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Istanbul University - Journal of Electrical & Electronics Engineering

Superdense Coding, Teleportation Algorithms, and Bell’s Inequality Test in Qiskit and IBM Circuit Composer

Yasemin Poyraz Koçak, Selçuk Sevgen

Published May 24, 2022• 0 citations
Publisher

Abstract

Quantum teleportation is a technique of sending information from one place to another place. Distance between two points can be hundreds of thousands of lightyears. For quantum teleportation, there is no need for a channel between two points when sending a state vector from one place to another. Since classical information sharing is possible, it is also possible to send a state vector from one place to another place. Teleportation is the transfer of a quantum state from one place to another through classical channels. Superdense coding, a dual to teleportation, uses a single quantum bit to transmit two bits classical information. Superdense coding uses a qubit to transfer two classical bits, while teleportation performs one qubit transfer using two classical bits. In this article, teleportation, superdense coding algorithms, and the Bell’s inequality test in which Bell’s inequality is violated with quantum mechanics are performed on both Qiskit and International Business Machines circuit composer, and results are compared and presented in detail. The results revealed that whether a faster-than-light signal transfer is possible using quantum mechanics depends on whether a copy of the quantum state is created or not. Finally, Bell’s inequality created by classical logic violated by quantum mechanics is shown by experimental results. Cite this article as: Y. Poyraz Koçak and S. Sevgen, "Superdense coding, teleportation algorithms, and bell’s inequality test in qiskit and IBM circuit composer," Electrica., 22(2), 120-131, 2022.

DOI
10.54614/electrica.2022.22021

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Quantum teleportation is a technique of sending information from one place to another place. Distance between two points can be hundreds of thousands of lightyears. For quantum teleportation, there is no need for a channel between two points when sending a state vector from one place to another. Since classical information sharing is possible, it is also possible to send a state vector from one place to another place. Teleportation is the transfer of a quantum state from one place to another through classical channels. Superdense coding, a dual to teleportation, uses a single quantum bit to transmit two bits classical information. Superdense coding uses a qubit to transfer two classical bits, while teleportation performs one qubit transfer using two classical bits. In this article, teleportation, superdense coding algorithms, and the Bell’s inequality test in which Bell’s inequality is violated with quantum mechanics are performed on both Qiskit and International Business Machines circuit composer, and results are compared and presented in detail. The results revealed that whether a faster-than-light signal transfer is possible using quantum mechanics depends on whether a copy of the quantum state is created or not. Finally, Bell’s inequality created by classical logic violated by quantum mechanics is shown by experimental results. Cite this article as: Y. Poyraz Koçak and S. Sevgen, "Superdense coding, teleportation algorithms, and bell’s inequality test in qiskit and IBM circuit composer," Electrica., 22(2), 120-131, 2022.
The beauty of the quantum circuit lies in the fact that it can perform certain tasks which are impossible in the classical world. For example, consider teleportation and superdense coding. Teleportation is a quantum task in which an unknown quantum state is transmitted from a sender (Alice) to a spatially separated receiver (Bob) via an entangled quantum channel and with the help of some classical communications. Dense coding is another communication scheme in which if Alice and Bob share a prior entanglement then one of them can send n bits of classical information to the other by communicating m-qubits (m < n). Before we go into the technical details of these two schemes let us try to lucidly visualize the uniqueness of teleportation. Suppose Alice and Bob are spatially separated and Alice wants to send an unknown quantum state |ψ〉 = α|0〉 + β|1〉 to Bob. For some reason she is not allowed to send the state directly through a quantum channel. She cannot measure it and send the information to Bob because the moment she will try to measure the state, it will collapse either to |0〉 or to |1〉. But the state can be sent by using a simple quantum circuit (pre-shared entanglement) and some classical communications. In the process the unknown quantum state gets destroyed at Alice’s end and reappears at Bob’s end. The state never exists in the communication channel. This process is called quantum teleportation. The uniqueness of quantum teleportation will be clearer if we note that the Fax is not an example of teleportation because the original copy remains with the sender. Again a letter posted in a letter box is not an example of teleportation because the letter exists (travels) in its original form in the communication channel. In brief, there is no classical analogue of quantum teleportation. The same is true for dense coding. In this chapter we will describe these two unique quantum communication schemes and discuss their significance and applications.
This chapter is concerned with the measure of information contained in qubits . This can be done only through quantum measurement , an operation that has no counterpart in the classical domain. I shall first describe in detail the case of single qubit measurements, which shows under which measurement conditions “classical” bits can be retrieved. Next, we consider the measurements of higher-order or n -qubits. Particular attention is given to the Einstein–Podolsky–Rosen (EPR) or Bell states , which, unlike other joint tensor states, are shown being entangled . The various single-qubit measurement outcomes from the EPR–Bell states illustrate an effect of causality in the information concerning the other qubit. We then focus on the technique of Bell measurement , which makes it possible to know which Bell state is being measured, yielding two classical bits as the outcome. The property of EPR–Bell state entanglement is exploited in the principle of quantum superdense coding , which makes it possible to transmit classical bits at twice the classical rate, namely through the generation and measurement of a single qubit. Another key application concerns quantum teleportation . It consists of the transmission of quantum states over arbitrary distances, by means of a common EPR–Bell state resource shared by the two channel ends. While quantum teleportation of a qubit is instantaneous, owing to the effect of quantum-state collapse, it is shown that its completion does require the communication of two classical bits , which is itself limited by the speed of light.
Abstract The superdense coding protocol is essential for quantum communication, allowing more efficient data transmission. This protocol facilitates the transfer of two bits of classical information using just one qubit by leveraging a pre-existing pair of Bell states. To achieve this capability, traditional implementations of superdense coding depend on entangled states, such as Bell states. This paper introduces a novel circuit that utilizes Bell diagonal states to implement the superdense coding protocol. We provide detailed instructions for the procedure using IBM’s Quantum Computing Lab, enabling practical applications in real-world contexts. Furthermore, the paper highlights the security features of this protocol, emphasizing its significance for secure communication in quantum networks. The combination of efficiency and security represents a notable advancement in quantum information science. We implemented and tested the proposed superdense coding circuit on the IBM Q quantum computing platform using Qiskit. Through extensive simulations on IBM’s Statevector and QASM simulators, we assessed the performance of the circuit based on Bell diagonal states (BDS)in terms of accuracy, noise resilience, and resource efficiency. Our findings indicate that, while Bell diagonal states pose challenges related to noise and decoherence, they also provide potential advantages in reducing qubit usage and enhancing error correction. This research contributes to the exploration of alternative techniques for superdense coding, which may have applications in quantum communication and future quantum networks. However, additional theoretical and experimental investigations are necessary to fully evaluate the scalability and practicality of this approach.
We are now ready to look at our first protocols for quantum information. In this section, we examine two communication protocols which can be implemented using the tools we have developed in the preceding sections. These protocols are known as superdense coding and quantum teleportation. Both are inherently quantum: there are no classical protocols which behave in the same way. Both involve two parties who wish to perform some communication task between them. In descriptions of such communication protocols (especially in cryptography), it is very common to name the two parties ‘Alice’ and ‘Bob’, for convenience. We will follow this tradition. We will repeatedly refer to communication channels. A quantum communication channel refers to a communication line (e.g. a fiberoptic cable), which can carry qubits between two remote locations. A classical communication channel is one which can carry classical bits (but not qubits).1 The protocols (like many in quantum communication) require that Alice and Bob initially share an entangled pair of qubits in the Bell state The above Bell state is sometimes referred to as an EPR pair. Such a state would have to be created ahead of time, when the qubits are in a lab together and can be made to interact in a way which will give rise to the entanglement between them. After the state is created, Alice and Bob each take one of the two qubits away with them. Alternatively, a third party could create the EPR pair and give one particle to Alice and the other to Bob. If they are careful not to let them interact with the environment, or any other quantum system, Alice and Bob’s joint state will remain entangled. This entanglement becomes a resource which Alice and Bob can use to achieve protocols such as the following. Suppose Alice wishes to send Bob two classical bits of information. Superdense coding is a way of achieving this task over a quantum channel, requiring only that Alice send one qubit to Bob. Alice and Bob must initially share the Bell state Suppose Alice is in possession of the first qubit and Bob the second qubit.
Abstract This laboratory work presents a practical implementation of quantum teleportation and superdense coding using the Qiskit framework. The material is based on educational resources developed by the International Quantum Center at CERN (Switzerland) and is designed to provide hands-on experience with multi-qubit quantum protocols and hybrid quantum-classical workflows. In Laboratory Work No. 5, participants implement the quantum teleportation protocol step by step. The procedure begins with the preparation of a randomly generated qubit by directly assigning complex probability amplitudes. The state vector is normalized to ensure physical validity, defining the amplitudes corresponding to the computational basis states ∣0⟩|0\rangle∣0⟩ and ∣1⟩|1\rangle∣1⟩. Once the qubit is prepared for teleportation, an entangled Bell pair is generated to establish a shared quantum channel between two parties, conventionally referred to as Alice and Bob. The protocol proceeds with joint operations and measurement of two classical bits on Alice’s side. The measurement outcomes determine conditional unitary corrections applied to Bob’s qubit, enabling the reconstruction of the original quantum state without physically transmitting the qubit itself. The laboratory exercise includes the construction of a circuit with separate quantum registers and classical bits, explicit amplitude assignment for Alice’s qubit, and verification of successful state transfer through measurement statistics. In addition to teleportation, the conceptual framework of superdense coding is discussed as a complementary protocol demonstrating how entanglement enhances classical information capacity. Together, these experiments illustrate the operational role of entanglement as a quantum communication resource. The guide emphasizes practical circuit design, normalization of quantum states, entanglement generation, conditional gate operations, and execution on both simulators and real quantum hardware. Through this laboratory work, participants gain experimental insight into two cornerstone protocols of quantum information science.
Quantum entanglement is a key feature of quantum mechanics. It describes connections between quantum systems that classical theories cannot explain. The idea of entanglement started with the Einstein–Podolsky–Rosen (EPR) argument. This argument questioned whether quantum theory was complete and showed the non-classical nature of quantum correlations. Schrödinger later defined the concept and introduced the term "entanglement" to describe composite quantum states that cannot be separated. Bell then created a framework that showed the predictions of quantum mechanics clash with local hidden-variable theories, leading to Bell’s inequality. Experiments by Aspect and others provided strong evidence for the violation of Bell’s inequalities and supported the reality of entanglement. Building on these theories and experiments, quantum teleportation became an important protocol in quantum information science. Bennett and his team proposed a scheme that showed how an unknown quantum state can be sent between distant parties using shared entanglement and classical communication, without sending the quantum system itself. Later experiments confirmed that this protocol works across different physical platforms. This paper reviews the historical development of quantum entanglement and its role in the emergence of quantum teleportation. In addition to the theoretical discussion, the teleportation protocol is implemented using IBM’s Qiskit framework. The simulation results demonstrate the successful transfer of quantum states within the circuit model, illustrating how fundamental quantum communication concepts can be explored using quantum computing simulation tools.