5.13 Density operators, and other things to come

The existence of entangled states leads to an obvious question: if we cannot attribute a state vector to an individual qubit, then how can we describe its quantum state? In the next few chapters we will see that, when we limit our attentions to a part of a larger system, states are not represented by vectors, measurements are not described by orthogonal projections, and evolution is not unitary. As a spoiler, here is a dictionary of some of the new concepts that will soon be introduced:

state vectors \rightsquigarrow density operators
orthogonal projectors \rightsquigarrow positive operator-valued measures
unitary evolutions \rightsquigarrow completely-positive trace-preserving maps