Quality Of Correlation In Quantum Information

Quantum information is a new cross-disciplinary subject of the combination ofquantum mechanics and classical information science. The earliest discoverednon-classical correlation is quantum entanglement. It plays an important role inquantum information processing. The other important non-classical correlation，quantum discord (QD), had been found in2001.With further research, one has found aquantum phenomenon which is called entanglement sudden death. When a quantumsystem appears entanglement sudden death, its quantum discord is still non-zero, andthe correlation is considered to be still used for quantum information processing, butthis is not a good time interval for quantum information processing. Due to a quantumgate needs an operation time interval, this requires selecting a time interval longerthan the operation time of the quantum gate, when the quantum correlation maintainsstrong and stable, for quantum gate operation. A strong and stable correlation in aquantum system is of high quality for quantum information processing.We select a two-qubit Heisenberg XXZ spin chain with Dzyaloshinskii-Moriyainteraction in an inhomogeneous magnetic field as an example, calculate the evolutionexpressions of the concurrence, QD and the GMQD, and finally compare the qualitiesof this three forms of quantum correlation. We define two quantities, selective averagecorrelation and ripple coefficient, to evaluate the quality of correlation in quantuminformation processing in a time interval. We use the two quantities to evaluate thequalities of the correlation with different measures under the same parameters, andalso evaluate the qualities of the correlation with a measure under the differentparameters. Our results show that, if the time evolutions of the correlation withdifferent measures under the same parameters are similar, there needs only evaluatingone of them to know when the correlation has high quality for quantum informationprocessing.