If two quantum particles are entangled and measurements are performed on them simultaneously, the measurement outcomes for each particle will still be subject to the probabilistic nature of quantum mechanics. The measurement results will exhibit correlations that are dependent on the entanglement between the particles, but they will not violate the fundamental principles of quantum uncertainty.
Let's consider an example using the entangled state of two particles, such as photons, called a Bell state. Suppose we have an entangled pair of photons in the Bell state:
|ψ⟩ = (1/√2)(|H⟩⨂|V⟩ - |V⟩⨂|H⟩)
In this state, |H⟩ represents horizontal polarization, and |V⟩ represents vertical polarization. When a measurement is performed on one of the photons to determine its polarization, the result will be completely random. It could be either horizontally polarized or vertically polarized with a certain probability associated with each outcome.
If the measurement is simultaneously performed on the other entangled photon, the measurement outcome will also be random. However, due to the entanglement, the measurement results of the two photons will be correlated. For example, if the first measurement yields a horizontally polarized photon, the second measurement will yield a vertically polarized photon, and vice versa.
The key point to note is that the measurement outcomes are still probabilistic, even when performed simultaneously. The entanglement between the particles does not allow for predetermined, deterministic outcomes. The measurement results will only exhibit statistical correlations dictated by the entangled state.
In summary, if measurements of entangled particles are performed at precisely the exact time, the outcomes will be probabilistic and correlated, but they will not bypass the inherent uncertainty of quantum mechanics.