@misc{oai:ir.soken.ac.jp:00001237,
 author = {長田, 宏二 and ナガタ, コウジ and NAGATA, Kouji},
 month = {2016-02-17},
 note = {Since the 1980s, there has been a physical problem relating to the detection of multipartite entangled states that helps us to investigate fundamental point of view on interpretations of quantum mechanics.  On the other hand, information theories based on the mathematical structure of quantum mechanics, for example, quantum cryptography and quantum computation, have been investigated by researchers whose number has been increasing day by day in the world.  This field became to be called quantum information theories.  A practical experimental realization of quantum information processing needs that we detect experimentally multipartite entangled states.  The number of researchers for multipartite entangled states is increasing rapidly.  Especially, Greenberger-Horne-Zeilinger (GHZ) states are useful for quantum information processing information processing using quantum mechanics, which improves the conventional information processing ability which had been based on classical theories.  However, practical experimental realization of the theories and controlling quantum states have inevitable difficulties due to the interaction with environments.  The requirement in maintaining multipartite entangled states in relation to the time that takes to make a practical experiment is also a problem.  Many experimentalists are tackling this problem, and recently, several groups have reported that multipartite entangled states have been physically detected in their laboratories.  The main difficulty is how to judge whether or not the observed quantum state is indeed a multipartite entangled state.  For this purpose, it is necessary to construct theoretical models to analyze such experimental data.<br />  In this thesis, we apply a mathematical structure as to density operators described in a high-dimensional Hilbert space, and we employ mathematical theories to prove if the corresponding density operator represents a multipartite entangled state or not.  The main aim for constructing such models is to analyze the raw experimental data.  Moreover, this model helps experimentalists in the sense that it allows them to see how to confirm that observed states are indeed the desired state.  With mathematical theories developed before this thesis, only limited applications for this purpose were allowed.  Some theories cover two-dimensional Hilbert space only.  It has not been even discussed how to analyze the fidelity to GHZ states of the observed state.  This has led to some doubt of that experimental data might not always confirm three-partite entangled states.  However, by using the method of this thesis, statistical check based on such experimental data of the existence of three particle-entangled states is possible under appropriate assumptions.  This example symbolizes that our analytical knowledge has improved very much in the last few years.  This thesis gives us an advanced mathematical model for analyzing experimental data., 総研大甲第712号},
 title = {Theory on detection of multipartite entanglement},
 year = {}
}