formation for such systems where located subsystems are coupled by the canonical anticommutation relations (not by tensor product), the state decompositions to be taken should respect the univalence superselection rule. (The usual entanglem...

متن کامل

Separable State Decompositions for a Class of Mixed States

We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of n × n bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT. Quantum entangled states have become one of the key resources in quantum in...

متن کامل

Quantum separability, time reversal and canonical decompositions

We propose an interpretation of quantum separability based on a physical principle: local time reversal. It immediately leads to a simple characterization of separable quantum states that reproduces results known to hold for binary composite systems and which thereby is complete for low dimensions. We then describe a constructive algorithm for finding the canonical decomposition of separable an...

متن کامل

Finding Decompositions of a Class of Separable States

We consider the class of separable states which admit a decomposition ∑ i Ai⊗Bi with the Bi’s having independent images. We give a simple intrinsic characterization of this class of states. Given a density matrix in this class, we construct such a decomposition, which can be chosen so that the Ai’s are distinct with unit trace, and then the decomposition is unique. We relate this to the facial ...

متن کامل

Strong and weak separability conditions for two-qubits density matrices

Explicit separable density matrices, for mixed–two-qubits states, are derived by using Hilbert-Schmidt (HS) decompositions and Peres-Horodecki criterion. A “strongly separable” two-qubits mixed state is defined by multiplications of two density matrices, given with pure states, while “weakly separable” two-qubits mixed state is defined, by multiplications of two density matrices, which includes...

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 2010