Summer Project on Quantum Dense Coding

This repository contains the implementation, simulation codes, and supporting materials developed during my summer research project work at IISER Bhopal, India on Quantum Dense Coding Using Bipartite and Multipartite Entangled States Over Noiseless and Noisy Quantum Channels: An IBM Quantum Experience. The project investigates the performance of dense coding protocols using different entangled quantum channels under both ideal and noisy quantum environments.

The simulations are implemented using Python and Qiskit, with a focus on understanding the influence of realistic quantum noise on communication efficiency and protocol robustness.

---

Project Objectives

• Study the fundamentals of quantum dense coding.
• Implement dense coding protocols using different entangled states.
• Analyze protocol performance under ideal conditions.
• Investigate the effects of Pauli noise channels.
• Compare different entangled resources based on communication capacity, efficiency, and robustness.
• Validate theoretical results through numerical simulations.

---

Entangled States Studied

The repository includes implementations and analyses for:

• Bell State
• Three-Qubit GHZ State
• Four-Qubit Cluster State
• Five-Qubit Cluster State
• Six-Qubit Cluster State

---

Noise Models

The protocols are evaluated under several realistic quantum noise models, including:

• Bit Flip Channel
• Phase Flip Channel
• Bit-Phase Flip Channel

Performance metrics such as fidelity, success probability, communication efficiency etc. are computed and compared.

---

Repository Structure

Summer-Project-on-Quantum-Dense-coding/
│
├── Bell_State/
├── GHZ_State/
├── Cluster_States/
├── Noise_Models/
├── Figures/
├── Report/
├── Results/
└── README.md

The folder names may vary slightly depending on future updates.

---

Technologies Used

• Python
• Qiskit
• NumPy
• Matplotlib
• Jupyter Notebook

---

Highlights

• Analytical derivation of quantum dense coding protocols.
• Qiskit-based simulation of multiple entangled channels.
• Comparative study under different Pauli noise models.
• Performance evaluation using various communication metrics.
• Reproducible simulation framework for quantum communication research.

---

Results

The study demonstrates that:

• Theoretical predictions agree closely with simulation results.
• Different entangled channels exhibit different levels of robustness against quantum noise.
• Increasing circuit depth and gate complexity generally reduce protocol performance in noisy environments.
• Cluster-state-based protocols provide higher communication capacity, whereas Bell-state protocols exhibit superior robustness under certain noise models.

---

Requirements

Install the required Python packages:

pip install qiskit numpy matplotlib

or

pip install -r requirements.txt

if a requirements.txt file is provided.

---

Future Work

Possible extensions include:

• Implementation on IBM Quantum hardware.
• Study of amplitude damping and depolarizing channels.
• Error mitigation techniques.
• Controlled and probabilistic dense coding.
• Qudit-based dense coding protocols.

---

Citation

If you use this repository in your research, please cite it as:

@misc{rchak2026,
  author       = {Rangan Chakrabarty},
  title        = {Summer Project on Quantum Dense Coding Using Bipartite and Multipartite Entangled States Over Noiseless and Noisy Quantum Channels: An IBM Quantum Experience},
  year         = {2026},
  howpublished = {\url{https://github.com/rangan269-ju/Summer-Project-on-Quantum-Dense-coding}}
  note         = {GitHub repository.}
}

---

Author

Rangan Chakrabarty

Email ID:

B.Sc. (Hons.) Physics

Jadavpur University, India

---

License

This project is licensed under the GPL-V3.0 License. See the LICENSE file for details.