Abstract
Quantum entanglement is one of important resources for quantum communication. Entanglement criteria help us detect entangled states. One of important criteria is the local uncertainty relation (LUR) entanglement criteria, which is studied extensively. However, all existent LUR criteria are dependent on the chosen observables. In the paper, applying the uncertainty principle, we improve the LUR criteria to obtain entanglement criteria for multipartite Gaussian states, which are independent on observalbes.
Highlights
Entanglement, as an important resource in quantum communication, has been focused on extensively in both finite dimensional and infinite dimensional quantum systems[1,2,3,4]
Entanglement criteria based on uncertainty relations have been studied in multi partite continuous variable systems[17,18,19,20,21,22]
Such a technique is found by Duan, Giedke, Cirac and Zoller[17] and the so-called local uncertainty relation (LUR) criteria are developed by Hofmann and Takeuchi[18]
Summary
Entanglement, as an important resource in quantum communication, has been focused on extensively in both finite dimensional and infinite dimensional (esp. continuous variable) quantum systems[1,2,3,4]. Other techniques are used to build the entanglement criteria for multi partite Gaussian states[14,15,16]. Loock and Furusawa[21] improve the LUR and says that: for an N-party and N-mode CV state ρ, ρ is separable if for arbitrary scalar h1, h2, ..., hN, g1, g2, ..., gN In the present paper, improving the LUR criteria, we devote to building an entanglement criterion of Gaussian states, which is independent on observables.
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