When a quantum-entangled particle is destroyed or undergoes a measurement, the state of the entangled system as a whole changes. However, the specific outcome and the effect on the "other" entangled particle depend on the nature of the measurement or destruction process applied to the first particle.
In quantum entanglement, two or more particles can become correlated in such a way that the state of one particle is inherently connected to the state of the others, regardless of the physical distance between them. This entangled state is described by a mathematical object called a wavefunction, which contains information about the probabilities of different outcomes when measurements are made on the entangled particles.
When a measurement or destruction is performed on one entangled particle, it effectively "collapses" the wavefunction, determining a definite value for the measured property of that particle. This collapse of the wavefunction is a non-reversible process. The outcome of the measurement is determined probabilistically according to the probabilities encoded in the wavefunction.
The consequence of this collapse is that the wavefunction of the other entangled particle also changes instantaneously, regardless of the spatial separation between the particles. The change in the wavefunction of the second particle ensures that the correlations between the two particles are maintained.
However, it is important to note that the specific outcome of the measurement or destruction on the first particle does not determine the immediate state or outcome of the second particle. The measurement outcomes on the entangled particles are inherently random, and it is only through subsequent measurements or interactions that the correlation between the particles becomes apparent.
This characteristic of quantum entanglement, known as "spooky action at a distance," has been experimentally verified through numerous tests of Bell's inequalities. It demonstrates that information about the state of one particle can instantaneously affect the state of the other particle, even when they are physically separated.
In summary, when an entangled particle is destroyed or measured, the state of the other entangled particle changes instantaneously, maintaining the correlation between the two particles. The specific outcome of the second particle's state is determined by subsequent measurements or interactions.