Conditions for entanglement purification with general two-qubit states

Abstract

We present the convergence study of a recurrence entanglement purification protocol using arbitrary two-qubit initial states. The protocol is based on a rank two projector in the Bell basis which serves as a two-qubit operation replacing the usual controlled-NOT gate. We show that the whole space of two-qubit density matrices is mapped onto an invariant subspace characterized by seven real parameters. By analyzing this type of density matrices we are able to find general conditions for entanglement purification in the form of two inequalities between pairs of diagonal elements and pairs of coherences. We show that purifiable initial states do not necessary require a fidelity larger than one half with respect to any maximally entangled pure state. Furthermore, we find a family of states parametrized by their concurrence that can be perfectly converted into a Bell state in just one step of the protocol with probability proportional to the square of the concurrence.

arXiv comment7 pages, 3 figures

References in corpus (7)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
• Quantum privacy amplification and the security of quantum cryptography over noisy channels
• Entanglement purification and quantum error correction
• On the analytical convergence of the QPA procedure
• Multiphoton-state-assisted entanglement purification of material qubits

Cited by in corpus (11)

• Measurement-induced chaos and quantum state discrimination in an iterated Tavis-Cummings scheme
• Hybrid quantum repeater based on resonant qubit-field interactions
• Entangling operations in nonlinear two-atom Tavis-Cummings models
• Two-qubit mixed states and teleportation fidelity: Purity, concurrence, and beyond
• Improving entanglement purification through coherent superposition of roles
• Statistical evaluation and optimization of entanglement purification protocols
• Universal, unambiguous concentration and distillation of Bell pairs
• Performance of entanglement purification including maximally entangled mixed states
• Optimality of universal conclusive entanglement concentration protocols
• Optimal two-qubit gates in recurrence protocols of entanglement purification
• Strategies for entanglement distribution in optical fiber networks