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arXiv:1006.5474 · Quantum Information Processing

Disappearance of entanglement: a topological point of view

Dong Zhou, Robert Joynt

Published Aug 1, 2011• 5 citations
arXivHTMLPDF
DOI
10.1007/s11128-011-0272-8

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The dynamics of a two-qubit system is considered with the aim of a general categorization of the different ways in which entanglement can disappear in the course of the evolution, e.g., entanglement sudden death. The dynamics is described by the function ~n(t), where ~n is the 15-dimensional polarization vector. This representation is particularly useful because the components of ~n are direct physical observables, there is a meaningful notion of orthogonality, and the concurrence C can be computed for any point in the space. We analyze the topology of the space S of separable states (those having C = 0), and the often lower-dimensional linear dynamical subspace D that is characteristic of a specific physical model. This allows us to give a rigorous characterization of the four possible kinds of entanglement evolution. Which evolution is realized depends on the dimensionality of D and of D \cap S, the position of the asymptotic point of the evolution, and whether or not the evolution is distance-Markovian, a notion we define. We give several examples to illustrate the general principles, and to give a method to compute critical points. We construct a model that shows all four behaviors.
Abstract We investigate from a philosophical point of view the concept of relation that is used to explain the physical phenomenon of Entanglement. If the concept of relation is understood in the ordinary sense of the mono‐dyadic construct, which requires a middle term between the two extremes, it is aporetic and, thus, incapable of explaining the phenomenon. To the contrary, we propose to think the relation as the act of self‐referring of related terms, which is unique and identical for both terms. In the unity of this act, the duality of terms disappears, so that the authentic unity is obtained. Moving from this concept of unity, the phenomenon of Entanglement becomes intelligible, since the two particles emerge as the two abstract sections of a unique reality.
Einstein's field equations of gravitation are known to admit closed timelike curve (CTC) solutions. Deutsch approached the problem from the quantum information point of view and proposed a self-consistency condition. In this work, the Deutsch equation is formulated as an eigenvalue problem. The disappearance of entanglement between two qubits in an Einstein-Podolsky-Rosen (EPR) state near a CTC is demonstrated. The method is utilized to analyze the discontinuous evolution of two chronology respecting (CR) qubits near a CTC.