  We derive two complementarity relations that constrain the individual and
bipartite properties that may simultaneously exist in a multi-qubit system. The
first expression, valid for an arbitrary pure state of n qubits, demonstrates
that the degree to which single particle properties are possessed by an
individual member of the system is limited by the bipartite entanglement that
exists between that qubit and the remainder of the system. This result implies
that the phenomenon of entanglement sharing is one specific consequence of
complementarity. The second expression, which holds for an arbitrary state of
two qubits, pure or mixed, quantifies a tradeoff between the amounts of
entanglement, separable uncertainty, and single particle properties that are
encoded in the quantum state. The separable uncertainty is a natural measure of
our ignorance about the properties possessed by individual subsystems, and may
be used to completely characterize the relationship between entanglement and
mixedness in two-qubit systems. The two-qubit complementarity relation yields a
useful geometric picture in which the root mean square values of local
subsystem properties act like coordinates in the space of density matrices, and
suggests possible insights into the problem of interpreting quantum mechanics.
