Impossibility of partial swapping of Quantum Information

Abstract

It is a well known fact that a quantum state $|ψ(θ,ϕ)>$ are represented by a point on the Bloch sphere, characterized by two parameters $θ$ and $ϕ$. Here in this work, we find out another impossible operation in quantum information theory . We name this impossibility as 'Impossibility of partial swapping of quantum information '. By this we mean that if two unknown quantum states are given at the input port, there exists no physical process, consistent with the principles of quantum mechanics, by which we can partially swap either of the two parameters $θ$ and $ϕ$ between these two quantum states. In this work we provided the impossibility proofs for the qubits(i.e the quantum states taken from two dimensional Hilbert space) and this impossible operation can be shown to hold in higher dimension also.