| Quantum information is a new and rapidly developing interdiscipline. It is a new way to make quantum computation, quantum encoding or quantum information transmission by using quantum characters. Quantum correlation, as a core concept, plays an important role in quantum information.It is widely believed that quantum correlation is showed by quantum entanglement at the preliminary stage of researching quantum information. Quantum entanglement, a particular and complex quantum effect, reflects the natural feature of quantum physics. It can be a significant source for all aspects of quantum information science as its own inherent features. For example, it can solve the special algorithm or work that cannot be solved by classical computer, and achieve parallel computing as a natural parallel computer. It can also raise the computing speed for computer through purifying. As further research, it has quantum correlations beyond quantum entanglement for a general quantum state. Those quantum correlations have different properties with quantum entanglement. Thus, they will play a role in quantum computing and information.Quantum discord, based on measurement as a measure of quantum correlation beyond quantum entanglement, is defined by the difference between the quantum mutual information and the classical correlation in a bipartite system. It can be a more essential quantum correlation. Because, it has quantum discord for separable state, with none of quantum entanglement. It is well-known that the key step in computing classical correlation as well as quantum discord is to obtain the minimum value of the conditional entropy. As the optimization for that entropy requires the solution to a pair of transcendental equations, a closed expression for the discord of arbitrary two-qubit states cannot be obtained. Ones have to use numerical method to get quantum discord. Meanwhile, the quantum discord is affected by the diverse measurement. This paper will calculate quantum discord by positive operator valued measure(POVM for short), which projected vectors are not orthogonal. While, after examining 105 random quantum states for a two-qubit system, we find that POVM should be taken account into the evaluation of quantum discord if a higher accuracy is required. In fact, we find the minimum conditional entropy for about 0.1% of the chosen random states must be obtained through POVM. We provide the maximum relative errors of the quantum discord from both von Neumann measurement and POVM. In addition, we also examine a four-direction projection measurement for 105 random states for the two-qubit system, which turns out that von Neumann measurement and threedirection POVM are sufficient to obtain the value of quantum discord.Measuring error are only due to technological limitations in a classical world. While it entails that two noncommuting observables cannot be jointly measured with arbitrary precision, no matter how precise the measurement device is, in quantum mechanics. And the uncertainty relations connects with distinctive quantum features. The uncertainty of measurement is crucial in quantum theory and reflects the degree of quantum features. The notion of local quantum uncertainty(LQU for short) is entwined to the notion of quantum discord. LQU is a measure for non-classical correlation in a new point of view and is also a hot research topic. This article design a quantum circuit to produce two-qubit X-states. After that, it investigates the quantum correlation properties of several classes of given separable two-qubit states and also discusses these states in regarding to their robustness against noise. It can conclude that the robustness measured by LQU and that measured by fidelity are different. Finally, it can be conclude that LQU may be an independent measure comparing with quantum entanglement and discord after taking making detailed statistical analysis for 105 random quantum states. In the end, we discuss our work for the next step. |
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