Symmetrization and Entanglement of Arbitrary States of Qubits

Abstract

Given two arbitrary pure states $ |ϕ>$ and $ |ψ>$ of qubits or higher level states, we provide arguments in favor of states of the form $ \frac{1}{\sqrt{2}}(|ψ> |ϕ> + i |ϕ> |ψ>) $ instead of symmetric or anti-symmetric states, as natural candidates for optimally entangled states constructed from these states. We show that such states firstly have on the average a high value of concurrence, secondly can be constructed by a universal unitary operator independent of the input states. We also show that these states are the only ones which can be produced with perfect fidelity by any quantum operation designed for intertwining two pure states with a relative phase. A probabilistic method is proposed for producing any pre-determined relative phase into the combination of any two arbitrary states.