Majorization criterion for distillability of a bipartite quantum state

Abstract

Bipartite quantum states are classified into three categories: separable states, bound entangled states, and free entangled states. It is of great importance to characterize these families of states for the development of quantum information science. In this paper, I show that the separable states and the bound entangled states have a common spectral property. More precisely, I prove that for undistillable -- separable and bound entangled -- states, the eigenvalue vector of the global system is majorized by that of the local system. This result constitutes a new sufficient condition for distillability of bipartite quantum states. This is achieved by proving that if a bipartite quantum state satisfies the reduction criterion for distillability, then it satisfies the majorization criterion for separability.

4 pages, no figures, REVTEX. A new lemma (Lemma 2) added. To appear in Physical Review Letters

References in corpus (11)

• 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
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Characterizing Entanglement
• An improved bound on distillable entanglement
• Separable states are more disordered globally than locally
• Maximally entangled mixed states in two qubits
• Reflections upon separability and distillability
• Conditional entropies and their relation to entanglement criteria
• Characterizing mixing and measurement in quantum mechanics

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