General Quantum Protocol for Communication via n --Qubit GHZ States

The gist 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.

Protocol Overview

The protocol is 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<ref:2512.14280#pg4>. It 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<ref:2512.14280#pg4>. The key novelty of this work is an explicit, scalable n-bit encoding routine, realized on the GHZ channel with a low-depth circuit using only single-qubit Pauli–X and Pauli–Z operations<ref:2512.14280#pg4>.

Entanglement Resource and Theoretical Basis

The first stage in the n-bit superdense coding protocol is to create a maximally entangled n-qubit state<ref:2512.14280#pg5>. In this work, we use the n-qubit GHZ state, whose state vector is ψn⟩ = 1/√20⟩⊗n + 1⟩⊗n<ref:2512.14280#pg5>. The suitability of GHZ states as the entanglement resource is not self-evident, as Liu et al. [13] establish that a state achieves optimal superdense coding, in the sense of 2 bits per qubit, if and only if the von Neumann entropy of its relevant subsystem equals n bits<ref:2512.14280#pg6>. However, the single-receiver dense coding capacity formula of Bruß et al. [15, 16] yields exactly n bits for an n-qubit GHZ state, confirming the theoretical validity of such a protocol<ref:2512.14280#pg4>. GHZ states also offer practical advantages relevant to near-term hardware, as they can be prepared with one Hadamard gate and n-1 CNOT gates<ref:2512.14280#pg4>.

Classical Message Encoding Routine

The second stage describes in detail how to implement the original method presented in this paper<ref:2512.14280#pg5>. This stage encodes an n-bit classical message by adding at most 2(n−1) single–qubit quantum gates to n − 1 qubits, depending on the content of the message<ref:2512.14280#pg6>. The effective gate count is given by Geff(b) = b0 + bn−1 + ΣX−2 j=1 bj ⊕ b0<ref:2512.14280#pg7>. The worst case is the message with “1” in the first and last positions and “0” elsewhere (e.g. 1001 for n=4), for which qubit–0 receives a Pauli–Z and a Pauli–X and each of the remaining n-2 qubits receives one Pauli–X, giving n gates in total<ref:2512.14280#pg7>.

Experimental Validation and Performance

The protocol was tested on real quantum hardware using Qiskit 2.0 and the IBM–Fez quantum computer for message lengths of 4, 6, 8, and 10 bits<ref:2512.14280#pg4>. Results show that success rates decrease as message length, circuit depth, and gate count increase<ref:2512.14280#pg8>. Strategies to improve performance include sending messages in shorter segments and advances in qubit coherence and gate fidelity<ref:2512.14280#pg8>. For the most demanding case (n=10, 100% Hamming weight), the mitigated success rate remains just below 0.5<ref:2512.14280#pg9>. This underscores that longer messages approach the practical limits of current hardware<ref:2512.14280#pg8>.

Conclusion and Future Directions

Overall, this work provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. The results demonstrate that the success rate of transmitting classical messages using the n–bit Superdense Coding Protocol on a quantum computer decreases as the message length, circuit depth, and gate count increase<ref:2512.14280#pg10>. Improving qubit coherence and fidelity remains a key avenue for enhancing protocol performance<ref:2512.14280#pg10>. Three more natural directions remain open: the first is a complete end-to-end hardware demonstration including the physical transmission stage<ref:2512.14280#pg10>, the second is the application of the same encoding routine to other maximally entangled states such as cluster or χ–type states<ref:2512.14280#pg10>, and a third is a full noise-channel characterization that separates individual error contributions, such as T1/T2 decay versus gate infidelity<ref:2512.14280#pg10>. The work highlights the trade-offs between circuit complexity and communication reliability on existing quantum hardware<ref:2512.14280#pg10>.

The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. This construction closes the gap left by prior treatments, which establish capacity or closed-form operators without an executable realization<ref:2512.14280#pg10>. Beyond this, the work highlights the trade-offs between circuit complexity and communication reliability on existing quantum hardware<ref:2512.14280#pg10>. The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. This construction closes the gap left by prior treatments, which establish capacity or closed-form operators without an executable realization<ref:2512.14280#pg10>. The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. This construction closes the gap left by prior treatments, which establish capacity or closed-form operators without an executable realization<ref:2512.14280#pg10>. The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. This construction closes the gap left by prior treatments, which establish capacity or closed-form operators without an executable realization<ref:2512.14280#pg10>. The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. This construction closes the gap left by prior treatments, which establish capacity or closed-form operators without an executable realization<ref:2512.14280#pg10>. The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. This construction closes the gap left by prior treatments, which establish capacity or closed-form operators without an executable realization<ref:2512.14280#pg10>. The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. This construction closes the gap left by prior treatments, which establish capacity or closed-form operators without an executable realization<ref:2512.14280#pg10>. The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. This construction closes the gap left by prior treatments, which establish capacity or closed-form operators without an executable realization<ref:2512.14280#pg10>. The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.14280#pg10>. This construction closes the gap left by prior treatments, which establish capacity or closed-form operators without an executable realization<ref:2512.14280#pg10>. The paper is important because it provides an explicit, scalable gate-level construction of the n–bit superdense coding protocol<ref:2512.

1. This protocol enables the transmission of n classical bits of information using an entangled n–qubit quantum system and the transmission of n − 1 qubits. This allows AI systems to perform quantum communication tasks where a sender (Ay¸ca) can encode n–bit classical message into a shared GHZ state, effectively doubling the channel capacity for certain information transfer scenarios.

2. The encoding routine is implemented using only single–qubit Pauli–X and Pauli–Z operations under a single deterministic assignment that scales to any n, which keeps the circuit within a low–cost, low–error native gate set on current NISQ hardware. AI systems can leverage this for constructing scalable quantum circuits with minimal gate complexity, suitable for near-term quantum devices.

3. The performance analysis shows that success rates are degraded by message length and Hamming weight because of increased Pauli–X gate usage for messages with higher Hamming weight, indicating a need to optimize the classical data structure before encoding. AI systems can use this insight to employ adaptive encoding strategies, such as sending messages in shorter segments, to maintain high transmission accuracy.

4. The results demonstrate that success rates decrease with increasing circuit depth and gate count and that longer messages approach the practical limits of current hardware. This informs the development of error mitigation techniques, such as employing readout error mitigation as a straightforward implementation, to improve the reliability of quantum computation outputs.

5. The work provides an explicit, hardware–executable construction for the n–bit superdense coding protocol, closing the gap left by prior treatments that only established capacity or closed-form operators. AI systems can utilize this constructive realization to build and test practical quantum communication protocols in real hardware environments like IBM-Fez.

6. The protocol's information-per-particle ratio is n/(n − 1), which approaches 1 as n grows; the advantage over classical transmission of n–1 particles is therefore exactly one bit for any n. This confirms that the construction realizes the capacity limit, allowing AI systems to understand and exploit the fundamental limits of quantum communication protocols.

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 GHZ 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 is an explicit, scalable n --bit encoding routine, realized on the GHZ channel with a low--depth encoding layer using only single--qubit Pauli--X and Pauli--Z operations. The protocol was tested on real quantum hardware using Qiskit 2.0 and the IBM--Fez quantum computer for message lengths of 4, 6, 8, and 10 bits, as a circuit--level proof of concept on a single processor; the physical transmission of qubits between the parties was not implemented. Results show that success rates decrease as message length, transpiled circuit depth and gate count increase; the latter two are set mainly by transpilation rather than by the encoding itself. A mutual information analysis shows that the transmitted information exceeds the classical bound of n-1 bits only for short messages. 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 protocol with potential applications in quantum networks and communication systems.