  Identical particles and entanglement are both fundamental components of
quantum mechanics. However, when identical particles are condensed in a single
spatial mode, the standard notions of entanglement, based on clearly
identifiable subsystems, break down. This has led many to conclude that such
systems have limited value for quantum information tasks, compared to
distinguishable particle systems. To the contrary, we show that any
entanglement formally appearing amongst the identical particles, including
entanglement due purely to symmetrization, can be extracted into an entangled
state of independent modes, which can then be applied to any task. In fact, the
entanglement of the mode system is in one-to-one correspondence with the
entanglement between the inaccessible identical particles. This settles the
long-standing debate about the resource capabilities of such states, in
particular spin-squeezed states of Bose-Einstein condensates, while also
revealing a new perspective on how and when entanglement is generated in
passive optical networks. Our results thus reveal new fundamental connections
between entanglement, squeezing, and indistinguishability.
