General Quantum Instruction for Communication via Maximally Entangled $n$-Qubit States

TL;DR

This paper introduces a scalable n-bit superdense coding protocol using maximally entangled n-qubit states, with practical implementation on IBM quantum hardware, enabling efficient quantum communication.

Contribution

It provides the first explicit, scalable recipe for constructing n-bit superdense coding circuits, optimizing error minimization and demonstrating real hardware performance.

Findings

Success rates decrease with longer messages and more complex circuits.

Shorter message segments improve transmission success.

Hardware improvements can enhance protocol performance.

Abstract

This study presents a generalized $n$-bit superdense coding protocol that enables the transmission of n classical bits of information using an entangled n--qubit quantum system and the transmission of $n-1$ qubits. The protocol involves creating a maximally entangled n--qubit state, encoding the classical message with Pauli--Z and Pauli--X gates, and then transmitting and decoding the message via quantum communication, quantum operations, and measurements. The key novelty of this work lies in the proposed n--bit encoding routine, which, to the best of our knowledge, is the first explicit and scalable recipe for constructing quantum circuits for n--bit Superdense Coding, minimizing errors through a simple circuit design. The protocol was tested on real quantum hardware using Qiskit 2.0 and the IBM--Torino quantum computer for message lengths of 4, 6, 8, and 10 bits. Results show that success rates decrease as message length, circuit depth, and gate count increase, largely due to increased Pauli--X gate usage for messages with more ``1" bits. Strategies to improve performance include sending messages in shorter segments and advances in qubit coherence and gate fidelity. This work offers a practical and easily scalable quantum communication instruction with potential applications in quantum networks and communication systems.