Extended Weyl-Heisenberg algebra, phase operator, unitary depolarizers and generalized Bell states

Finite dimensional representations of extended Weyl-Heisenberg algebra are studied both from mathematical and applied viewpoints. They are used to define unitary phase operator and the corresponding eigenstates (phase states). It is also shown that the unitary depolarizers can be constructed in a general setting in terms of phase operators. Generation of generalized Bell states using the phase operator is presented and their expressions in terms of the elements of mutually unbiased bases are given. -- Highlights: → Hermitian phase operators and phase states are given for a large class of extended Weyl-Heisenberg algebras. → The unitary phase depolarizers are expressed in terms of phase operators. → The entanglement of generalized Bell states is examined.