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

TL;DR

This paper introduces a novel quantum teleportation protocol using q-deformed non-maximal entangled states, which enhances cryptographic security through the use of arbitrary functions of the deformation parameter.

Contribution

It develops a new teleportation method employing q-deformed states with additional parameters, improving cryptographic security compared to traditional protocols.

Findings

Deformed Bell-like states reduce to standard Bell states as q→1.

New protocols with q-deformed non-maximal entanglement enhance security.

Additional parameters in states require sharing for decryption, increasing security.

Abstract

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 $q\rightarrow 1$. 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.