![]() ![]() Those are instructive for the understanding of quantum coherence and correlation in the theory of quantum information, and quantum phase transitions and factorization in condensed-matter physics. Moreover, the obvious relation among model parameters is extracted for the factorized line in the extended model. In contrast to the entanglement, quantum coherence reveals a kind of long-range nonclassical correlation. An explicit scaling law of BGD is captured at low temperature in the XY model. However, the l 1 norm is trivial for the factorization. It is shown that the susceptibility of the skew information and BGD is a genuine indicator of quantum phase transitions, and characterizes the factorization. A two-dimensional susceptibility is introduced to explore their capability in highlighting the critical lines associated with quantum phase transitions in the model. The entanglement measured via concurrence is calculated for reference. This should align the two signals.Quantum coherence and correlation of thermal states in the extended XY spin chain are studied in terms of the recently proposed l 1 norm, skew information, and Bures distance of geometry discord (BGD), respectively. Again, open the menu and click Shift Curve.Another two columns will be added and the source data of current curve will be copied to these two new columns. Open the menu again, select Translate Duplication in: New Columns from the menu. A correlation coefficient is used to evaluate similarity. Correlation is another measure of the relationship between two signals. If they are totally unrelated coherence will be 0. Click on the triangle button to open a menu and uncheck Keep Tool after Translation. If two signals correspond to each other perfectly at a given frequency, the magnitude of coherence is 1. Select the top plot, then select menu Analysis: Data Manipulation: Horizontal Translate to add a vertical line to the layer, together with a triangle button.Click OK if the Reminder Message dialog pops up. To make the datasets movable, delete the lock by clicking on it and choosing Recalculate Mode: None.Click OK and both X axes now have the same scale.Go to the Link Axes Scales tab in the right panel and click the Straight (1 to 1) radio button in the X Axis Link group. In the left panel, select Layer 2 (take care not to clear the check box). Double click on the top plot to open the Plot Details dialog box.Return to the worksheet, highlight column A and B, then from the menu select Plot > Multi-Panel/Axis: Vertical 2 Panel to plot the two signals to two separate graph layers.The Data Reader in the image above shows that at Time = 49, there is a strong positive peak, which means that the second dataset needs to be translated forward 49 units to align these two signals.Highlight column D, and from the menu select Plot > Basic 2D: Line to plot the result. The correlation result and a time lag column are output to the worksheet.Click OK to perform a correlation on the two signals.This opens the Correlation:corr1 dialog box. Highlight the two columns and from the menu select Analysis: Signal Processing: Correlation.Right click on it to open the shortcut menu, then choose item Set As: Y to set this column's plot designation to Y. and import the file \Samples\Signal Processing\Correlation.dat. Select menu File: Import: Single ASCII.The image above shows that at a frequency of 0.25 there is a strong peak, indicating a strong correspondence between the two signals at this frequency. Select the Data Reader on the Tools toolbar to read the strongest peak in the graph.Highlight these two new columns and from the menu select Plot > Basic 2D: Line to plot coherence against frequency. Two columns of data are added to the worksheet.Change the Window Type to Welch, and click OK.This opens the Coherence: cohere dialog box. Highlight the two columns and from the menu select Analysis: Signal Processing: Coherence.This sets the plot designation for column A to Y. Select column A, then right-click and select Set As: Y from the shortcut menu.Drag-and-drop this file into the empty worksheet to import it. In this folder, open the Signal Processing subfolder and find the file Coherence.dat. Perform correlation and find the lag to translate a dataset.Test coherence and find out the frequency where two signals are in the highest degree of linear dependency.If there is little or no linear relationship between two signals, the magnitude of the coefficient is small. ![]() If two signals have a high degree of similarity, the magnitude of the computed correlation coefficient is large. If they are totally unrelated coherence will be 0.Ĭorrelation is another measure of the relationship between two signals. If two signals correspond to each other perfectly at a given frequency, the magnitude of coherence is 1. Coherence measures the degree of linear dependency of two signals by testing for similar frequency components. ![]()
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