We show that the probability distribution of the Greenberger-Horne-Zeilinger quantum state (GHZ) under local action of independent von Neumann measurements follows a convex distribution of two distributions. The coef?cients of the combination are related to the equatorial parts of the measurements, and the distributions associated with those coef?cients are associated with the real parts of the measurements. One possible application of the result is that it allows one to split into two pieces the simulation of the GHZ state. Simulating, in worst-case or in average case, a quantum state like the GHZ state with random resources, shared or private, as well as with classical communication resources or even odd resources like nonlocal boxes is a very important in the theory of quantum communication complexity.

Laser pulses with picosecond and femtosecond durations are now indispensable tools in many scienti?c disciplines. These ultrashort pulses provide unique temporal resolutions for investigations of phenomena taking place in comparable time ranges. In addition, optical energies squeezed into such short time windows yield extremely high peak powers and intensities, paving the way to generate unprecedented light-matter interactions. On the other side, recent advances in spatial light intensity and phase modulation devices enables generation of laser beam pro?les with intriguing physical properties. By merging the two realms, optics researchers can now have the ability to harness light both in space and time. These possibilities bring about new physical interactions and signi?cantly facilitate many applications of lasers.