Quantum States and Quantum State Manipulations (Englisch)

In this chapter, we review continuous-variable quantum states and quantum state manipulations. First, we show several formalisms of quantum states including state vectors, stabilizers, nullifiers and covariance matrices. Second, we show their transformations by unitary operations. Since we mainly handle Gaussian operations in this thesis, which are members of a subgroup of unitary operations, we then discuss Gaussian operations by focusing on their matrix-based formalisms and examples of their unitary operators. As the last issue, we discuss entangled states and entanglement criteria. We show an extension of the van Loock-Furusawa entanglement criteria, which enables us to detect entanglement in cluster states of arbitrary graphs.