A universal entangler (UE) is a unitary operation which maps all pure product

states to entangled states. It is known that for a bipartite system of

particles $1,2$ with a Hilbert space $\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}$,

a UE exists when $\min{(d_1,d_2)}\geq 3$ and $(d_1,d_2)\neq (3,3)$. It is also

known that whenever a UE exists, almost all unitaries are UEs; however to

verify whether a given unitary is a UE is very difficult since solving a

quadratic system of equations is NP-hard in general. This work examines the

existence and construction of UEs of bipartite bosonic/fermionic systems whose

wave functions sit in the symmetric/antisymmetric subspace of

$\mathbb{C}^{d}\otimes\mathbb{C}^{d}$. The development of a theory of UEs for

these types of systems needs considerably different approaches from that used

for UEs of distinguishable systems. This is because the general entanglement of

identical particle systems cannot be discussed in the usual way due to the

effect of (anti)-symmetrization which introduces "pseudo entanglement" that is

inaccessible in practice. We show that, unlike the distinguishable particle

case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are

symmetric (resp. antisymmetric) subspaces of

$\mathbb{C}^{d}\otimes\mathbb{C}^{d}$ if and only if $d\geq 3$ (resp. $d\geq

8$). To prove this we employ algebraic geometry to reason about the different

algebraic structures of the bosonic/fermionic systems. Additionally, due to the

relatively simple coherent state form of unentangled bosonic states, we are

able to give the explicit constructions of two bosonic UEs. Our investigation

provides insight into the entanglement properties of systems of

indisitinguishable particles, and in particular underscores the difference

between the entanglement structures of bosonic, fermionic and distinguishable

particle systems.