Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2512.14280

General Quantum Protocol for Communication via Maximally Entangled nnn-Qubit States

Saba Arife Bozpolat

quant-phSubmitted Dec 16, 2025• Announced Dec 17, 2025• 0 citations• Revised Aug 27, 2026 (v2)
v1 · Dec 16, 2025v2 · Aug 27, 2026v3 · Oct 14, 2026
arXivHTMLPDF

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 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. 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. 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 higher Hamming weight. 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.

Comments
10 pages, 5 figures

Related papers

Superdense coding using multipartite states

Gustavo Rigolin

We show that with the fourpartite quantum channel used to teleport an arbitrary two qubit state, we can construct a superdense coding protocol where it is possible to transmit 4 bits of classical information sending only 2 qubits. Alice and Bob initially share a four qubit maximally entangled state and by locally manipulating her two qubits Alice can generate 16 orthogonal maximally entangled states, which are used to encode the message transmitted to Bob. He reads the 4 bit message by a generalized Bell state measurement. A generalized protocol in which 2N bits of classical information is transmitted via N qubits is also presented. We also show that this four(2N-)partite channel is equivalent to two(N) Bell states, which proves that we need two(N) Bell states to teleport a two(N) qubit system.

arXiv:quant-ph/0407193•Jul 23, 2004•3 citations

Scalable Quantum Key Distribution via GHZ Entanglement and Qubit Reuse

Tasdiqul Islam, Rasman Mubtasim Swargo, Engin Arslan +1 more

Conventional Quantum Key Distribution (QKD) requires the transmission of qubits proportional to or exceeding the length of the key, as protocols such as BB84 transmit more qubits than the final key size due to basis sifting and privacy amplification. Since quantum networks are still in their infancy and have limited capacity, this overhead puts significant pressure on network resources. To address this issue, we propose a Multi-Qubit Greenberger--Horne--Zeilinger (GHZ) State-based QKD scheme that reduces the number of qubits transmitted over the quantum channel. The proposed method transmits one GHZ qubit between endpoints and reuses the resulting entanglement to convey multiple classical key bits with the help of Quantum Non-Demolition (QND) measurements. Under the stated assumptions on authenticated classical communication, local reset verification, and bounded-error QND discrimination, one can transfer $L$ classical bits by generating an (L+1)-qubit GHZ state and transferring one qubit to the remote party. We verify correctness using the NetSquid quantum network simulator: the protocol achieves 100\% raw-key fidelity for keys of length up to 12 bits under both ideal conditions and depolarizing noise up to p = 0.005 per round. We further show that the proposed QKD algorithm can be extended to multi-party QKD and server-client deployment. The proposed scheme offers a transmitted-qubit-efficient, noise-tolerant alternative for bandwidth-limited quantum networks.

quant-pharXiv:2608.21667•Aug 25, 2026•0 citations

An N-Qubit Teleportation Protocol with a Generalized GHZ State

Abdelrahman E. Ahmed

Quantum teleportation is a cornerstone protocol for future quantum networks and distributed quantum com- puting. However, scaling teleportation to an arbitrary N- qubit state using conventional methods, which require N separate Bell pairs, presents a significant challenge in terms of both quantum and classical resource overhead. This paper introduces a novel and resource-efficient protocol for tele- porting an arbitrary N-qubit state using a single, pre-shared (N+1)-qubit Greenberger-Horne-Zeilinger (GHZ) state. Our approach reduces the required entangled channel qubits and classical communication bits from O(2N) to N+1, offering a substantial improvement in communication efficiency. The protocol mechanism involves a sequence of local and non-local CNOT gates performed by the sender (Alice), followed by local measurements on her N+1 qubits. The N+1 classical measurement outcomes are then transmitted to the receiver (Bob), who recovers the original quantum state by applying a specific corrective unitary transformation U-f, followed by a set of conditional Pauli gates. We provide a high-level proof of the protocol’s correctness and show that the corrective trans- formation U-f can be implemented efficiently using only local operations on the receiver’s side. Recognizing the practical difficulty of implementing non-local quantum gates between spatially separated nodes, we also propose a modified scheme to enhance near-term feasibility. This practical approach re- locates the non-local operations to a co-located preparation phase, thereby trading the formidable challenge of non-local interactions for a high-fidelity quantum memory requirement. This work analyzes the critical trade-offs between communication efficiency and operational complexity, presenting a vi- able alternative for designing scalable and resource-optimized quantum communication systems.

Novel Intelligent and Leading Emerging Sciences Conference (NILES)•Oct 25, 2025•0 citations

Coherence Scaling in Quantum Communication Protocols

Pedro H. Alvarez, Marcos C. de Oliveira

We investigate how quantum coherence scales and is redistributed in quantum communication protocols, using superdense coding and quantum teleportation as paradigmatic case studies. Employing the relative entropy of coherence as a circuit-level resource measure, we show that multipartite resource states relevant to generalized superdense coding can enable scalable communication while exhibiting only logarithmic or even constant coherence growth, depending on their entanglement structure. In sharp contrast, quantum teleportation displays an unavoidable, protocol-induced coherence cost that grows linearly with the number of teleported qubits and is independent of the input state. Through a stage-resolved analysis of the teleportation circuit, we separate protocol-generated coherence from message-dependent contributions and identify a universal two-bit coherence offset per teleported qubit at the maximal-coherence stage. We further demonstrate explicitly that this extensive intermediate coherence generation is fully consistent with information-theoretic bounds, including the Holevo limit, and does not correspond to an increase in accessible classical information.

quant-pharXiv:2601.12516•Jan 20, 2026•0 citations

Exploring the Scalability and Error Tolerance of N-Qubit Superdense Coding

Heinz, Benjamin

Superdense coding is a quantum communication protocol that enables the transmission of more than one classical bit of information per qubit, using entangled states. While superdense coding with 2-qubits is well understood and directly maps to the Bell states, the same cannot be said for higher numbers of qubits. This project aims to develop an algorithm for superdense coding using a larger number of qubits, while analyzing how the capacity for information transmission scales with qubit count. Additionally, we will determine the error thresholds for accurately reconstructing the encoded information and investigate how error scales as the number of qubits increases. Gaining a deeper understanding of superdense coding has significant applications in quantum cryptography, as superdense coding schemes can be used to set up quantum secure direct communication (QSDC) protocols.

•Apr 12, 2025•0 citations

Superdense coding facilitated by hyper-entanglement and quantum networks

James F. Smith

A method of generating superdense coding based on quantum hyper-entanglement and facilitated by quantum networks is discussed. Superdense coding refers to the coding of more than one classical bit into each qubit. Quantum hyperentanglement refers to quantum entanglement in more than one degree of freedom, e.g. polarization, energy-time, and orbital angular momentum (OAM). The new superdense coding scheme permits 2L bits to be encoded into each qubit where L is the number of degrees of freedom used for quantum hyper-entanglement. The superdense coding procedure is based on a generalization of the Bell state for L degrees of freedom. Theory describing the structure, generation/transmission, and detection of the generalized Bell state is developed. Circuit models are provided describing the generation/transmission process and detection process. Detection processes are represented mathematically as projection operators. A mathematical proof that that the detection scheme permits the generalized Bell states to be distinguished with 100% probability is provided. Measures of effectiveness (MOEs) are derived for the superdense coding scheme based on open systems theory represented in terms of density operators. Noise and loss related to generation/transmission, detection and propagation are included. The MOEs include various probabilities, quantum Chernoff bound, a measure of the number of message photons that must be transmitted to successfully send and receive a message, SNR and the quantum Cramer Rao’ lower bound. Quantum networks with quantum memory are used to increase the efficiency of the superdense coding scheme.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 8, 2017•9 citations
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−1n-1n−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 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.
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. 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 higher Hamming weight. 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.
We show that with the fourpartite quantum channel used to teleport an arbitrary two qubit state, we can construct a superdense coding protocol where it is possible to transmit 4 bits of classical information sending only 2 qubits. Alice and Bob initially share a four qubit maximally entangled state and by locally manipulating her two qubits Alice can generate 16 orthogonal maximally entangled states, which are used to encode the message transmitted to Bob. He reads the 4 bit message by a generalized Bell state measurement. A generalized protocol in which 2N bits of classical information is transmitted via N qubits is also presented. We also show that this four(2N-)partite channel is equivalent to two(N) Bell states, which proves that we need two(N) Bell states to teleport a two(N) qubit system.
Conventional Quantum Key Distribution (QKD) requires the transmission of qubits proportional to or exceeding the length of the key, as protocols such as BB84 transmit more qubits than the final key size due to basis sifting and privacy amplification. Since quantum networks are still in their infancy and have limited capacity, this overhead puts significant pressure on network resources. To address this issue, we propose a Multi-Qubit Greenberger--Horne--Zeilinger (GHZ) State-based QKD scheme that reduces the number of qubits transmitted over the quantum channel. The proposed method transmits one GHZ qubit between endpoints and reuses the resulting entanglement to convey multiple classical key bits with the help of Quantum Non-Demolition (QND) measurements. Under the stated assumptions on authenticated classical communication, local reset verification, and bounded-error QND discrimination, one can transfer LLL classical bits by generating an (L+1)-qubit GHZ state and transferring one qubit to the remote party. We verify correctness using the NetSquid quantum network simulator: the protocol achieves 100\% raw-key fidelity for keys of length up to 12 bits under both ideal conditions and depolarizing noise up to p = 0.005 per round. We further show that the proposed QKD algorithm can be extended to multi-party QKD and server-client deployment. The proposed scheme offers a transmitted-qubit-efficient, noise-tolerant alternative for bandwidth-limited quantum networks.
Quantum teleportation is a cornerstone protocol for future quantum networks and distributed quantum com- puting. However, scaling teleportation to an arbitrary N- qubit state using conventional methods, which require N separate Bell pairs, presents a significant challenge in terms of both quantum and classical resource overhead. This paper introduces a novel and resource-efficient protocol for tele- porting an arbitrary N-qubit state using a single, pre-shared (N+1)-qubit Greenberger-Horne-Zeilinger (GHZ) state. Our approach reduces the required entangled channel qubits and classical communication bits from O(2N) to N+1, offering a substantial improvement in communication efficiency. The protocol mechanism involves a sequence of local and non-local CNOT gates performed by the sender (Alice), followed by local measurements on her N+1 qubits. The N+1 classical measurement outcomes are then transmitted to the receiver (Bob), who recovers the original quantum state by applying a specific corrective unitary transformation U-f, followed by a set of conditional Pauli gates. We provide a high-level proof of the protocol’s correctness and show that the corrective trans- formation U-f can be implemented efficiently using only local operations on the receiver’s side. Recognizing the practical difficulty of implementing non-local quantum gates between spatially separated nodes, we also propose a modified scheme to enhance near-term feasibility. This practical approach re- locates the non-local operations to a co-located preparation phase, thereby trading the formidable challenge of non-local interactions for a high-fidelity quantum memory requirement. This work analyzes the critical trade-offs between communication efficiency and operational complexity, presenting a vi- able alternative for designing scalable and resource-optimized quantum communication systems.
We investigate how quantum coherence scales and is redistributed in quantum communication protocols, using superdense coding and quantum teleportation as paradigmatic case studies. Employing the relative entropy of coherence as a circuit-level resource measure, we show that multipartite resource states relevant to generalized superdense coding can enable scalable communication while exhibiting only logarithmic or even constant coherence growth, depending on their entanglement structure. In sharp contrast, quantum teleportation displays an unavoidable, protocol-induced coherence cost that grows linearly with the number of teleported qubits and is independent of the input state. Through a stage-resolved analysis of the teleportation circuit, we separate protocol-generated coherence from message-dependent contributions and identify a universal two-bit coherence offset per teleported qubit at the maximal-coherence stage. We further demonstrate explicitly that this extensive intermediate coherence generation is fully consistent with information-theoretic bounds, including the Holevo limit, and does not correspond to an increase in accessible classical information.
Superdense coding is a quantum communication protocol that enables the transmission of more than one classical bit of information per qubit, using entangled states. While superdense coding with 2-qubits is well understood and directly maps to the Bell states, the same cannot be said for higher numbers of qubits. This project aims to develop an algorithm for superdense coding using a larger number of qubits, while analyzing how the capacity for information transmission scales with qubit count. Additionally, we will determine the error thresholds for accurately reconstructing the encoded information and investigate how error scales as the number of qubits increases. Gaining a deeper understanding of superdense coding has significant applications in quantum cryptography, as superdense coding schemes can be used to set up quantum secure direct communication (QSDC) protocols.
A method of generating superdense coding based on quantum hyper-entanglement and facilitated by quantum networks is discussed. Superdense coding refers to the coding of more than one classical bit into each qubit. Quantum hyperentanglement refers to quantum entanglement in more than one degree of freedom, e.g. polarization, energy-time, and orbital angular momentum (OAM). The new superdense coding scheme permits 2L bits to be encoded into each qubit where L is the number of degrees of freedom used for quantum hyper-entanglement. The superdense coding procedure is based on a generalization of the Bell state for L degrees of freedom. Theory describing the structure, generation/transmission, and detection of the generalized Bell state is developed. Circuit models are provided describing the generation/transmission process and detection process. Detection processes are represented mathematically as projection operators. A mathematical proof that that the detection scheme permits the generalized Bell states to be distinguished with 100% probability is provided. Measures of effectiveness (MOEs) are derived for the superdense coding scheme based on open systems theory represented in terms of density operators. Noise and loss related to generation/transmission, detection and propagation are included. The MOEs include various probabilities, quantum Chernoff bound, a measure of the number of message photons that must be transmitted to successfully send and receive a message, SNR and the quantum Cramer Rao’ lower bound. Quantum networks with quantum memory are used to increase the efficiency of the superdense coding scheme.