Entanglement Of Stabilizer Codes For Graph States

Like classical information coding, quantum error correcting code encodes information in quantum states with a particular structure. A quantum code processes quantum information or transmits quantum information correctly in presence of noise. The degree of difficulty to construct quantum error-correcting codes is closely related to the quantum entanglement in the codes. Therefore it is necessary to measure the entanglement of quantum codes. One important class of quantum error correction codes is called stabilizer codes. The code space of a code is some eigenspace with common eigenvalues+1of the stabilizer operators. During the processing of error correction, the properties of stabilizer codes can be described by graph states which are closely related to the codes.Graph states are important multipartite entangled states. They can be seen as linear superposition of many terms of the direct product states, and can be described by mathematical graphs of vertices and lines. The way to construct an additive (or stabilizer) quantum code is intimately related to a graph state. We use a highly entangled graph state and a classical code to construct a quantum error correcting code.In this thesis, we focus on the entanglement of multi-qubit quantum error correcting stabilizer codes. The entanglement properties of graphical codes are determined by calculation and analysis. We calculate the entanglement properties of stabilizers codes with seven or less qubits (including [[7,1,3]] code,[[6,1,3]] code,[[5,1,3]] code, and [[4,1,3]] code) by iterative algorithm and entanglement analysis. Finally, we identify entanglement pattern of these stabilizer codes, and we get a better understanding of their entanglement properties.