Bound entangled Bell diagonal states of unequal local dimensions, and their witnesses

Bell diagonal states constitute a well-studied family of bipartite quantum states that arise naturally in various contexts in quantum information. In this paper we generalize the notion of Bell diagonal states to the case of unequal local dimensions and investigate their entanglement properties. We extend the family of entanglement criteria of Sarbicki et al. to non-Hermitian operator bases to construct entanglement witnesses for the class of generalized Bell diagonal states. We then show how to optimize the witnesses with respect to noise robustness. Finally, we use these witnesses to construct bound entangled states that are not detected by the usual computable cross norm or realignment and de Vicente criteria.Comment: 11 pages, 4 figures, 1 tabl

A class of Bell diagonal states and entanglement witnesses

We analyze special class of bipartite states - so called Bell diagonal states. In particular we provide new examples of bound entangled Bell diagonal states and construct the class of entanglement witnesses diagonal in the magic basis.Comment: 17 page

Convertibility between two-qubit states using stochastic local quantum operations assisted by classical communication

In this paper we classify the four-qubit states that commute with UUVV, where U and V are arbitrary members of the Pauli group. We characterize the set of separable states for this class, in terms of a finite number of entanglement witnesses. Equivalently, we characterize the two-qubit, Bell-diagonal-preserving, completely positive maps that are separable. These separable completely positive maps correspond to protocols that can be implemented with stochastic local operations assisted by classical communication (SLOCC). This allows us to derive a complete set of SLOCC monotones for Bell-diagonal states, which, in turn, provides the necessary and sufficient conditions for converting one two-qubit state to another by SLOCC

Experimental implementation of a NMR entanglement witness

Entanglement witnesses (EW) allow the detection of entanglement in a quantum system, from the measurement of some few observables. They do not require the complete determination of the quantum state, which is regarded as a main advantage. On this paper it is experimentally analyzed an entanglement witness recently proposed in the context of Nuclear Magnetic Resonance (NMR) experiments to test it in some Bell-diagonal states. We also propose some optimal entanglement witness for Bell-diagonal states. The efficiency of the two types of EW's are compared to a measure of entanglement with tomographic cost, the generalized robustness of entanglement. It is used a GRAPE algorithm to produce an entangled state which is out of the detection region of the EW for Bell-diagonal states. Upon relaxation, the results show that there is a region in which both EW fails, whereas the generalized robustness still shows entanglement, but with the entanglement witness proposed here with a better performance

Entanglement Witnesses for Graph States: General Theory and Examples

We present a general theory for the construction of witnesses that detect genuine multipartite entanglement in graph states. First, we present explicit witnesses for all graph states of up to six qubits which are better than all criteria so far. Therefore, lower fidelities are required in experiments that aim at the preparation of graph states. Building on these results, we develop analytical methods to construct two different types of entanglement witnesses for general graph states. For many classes of states, these operators exhibit white noise tolerances that converge to one when increasing the number of particles. We illustrate our approach for states such as the linear and the 2D cluster state. Finally, we study an entanglement monotone motivated by our approach for graph states.Comment: 12 pages + appendix, 7 figure

Generalized qudit Choi maps

Following the linear programming prescription of Ref. \cite{PRA72}, the $d\otimes d$ Bell diagonal entanglement witnesses are provided. By using Jamiolkowski isomorphism, it is shown that the corresponding positive maps are the generalized qudit Choi maps. Also by manipulating particular $d\otimes d$ Bell diagonal separable states and constructing corresponding bound entangled states, it is shown that thus obtained $d\otimes d$ BDEW's (consequently qudit Choi maps) are non-decomposable in certain range of their parameters.Comment: 22 page