Complete entanglement witness for quantum teleportation

Abstract

We propose a set of linear quantum entanglement witnesses constituted by local quantummechanical observables with each two possible measurement outcomes. These witnesses detect all the entangled resources which give rise to a better fidelity than separable states in quantum teleportation and present both sufficient and necessary conditions in experimentally detecting the useful resources for quantum teleportation.PACS numbers: 03.65. Ud, 03.67.Mn Introduction. Quantum entanglement plays important roles in many quantum information processing such as quantum teleportation. However, not all entangled states are useful for quantum teleportation. The fidelity of optimal teleportation is determined by the fully entangled fraction (FEF) [1][2][3]. A bipartite n ⊗ n state ρ gives rise to a better fidelity of teleportation than separable states if its FEF is great than 1/n. For a known quantum state, analytical formula of FEF for two-qubit states has been derived by using the method of Lagrange multiplier [4]. The upper bounds of FEF for general high dimensional quantum states have been estimated [5]. Exact results of FEF are also obtained for some special quantum states like isotropic states and Werner states [6].For a given unknown state, an important issue is to determine whether it is useful for quantum teleportation by experimental measurements. For the experimental detection of quantum entanglement, the Bell inequalities [7][8][9][10][11] and entanglement witness [12][13][14][15][16][17][18][19][20][21] have been extensively investigated. The Bell inequalities only involve measurements on local quantum mechanical observables. The entanglement witnesses are in general Hermitian operators with at least one negative eigenvalue. Since the set of the separable states is convex and compact, these witnesses give rise to inequalities (supersurfaces) separating a part of the entangled states from the rest ones including all the separable states. Different inequalities detect different entangled states. However, so far we do not have complete witnesses that detect all the entangled states in general.Recently in Ref.[22], the authors show that the set of entangled states which are useful for quantum teleportation, i.e. their FEFs are great than 1/n, is also convex and compact. They presented a witness operator which detects some entangled states that are useful for teleportation.In this brief we give a general way to enquire how to determine experimentally whether an unknown entangled state could be used as a resource for quantum teleportation. We present a linear witness operator which can detect all the entangled states that are useful for teleportation. This witness operator gives rise to a Bell-like inequality which requires only measurements on local observables and gives the sufficient and necessary condition

Quantum entanglement for two electrons in the excited states of helium-like systems

“…Here, 2 Tr ( ) r is referred to as the purity of the state and in general r is for the total system, but entanglement reflects the relationship between different parts in the system. Now in Eq.…”

“…For the helium atom (Z=2), there are infinite number of bound states in the system due to the Coulomb nature of the potential. When Z is reduced continuously to the critical charge Z=1, the system now consists of a proton and two electrons and has only one bound state, the ground state (denoted as 1s 2 …”

“…Understanding of entangled systems is important in other research areas such as quantum information [1], quantum computation [2] and quantum cryptography [3]. The investigations of quantum entanglement include the works on some model atoms like the Moshinsky atom [4][5][6][7][8], the Crandall atom [9] and the Hooke atom [9][10][11][12], and the works on artificial atoms like quantum dots [13][14][15][16][17].…”

Entanglement measures in doubly excited states and nondispersive wave packets in planar helium

“…Entanglement is one of the most significant characteristics in the quantum mechanical description of multipartite systems [1] and plays an important role in understanding fundamental phenomena such as quantum correlations [2]. Motivated not only for the interest on the foundations of quantum mechanics but also for the possible technological applications in quantum information, quantum computing [3], quantum cryptography [4], and quantum teleportation [5] there has been an increasing activity in the entanglement properties in atomic systems. While most studies on entanglement in atoms have been focused on bound levels of simplified models [6][7][8][9][10][11], there is rather few information on the entanglement properties of realistic atomic systems.…”

Detection of the ideal resource for multiqubit teleportation

“…Then a complete set of teleportation witness to detect all the ideal resource for teleportation is constructed in Ref. [12]. In Ref.…”