Complementarity and entanglement in quantum information by Tracey E Tessier

By Tracey E Tessier

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63) It then follows that the relation in Eq. 61) holds since the scaled negativity and the I-concurrence are convex functions on the space of density matrices that agree 37 Chapter 2. Measures of Entanglement on the extreme points (the pure states) of this space, while the I-concurrence is by definition the largest of all such functions. 64) is a lower bound on the mixed-state I-tangle, Lτ (ρ) ≤ τ (ρ) . 65) These bounds, which are entanglement monotones in their own right, may be evaluated for a bipartite system with subsystems of arbitrary dimensions in a straightforward manner with the help of a standard linear algebra package.

In preparation. 1: List of chapters in this dissertation and the corresponding published, submitted, or in progress papers. 17 Chapter 1. 3, a great deal of quantum information theory is concerned with answering the following question: In what way, if any, does the potential use of entanglement enhance the performance of a given classical information processing task? In this context, where quantum mechanical correlations are viewed as a resource, it is important to have a consistent way of quantifying entanglement.

Measures of Entanglement to new insights into the operation of quantum algorithms [59, 60] and in the problem of optimal Hamiltonian simulation [55]. The majorization relation between the global and local eigenvalue vectors of a bipartite system has also been used to shed light on the phenomenon of bound entanglement [61]. The following is a brief review of the main tenets of majorization theory. The reader is referred to [54] for extensive background on the subject. Given two ddimensional vectors x and y in Rd , we say that x is majorized by y, denoted by the expression x ≺ y, when the following two conditions hold: k k x↓i i=1 ≤ yi↓; i=1 ∀k = 1, .

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