Nonmaximally entangled bases and their application in entanglement purification via swapping
| Authors | |
|---|---|
| Year of publication | 2005 |
| Type | Article in Periodical |
| Magazine / Source | Physical Review A |
| MU Faculty or unit | |
| Citation | |
| Field | Theoretical physics |
| Keywords | nonmaximally entangled bases; entanglement purification; entanglement swapping |
| Description | Four basis vectors of the Hilbert space of two qubits have the property that if three of them are product states, then the fourth one has to be a product state as well. We address the following situation: Consider a set of orthogonal vectors, each exhibiting a certain degree of entanglement. What is the bound on entanglement of the rest of the basis vectors to form a complete orthonormal basis? Specifically, we present an orthonormal basis, the Xi basis in the Hilbert space of two qubits, with one product state and three equally entangled states. The maximum of the so available entanglement is quantified. A close-to-optimal protocol is presented for entanglement purification via entanglement swapping of two-qubit states. It is based on a suitably chosen nonmaximally entangled basis and carried out in a single step without any ancillas. A similar application of the Xi basis is examined. In this latter case, all the involved entangled states have different and nonorthogonal Schmidt decompositions and, except for some possibly resulting states, none of them are maximally entangled. Entanglement of single pair purification is not conserved on average in this case. |
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