Suranjana Rai, Jagdish Rai
Group--Theoretical Structure of the Entangled States of N Identical Particles
Preprint series: ESI preprints

MSC:

94A99 None of the above but in this section

81P99 None of the above but in this section

Abstract: We provide a group-theoretical classification of the entangled states of N
identical particles. The connection between quantum entanglement and the
exchange symmetry of the states of N identical particles is made explicit
using the duality between the permutation group and the simple unitary
group. Each particle has n-levels and spans the n-dimensional Hilbert space.
We shall call the general state of the particle as a qunit. The direct
product of the N qunit space is given a decomposition in terms of states
with definite permutation symmetry. The nature of fundamental entanglement
of a state can be related to the classes of partitions of the integer N. The
maximally entangled states are generated from linear combinations of the
less entangled states of the direct product space. We also discuss the
nature of maximal entanglement and its measures.
Keywords: Quantum Entanglement, Symmetric groups, Group representations