Explicit product ensembles for separable quantum states
نویسندگان
چکیده
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.
منابع مشابه
Coherent Transport of Single Photon in a Quantum Super-cavity with Mirrors Composed of Λ-Type Three-level Atomic Ensembles
In this paper, we study the coherent transport of single photon in a coupled resonator waveguide (CRW) where two threelevel Λ-type atomic ensembles are embedded in two separate cavities. We show that it is possible to control the photon transmission and reflection coefficients by using classical control fields. In particular, we find that the total photon transmission and reflection are achieva...
متن کاملContinuous optimal ensembles I: A geometrical characterization of robustly separable quantum states
A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be represented as a normal vector to a hypersurface in the Euclidean space of all self-adjoint operators in the state space of the whole system. The expression for t...
متن کاملLocal description of quantum inseparability
We show how to decompose any density matrix of the simplest binary composite systems, whether separable or not, in terms of only product vectors. We determine for all cases the minimal number of product vectors needed for such a decomposition. Separable states correspond to mixing from one to four pure product states. Inseparable states can be described as pseudomixtures of four or five pure pr...
متن کاملGeometry and product states
As separable states are a convex combination of product states, the geometry of the manifold of product states, Σ is studied. Prior results by Sanpera, Vidal and Tarrach are extended. Furthermore, it is proven that states in the set tangent to Σ at the maximally mixed state are separable; the set normal constains, among others, all maximally entangled states. A canonical decomposition is given....
متن کاملGeometry of entangled states
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K3M problem and characterize the set of effectively different states ~which cannot be related by local transformations!. Thus, we generalize earlier results obtained for the simplest 232 system, which lead to a st...
متن کامل