Improved cryptographic security in teleportation with q-deformed non-maximal entangled states

In this work the machinery of q-deformed algebras are used to enhance cryptographic security during teleportation. We use q-deformed harmonic oscillator states to develop a novel method of teleportation. The deformed states can be expressed in terms of standard oscillator states and the expressions contain certain arbitrary functions of q. It is the presence of these arbitrary functions that allows an enhancement of cryptographic security. The specifics are : (a) q-deformed Bell-like states are constructed which reduce to the usual Bell states when the deformation parameter q→ 1. These deformed states form an orthonormal basis for q-deformed entangled bipartite states when certain arbitrary functions of q satisfy a constraint. (b) We discuss the generalisation of the usual teleportation protocol with non-maximally entangled states. This generalisation is then employed to construct two new protocols using q-deformed non-maximally entangled states. These states have additional parameters and these have to be shared for decryption after teleportation. Consequently, the cryptographic security is improved.