Entanglement witnesses for many qubit systems

Richard E. F. Bonde, Andrew Schauf, Elizabeth Behrman

Kathleen Walsh, Andrew Schauf, Joseph Lesniak +3 more

Waldemar Kłobus, Paweł Cieśliński, Lukas Knips +2 more

We study the possibility of witnessing Gaussian entanglement between two continuous-variable systems with the help of two spatially separated qubits. Its key ingredient is a local lossy state transfer from the original systems onto local qubits. The qubits are initially in a pure product state, therefore by detecting entanglement between the qubits we witness entanglement between the two original systems.

Satyabrata Adhikari, Nirman Ganguly, A. S. Majumdar

Teleportation witnesses are Hermitian operators which can identify useful entanglement for quantum teleportation. Here we provide a systematic method to construct teleportation witnesses from entanglement witnesses corresponding to general qudit systems. The witnesses so constructed are shown to be optimal for qubit and qutrit systems and therefore detect the largest set of states useful for teleportation within a given class. We demonstrate the action of the witness pertaining to different classes of states in qubits and qutrits. Decomposition of the witness in terms of spin operators facilitates experimental identification of useful resources for teleportation.

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Justyna P. Zwolak, Dariusz Chruściński

We provide a recurrent construction of entanglement witnesses for a bipartite systems living in a Hilbert space corresponding to $2N$ qubits ($N$ qubits in each subsystem). Our construction provides a method of generalization of the Robertson map that naturally meshes with $2N$-qubit systems, i.e., its structure respects the ${2}^{2N}$ growth of the state space. We prove that for $N>1$ these witnesses are indecomposable and optimal. As a byproduct we provide a family of PPT (Positive Partial Transpose) entangled states.