General Monogamy Relation For The Entanglement Of Formation In Multiqubit Systems And Its Application

Quantum entanglement is one of the most important physical resources in quantum information processing, which has been widely applied to superdense coding, quantum teleportation, and the one-way quantum computing, etc. So far, quantum entanglement in two-qubit systems is well studied, but the characterization of entanglement in many-body systems is still an open problem even for the entanglement structure and quantification in multi-qubit systems. As a fundamental problem in quantum entanglement theory, multipartite entanglement characterization was paid a lot of attention over the last 20 years.Entanglement monogamy is an important property in multipartite quantum systems, which can be used to characterize the entanglement structure in multipartite systems. In 2000, Coffman, Kundu and Wootters proved that squared concurrence(SC) obeys monogamy inequality for three-qubit states, and introduced a genuine three-qubit entanglement measure named “Three-tangle”. In 2006, Osborne and Verstraete generalized the monogamy inequality to N-qubit systems. However, the monogamy inequality based on concurrence can not be used to characterize all kinds of multi-qubit entanglement structure. In order to solve this problem, we conduct in-depth research on entanglement monogamy and multipartite entanglement structure in this thesis. We mainly research two aspects of content: firstly, for multi-qubit systems, we analyze the relationship between the monogamy property of squared entanglement of formation(SEF) and multipartite entanglement structure, which is committed to explore a quantitative description of entanglement monogamy that corresponds to the property of multipartite entanglement. Secondly, we analyze the hierarchical monogamy relations for squared entanglement of formation(SEF) in multipartite systems.The thesis includes four chapters and our main contributions are given in Chap.2 through 4. In Chap.1, we introduce some basic concepts, such as: quantum entanglement measure and the property of entanglement distribution, etc. In Chap.2, we prove analytically that squared entanglement of formation(SEF) obeys general monogamy inequality in N-qubit pure states, and further generalize to N-qubit mixed states. In Chap.3, we construct two sets of multipartite entanglement indicators based on the monogamy property of SEF. The first kind of indicators can detect genuine multi-qubit entanglement in all N-qubit mixed states. The second kind of indicators have better computability and can be applied to the characterization of multipartite entanglement dynamics. In addition, we analyze the relationship between the monogamy property of SQD and that of SEF. In Chap.4, we show exactly that squared entanglement of formation(SEF) obeys a set of hierarchical k-partite monogamy relations in N-qubit systems. Based on this, we construct a set of hierarchical multipartite entanglement indicators, which can be used to detect multipartite entanglement in N-qubit W states and analyze multipartite entanglement dynamics in composite cavity-reservoir systems. Finally, for multipartite systems of arbitrary dimension, it is illustrated that SEF possesses a better monogamous property than SC. The last part of this thesis gives a brief conclusion and outlook on the future research.