Quantum Dialogue through Non-destructive Discrimination of Cluster State

TL;DR

The paper addresses secure quantum dialogue by using a LU-equivalent five-qubit cluster state and non-destructive discrimination (NDD) to keep entanglement intact while exchanging information. It introduces a group-structured encoding with 32 unitary operations that map to 32 orthogonal LU-equivalent states, enabling deterministic NDD-based decoding without revealing the initial state. A stabilizer-based single-qubit error correction scheme boosts robustness without extra qubits, and the security analysis covers passive, MITM, intercept-resend, and entangling-probe attacks; the approach generalizes to n-bit messages and includes a proof-of-concept on IBM Quantum hardware. This work provides a resource-efficient, scalable framework for two-way quantum dialogue with practical implications for secure quantum communication and fault-robustness in noisy devices.

Abstract

We propose an efficient, measurement-based quantum dialogue protocol through non-destructive discrimination (NDD) of cluster state. We use ancilla-based measurements that allow the state to be reused without destroying its entanglement. The initial state is a local unitary (LU-) equivalent of the five-qubit cluster state, which significantly reduces the state components from 32 to 4, simultaneously allowing one to write its different subspaces using two different bases. The protocol utilizes single qubit unitaries from the Pauli group to encode the messages, thus preserving the stabilizer nature of the initial state throughout. We demonstrate that the proposed protocol is secure under common quantum attacks and outlining the procedure for the scalability of the scheme to transmit an n-bit message. The proposed protocol has been experimentally verified using IBM quantum backend 'IBM-Torino' as a proof of concept. Using the stabilizer nature of the state, we further introduce a single-qubit error correction mechanism that enhances robustness against noise without requiring any additional qubits. further, the use of NDD allows one to reuse the quantum resources in advancing the two-way dialogue, marking the importance and novelty of the proposed scheme over preexisting methods.

Figures (13)

• Figure 1: Circuit diagram of five-qubit Cluster state $\ket{C_5}$
• Figure 2: Local unitary equivalent circuit of $\ket{C_5}$ state that produces state $\ket{\psi_5}$
• Figure 3: Circuit diagram for $\ket{\psi_5}$ state
• Figure 4: NDD of Bell States
• Figure 5: NDD of $\ket{\psi_5}$ state