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Apress eBooks

Start Your Engines: From Quantum Random Numbers to Teleportation, Pit Stop at Super Dense Coding

Vladimir Silva

Published Jan 1, 2018• 0 citations
Publisher

Abstract

This chapter takes you through a journey about three remarkable information processing capabilities of quantum systems. We start with one of the simplest procedures by exploring the fundamentally random nature of quantum mechanics as a source of true randomness. Next, the chapter looks at perhaps two exuberant but related procedures called super dense coding and quantum teleportation. In super dense coding, you will learn how it is possible to send 2 classical bits of information using a single qubit. In quantum teleportation, you will learn how the quantum state of a qubit can be recreated by a hybrid classical-quantum information transfer procedure. All algorithms include circuit design for the IBM Q Experience Composer as well as Python and QASM code. Results will be gathered for display and analysis, so let’s get started.

DOI
10.1007/978-1-4842-4218-6_5

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Start Your Engines: From Quantum Random Numbers to Teleportation and Super Dense Coding

Vladimir Silva

This chapter takes you on a journey about three remarkable information processing capabilities of quantum systems. We start with one of the simplest procedures by exploring the fundamentally random nature of quantum mechanics as a source of true randomness. Next, the chapter looks at perhaps two exuberant but related procedures called super dense coding and quantum teleportation. In super dense coding, you will learn how it is possible to send two classical bits of information using a single qubit. In quantum teleportation you will learn how the quantum state of a qubit can be recreated by a hybrid classical-quantum information transfer procedure. All algorithms include circuit design for the IBM Quantum Composer as well as Python and QASM code. Results will be gathered for display and analysis, so let’s get started.

Apress eBooks•Dec 18, 2023•0 citations

Quantum teleportation and superdense coding

Anirban Pathak

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.

CRC Press eBooks•Jun 20, 2013•0 citations

Simple Algorithms

Robert Hundt

Armed with the knowledge and infrastructure from the previous chapters, the first set of quantum algorithms is introduced. The algorithms in this chapter are typically shorter and require less preparation than those in later chapters. Additionally, the mathematical derivations are developed with great detail. The chapter starts with the simplest possible algorithm: a quantum random number generator. This is followed by several gate equivalences, a classical full adder implemented with quantum gates, and the Swap Test to measure similarity between states. Two algorithms that utilize entanglement come next: quantum teleportation and superdense coding. After this, three so-called oracle algorithms are discussed,the Bernstein–Vazirani algorithm, Deutsch’s algorithm, and Deutsch–Jozsa’s algorithm. These are the first quantum algorithms that perform better than their classical counterparts. Oracle construction itself is discussed at great length.

Cambridge University Press eBooks•Feb 28, 2022•0 citations

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Abstract Quantum teleportation and dense coding are quantum tasks in which an unknown quantum state sends from one location to another in first one and a classical bits sends between two locations in the later. We introduce a quantum circuit for creating generalized Bell states discussed by Gustavo Rigolin (PRA 71, 032303 (2005)). We develop appropriate quantum circuit for realizing two qubits teleportation and four bits dense coding. We experimentally demonstrate these circuits in IBM quantum computer and calculate fidelity of teleportation and efficiency of dense coding.

•Oct 29, 2024•0 citations

Coherent Communication with Noisy Resources

Mark M. Wilde

This chapter demonstrates the power of both coherent communication from Chapter 7 and the particular protocol for entanglement-assisted classical coding from the previous chapter. Recall that coherent dense coding is a version of the dense coding protocol in which the sender and receiver perform all of its steps coherently.1 Since our protocol for entanglement-assisted classical coding from the previous chapter is really just a glorified dense coding protocol, the sender and receiver can perform each of its steps coherently, generating a protocol for entanglement-assisted coherent coding. Then, by exploiting the fact that two coherent bits are equivalent to a qubit and an ebit, we obtain a protocol for entanglement-assisted quantum coding that consumes far less entanglement than a naive strategy would in order to accomplish this task. We next combine this entanglement-assisted quantum coding protocol with entanglement distribution (Section 6.2.1) and obtain a protocol for quantum communication at a rate equal to the channel's coherent information (Section 13.5). This sequence of steps demonstrates an alternate proof of the direct part of the quantum capacity theorem stated in Chapter 24. Entanglement-assisted classical communication is one generalization of superdense coding, in which the noiseless qubit channel becomes an arbitrary noisy quantum channel while the noiseless ebits remain noiseless. Another generalization of super-dense coding is a protocol named noisy super-dense coding , in which the shared entanglement becomes a shared noisy state ρ AB and the noiseless qubit channels remain noiseless. Interestingly, the protocol that we employ in this chapter for noisy super-dense coding is essentially equivalent to the protocol from the previous chapter for entanglement-assisted classical communication, with some slight modifications to account for the different setting. We can also construct a coherent version of noisy super-dense coding, leading to a protocol that we name coherent state transfer . Coherent state transfer accomplishes not only the task of generating coherent communication between Alice and Bob, but it also allows Alice to transfer her share of the state ρ AB to Bob.

Cambridge University Press eBooks•Nov 2, 2016•0 citations

Dense Coding and Teleportation

M. He

This paper explores the fundamental aspects and protocols of quantum dense coding and teleportation, which are essential for secure quantum information transfer. We demonstrate the robustness of these protocols against traditional forms of attack. To establish these findings, we delve into the core principles of quantum mechanics, including quantum measurements, entanglement, qubits, and both single and multi-qubit operations, with an emphasis on CNOT gates. Additionally, we delineate the requisite conditions for participants in these quantum protocols.

International Conference on Intelligent Communication and Networking (ICN)•Nov 15, 2024•0 citations
This chapter takes you through a journey about three remarkable information processing capabilities of quantum systems. We start with one of the simplest procedures by exploring the fundamentally random nature of quantum mechanics as a source of true randomness. Next, the chapter looks at perhaps two exuberant but related procedures called super dense coding and quantum teleportation. In super dense coding, you will learn how it is possible to send 2 classical bits of information using a single qubit. In quantum teleportation, you will learn how the quantum state of a qubit can be recreated by a hybrid classical-quantum information transfer procedure. All algorithms include circuit design for the IBM Q Experience Composer as well as Python and QASM code. Results will be gathered for display and analysis, so let’s get started.
This chapter takes you on a journey about three remarkable information processing capabilities of quantum systems. We start with one of the simplest procedures by exploring the fundamentally random nature of quantum mechanics as a source of true randomness. Next, the chapter looks at perhaps two exuberant but related procedures called super dense coding and quantum teleportation. In super dense coding, you will learn how it is possible to send two classical bits of information using a single qubit. In quantum teleportation you will learn how the quantum state of a qubit can be recreated by a hybrid classical-quantum information transfer procedure. All algorithms include circuit design for the IBM Quantum Composer as well as Python and QASM code. Results will be gathered for display and analysis, so let’s get started.
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.
Armed with the knowledge and infrastructure from the previous chapters, the first set of quantum algorithms is introduced. The algorithms in this chapter are typically shorter and require less preparation than those in later chapters. Additionally, the mathematical derivations are developed with great detail. The chapter starts with the simplest possible algorithm: a quantum random number generator. This is followed by several gate equivalences, a classical full adder implemented with quantum gates, and the Swap Test to measure similarity between states. Two algorithms that utilize entanglement come next: quantum teleportation and superdense coding. After this, three so-called oracle algorithms are discussed,the Bernstein–Vazirani algorithm, Deutsch’s algorithm, and Deutsch–Jozsa’s algorithm. These are the first quantum algorithms that perform better than their classical counterparts. Oracle construction itself is discussed at great length.
Abstract Quantum teleportation and dense coding are quantum tasks in which an unknown quantum state sends from one location to another in first one and a classical bits sends between two locations in the later. We introduce a quantum circuit for creating generalized Bell states discussed by Gustavo Rigolin (PRA 71, 032303 (2005)). We develop appropriate quantum circuit for realizing two qubits teleportation and four bits dense coding. We experimentally demonstrate these circuits in IBM quantum computer and calculate fidelity of teleportation and efficiency of dense coding.
This chapter demonstrates the power of both coherent communication from Chapter 7 and the particular protocol for entanglement-assisted classical coding from the previous chapter. Recall that coherent dense coding is a version of the dense coding protocol in which the sender and receiver perform all of its steps coherently.1 Since our protocol for entanglement-assisted classical coding from the previous chapter is really just a glorified dense coding protocol, the sender and receiver can perform each of its steps coherently, generating a protocol for entanglement-assisted coherent coding. Then, by exploiting the fact that two coherent bits are equivalent to a qubit and an ebit, we obtain a protocol for entanglement-assisted quantum coding that consumes far less entanglement than a naive strategy would in order to accomplish this task. We next combine this entanglement-assisted quantum coding protocol with entanglement distribution (Section 6.2.1) and obtain a protocol for quantum communication at a rate equal to the channel's coherent information (Section 13.5). This sequence of steps demonstrates an alternate proof of the direct part of the quantum capacity theorem stated in Chapter 24. Entanglement-assisted classical communication is one generalization of superdense coding, in which the noiseless qubit channel becomes an arbitrary noisy quantum channel while the noiseless ebits remain noiseless. Another generalization of super-dense coding is a protocol named noisy super-dense coding , in which the shared entanglement becomes a shared noisy state ρ AB and the noiseless qubit channels remain noiseless. Interestingly, the protocol that we employ in this chapter for noisy super-dense coding is essentially equivalent to the protocol from the previous chapter for entanglement-assisted classical communication, with some slight modifications to account for the different setting. We can also construct a coherent version of noisy super-dense coding, leading to a protocol that we name coherent state transfer . Coherent state transfer accomplishes not only the task of generating coherent communication between Alice and Bob, but it also allows Alice to transfer her share of the state ρ AB to Bob.
This paper explores the fundamental aspects and protocols of quantum dense coding and teleportation, which are essential for secure quantum information transfer. We demonstrate the robustness of these protocols against traditional forms of attack. To establish these findings, we delve into the core principles of quantum mechanics, including quantum measurements, entanglement, qubits, and both single and multi-qubit operations, with an emphasis on CNOT gates. Additionally, we delineate the requisite conditions for participants in these quantum protocols.