Abstract

This dissertation is focused on analysis of the symmetric extendibility of quantum states and its applications in the quantum information theory, with special attention paid to the area of quantum entanglement distillation, quantum channels theory, quantum security, and monogamy of quantum entanglement in time. We analyze geometry of the set of symmetric extendible states, i.e. such states that possess symmetric extensions and in particular, prove that the set is closed under action of the 1-LOCC operators which is of a great importance for further applications in one-way distillability of quantum states and quantum channels theory. Basing on the Choi-Jamiolkowski isomorphism between quantum states and quantum channels, we derive a simple test for the quantum channel capacity. We discuss also monogamy of quantum entanglement and its relations with Bell theorem, and the symmetric extendibility. Further, the subject of our analysis is also the theory of quantum entanglement measures and their relation to the symmetric extendibility. A new entanglement monotone and parameter are introduced basing on this concept, which are applied as new upper bounds on distillable entanglement. We introduce the concept of reduced variants of the quantum communication rates, showing that they can efficiently estimate non-reduced quantum measures. Finally, it is derived that in the paradigm of the entangled consistent histories, introducing the concept of quantum entanglement in time, a particular history is monogamous and we can derive the Tsirelson bound on the Leggett-Garg temporal inequalities. The results presented in this PhD thesis show importance of the concept of the symmetric extendibility for further development of quantum information theory, especially in domain of one-way communication.

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