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

TL;DR

The paper addresses cryptographic security in quantum teleportation by employing $q$-deformed algebras. It develops $q$-deformed Bell-like states that reduce to standard Bell states as $q\to 1$ and generalizes teleportation to non-maximally entangled resources, incorporating arbitrary functions of $q$ to enable enhanced security. Two protocols are proposed: one with undeformed information qubits using $q$-deformed non-maximally entangled states, and another with both deformed information and entangled states, each requiring sharing additional decryption parameters such as $|DetA_q|$, $\omega(q)$, $\delta(q)$, $\gamma(q)$, and the deformation parameter $q$. In the limit $q\to 1$, the methods reduce to standard teleportation, preserving fidelity bounds while offering increased security for $q\neq 1$.

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.

Figures (3)

• Figure 1: Teleportation circuit using usual non-maximally entangled states
• Figure 2: Teleportation Circuit using deformed entangled state
• Figure 3: Teleportation Circuit using both deformed information and deformed entangled state