For a system with more than one particle, we often write the complete state as the product of two kets, one for each particle. For example, if particle has spin, and particle has spin, we’d write

where A has spin Up and B has spin Down Often, we don’t know which is up and which is down so we write the system as a superposition, which reflects the uncertainty of the system. The expression reflects the probability of each possibility. The particles are entangles

There isn’t a real mathematical description of describing this state, so we just label each one, e.g. up and down.