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LETTERS Deterministic entanglement swapping with an iontrap quantum computer
, 2008
"... Entanglement—once only a subject of disputes about the foundation of quantum mechanics—has today become an essential issue in the emerging field of quantum information processing, promising a number of applications, including secure communication, teleportation and powerful quantum computation. Ther ..."
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Entanglement—once only a subject of disputes about the foundation of quantum mechanics—has today become an essential issue in the emerging field of quantum information processing, promising a number of applications, including secure communication, teleportation and powerful quantum computation. Therefore, a focus of current experimental work in the field of quantum information is the creation and manipulation of entangled quantum systems. Here, we present our results on entangling two qubits in an iontrap quantum processor not through a direct interaction of the ion qubits but instead through the action of a protocol known as entanglement swapping1. Our iontrap system enables us to implement all steps of the entanglement swapping protocol in a fully deterministic way. Thus, two ion qubits can be prepared on demand in a welldefined entangled state. This particular feature may facilitate
Black Holes, Qubits and Octonions
, 2008
"... We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory. The first example is provided by the measure of the tripartite entanglement of three qubits (Alice, Bob and Charlie), known a ..."
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We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory. The first example is provided by the measure of the tripartite entanglement of three qubits (Alice, Bob and Charlie), known as the 3tangle, and the entropy of the 8charge ST U black hole of N = 2 supergravity, both of which are given by the [SL(2)] 3 invariant hyperdeterminant, a quantity first introduced by Cayley in 1845. Moreover the classification of threequbit entanglements is related to the classification of N = 2 supersymmetric ST U black holes. There are further relationships between the attractor mechanism and local distillation protocols and between supersymmetry and the suppression of bit flip errors. At the microscopic level, the black holes are described by intersecting D3branes whose wrapping around the six compact dimensions T 6 provides the stringtheoretic interpretation of the charges and we associate the threequbit basis vectors, ABC〉 (A, B, C = 0 or 1), with the corresponding 8 wrapping cycles. The black hole/qubit correspondence extends to the 56 charge N = 8 black holes and the tripartite entanglement of seven qubits where the measure is provided by Cartan’s E7 ⊃ [SL(2)] 7 invariant. The qubits are naturally described by the seven vertices ABCDEF G of the Fano plane, which provides the multiplication table of the seven imaginary octonions,
Local Vs. Joint Measurements For The Entanglement Of Assistance
, 2001
"... this paper. In analogy to Eq. (5) we therefore de ne the concurrence of assistance p i C (j i i) : (9) The HJWtheorem ensures also in this case dependence on AB only ..."
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this paper. In analogy to Eq. (5) we therefore de ne the concurrence of assistance p i C (j i i) : (9) The HJWtheorem ensures also in this case dependence on AB only
Entanglement Distillation  A Discourse on Bound Entanglement in Quantum Information Theory
, 2006
"... In recent years entanglement has been recognised as a useful resource in quantum information and computation. This applies primarily to pure state entanglement which is, due to interaction with the environment, rarely available. Decoherence provides the main motivation for the study of entanglement ..."
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In recent years entanglement has been recognised as a useful resource in quantum information and computation. This applies primarily to pure state entanglement which is, due to interaction with the environment, rarely available. Decoherence provides the main motivation for the study of entanglement distillation. A remarkable effect in the context of distillation is the existence of bound entangled states, states from which no pure state entanglement can be distilled. The concept of entanglement distillation also relates to a canonical way of theoretically quantifying mixed state entanglement. This thesis is, apart from a review chapter on distillation, mainly a theoretical study of bound entanglement and the two major open problems in their classification. The first of these is the classification of PPT bound entanglement (separability problem). After having reviewed known tools we study in detail the multipartite permutation criteria, for which we present new results in their classification. We solve an open problem on the existence of certain PPT states. The Schmidt number of a quantum state is a largely unvalued concept, we analyse it in detail and introduce the Schmidt robustness. The notion of Schmidt number is exploited in the study of the second
Some bipartite states do not arise from channels
, 2008
"... It is wellknown that action of a quantum channel on a state can be represented, using an auxiliary space, as the partial trace of an associated bipartite state. Recently, it was observed that for the bipartite state associated with the optimal average input of the channel, the entanglement of forma ..."
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It is wellknown that action of a quantum channel on a state can be represented, using an auxiliary space, as the partial trace of an associated bipartite state. Recently, it was observed that for the bipartite state associated with the optimal average input of the channel, the entanglement of formation is simply the entropy of the reduced density matrix minus the Holevo capacity. It is natural to ask if every bipartite state can be associated with some channel in this way. We show that the answer is negative.
Optimal Decompositions with Respect to Entropy and Symmetries
, 1998
"... Abstract. The entropy of a subalgebra, which has been used in quantum ergodic theory to construct a noncommutative dynamical entropy, coincides for Nlevel systems and Abelian subalgebras with the notion of maximal mutual information of quantum communication theory. The optimal decompositions of mix ..."
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Abstract. The entropy of a subalgebra, which has been used in quantum ergodic theory to construct a noncommutative dynamical entropy, coincides for Nlevel systems and Abelian subalgebras with the notion of maximal mutual information of quantum communication theory. The optimal decompositions of mixed quantum states singled out by the entropy of Abelian subalgebras correspond to optimal detection schemes at the receiving end of a quantum channel. It is then worthwhile studying in some detail the structure of the convex hull of quantum states brought about by the variational definition of the entropy of a subalgebra. In this Letter, we extend previous results on the optimal decompositions for 3level systems.