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

IntechOpen eBooks

Can We Entangle Entanglement?

Mrittunjoy Guha Majumdar

Published Jul 27, 2021• 0 citations
Publisher

Abstract

In this chapter, nested multilevel entanglement is formulated and discussed in terms of Matryoshka states. The generation of such states that contain nested patterns of entanglement, based on an anisotropic XY model has been proposed. Two classes of multilevel-entanglement- the Matryoshka Q-GHZ states and Matryoshka generalised GHZ states, are studied. Potential applications of such resource states, such as for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are proposed and discussed, in terms of a Matryoshka state over seven qubits. We also discuss fractal network protocols, surface codes and graph states as well as generation of arbitrary entangled states at remote locations in this chapter.

DOI
10.5772/intechopen.98535

Related papers

Generation and Application of Nested Entanglement in Matryoshka Quantum Resource-States

Mrittunjoy Guha Majumdar

Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. Nested entanglement provides resource-states for quantum information processing. In this paper, Matryoshka quantum resource-states, which contain nested entanglement patterns, has been studied. A novel scheme for the generation of such quantum states has been proposed using an anisotropic XY spin-spin interaction-based model. The application of the Matryoshka GHZ-Bell states for n-qubit teleportation is reviewed and an extension to more general Matryoshka ExhS-Bell states is posited. An example of Matryoshka ExhS-Bell states is given in the form of the genuinely entangled seven-qubit Xin-Wei Zha state. Generation, characterisation and application of this seven-qubit resource state in theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are presented.

•Jul 10, 2020•1 citation

Linear, Bidirectional and Circular Controlled Quantum Teleportation and Quantum State Sharing using a Seven Qubit Genuinely Entangled State

Mrittunjoy Guha Majumdar

Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. In this paper, generation, characterisation and application of a genuine genuinely entangled seven-qubit resource state is studied. Theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation as well as three schemes for undertaking tripartite quantum state sharing are presented.

•May 23, 2020•0 citations

Entanglement

Binayak Samadder Choudhury, Soumen Samanta

This chapter deals with the concept of quantum entanglement which is the most precious resource in quantum communication science. Some topics on entanglement including construction of circuits for entanglement generation are presented. The materials presented here are limited by their requirements in the protocols presented here. Books and review articles [ 36 , 37 , 106 , 113 , 134 , 139 , 140 ] contain different aspects of quantum entanglement.

Chapman & Hall/CRC eBooks•Dec 10, 2025•0 citations

Controlled bidirectional remote implementations of partially unknown quantum operations

Miao Liu, Nueraminaimu Maihemuti, Peng Jia-yin

Abstract By blending the ideas of controlled teleportation, bidirectional teleportation and remote implementation of quantum operations, we investigate the bidirectional transmission of quantum operations under the control of one supervisor. Firstly, we provide a method for generating a class of multi-particle entangled states, including five-particle and seven-particle entangled states, using a nine-particle entangled state as an example. Then using our constructed five-particle entangled state as a quantum channel, we propose a new controlled bidirectional protocol for remotely implementing partially known quantum operations (PUQOs for short) of one qubit within the two restricted sets satisfying specific conditions. Subsequently, exploiting a nine-particle entangled state as the quantum channel, we extend it to the case of two-qubit quantum operations which come from eight restricted sets. Replacing two PUQO of two qubits by a PUQO of one qubit and a PUQO of two qubits, we put forward another new asymmetric controlled bidirectional protocol for remotely implementing PKQOs via a seven-particle entangled state as the quantum channel. In these protocols, by using universal recovered operations performed by the receivers, the senders can simultaneously exchange their PUQOs as long as the controller collaborates, where each PUQO acts on the corresponding unknown state owned by the remote recipient.

Physica Scripta•Feb 27, 2024•13 citations

Entanglement generation and applications in quantum information

Tiegang Di

This dissertation consists of three sections. In the first section, we discuss the generation \nof arbitrary two-qubit entangled states and present three generation methods. \nThe first method is based on the interaction of an atom with classical and quantized \ncavity fields. The second method is based on the interaction of two coupled two-level \natoms with a laser field. In the last method, we use two spin-1/2 systems which \ninteract with a tuned radio frequency pulse. Using those methods we have generated \ntwo qubit arbitrary entangled states which is widely used in quantum computing and \nquantum information. In the second section, we discuss a possible experimental implementation \nof quantum walk which is based on the passage of an atom through a \nhigh-Q cavity. The chirality is determined by the atomic states and the displacement \nis characterized by the photon number inside the cavity. Our scheme makes quantum \nwalk possible in a cavity QED system and the results could be widely used on \nquantum computer. In the last section, we investigate the properties of teleporting \nan arbitrary superposition of entangled Dicke states of any number of atoms (qubits) \nbetween two distant cavities. We also studied teleporting continuous variables of an \noptical field. Teleportation of Dicke states relies on adiabatic passage using multiatom \ndark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate \nthe protocol of quantum teleportation of arbitrary input optical field states in \nthe density matrix form, and established the relation between the P-function of the \ninput and output states. We then present a condition involving squeeze parameter \nand detection efficiency under which the P-function of the output state becomes the \nQ function of the input state such that any nonclassical features in the input state \nwill be eliminated in the teleported state. Based on the research in this section we \nhave made it possible of arbitrary atomic Dicke states teleportation from one cavity \nto another, and this teleortation will play an essential role in quantum communication. \nSince quantum properties is so important in quantum communication, the \ncondition we give in this section to distinguish classical and quantum teleportation is \nalso important.

•Aug 16, 2006•0 citations

A universal protocol for bidirectional controlled teleportation with network coding

Meng-Yao He, Song-Ya Ma, Kun-Peng Kang

Abstract We investigate bidirectional teleportation that works in a fair and efficient manner. Two explicit protocols are proposed to realize bidirectional teleportation with a controller. One is a symmetric protocol for two-qubit states. The other is an asymmetric protocol for single- and two-qubit states. We then devise a universal protocol for arbitrary n 1 - and n 2 -qubit states via a (2 n 1 + 2 n 2 + 1)-qubit entangled state, where n 1 ≤ n 2 . The receiver only needs to perform the single-qubit recovery operation, which is derived by a general expression. Moreover, a (2 n 1 + 1)-bit classical communication cost can be saved within the controller’s broadcast channel by the use of network coding technology.

Communications in Theoretical Physics•Jul 6, 2021•15 citations
In this chapter, nested multilevel entanglement is formulated and discussed in terms of Matryoshka states. The generation of such states that contain nested patterns of entanglement, based on an anisotropic XY model has been proposed. Two classes of multilevel-entanglement- the Matryoshka Q-GHZ states and Matryoshka generalised GHZ states, are studied. Potential applications of such resource states, such as for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are proposed and discussed, in terms of a Matryoshka state over seven qubits. We also discuss fractal network protocols, surface codes and graph states as well as generation of arbitrary entangled states at remote locations in this chapter.
Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. Nested entanglement provides resource-states for quantum information processing. In this paper, Matryoshka quantum resource-states, which contain nested entanglement patterns, has been studied. A novel scheme for the generation of such quantum states has been proposed using an anisotropic XY spin-spin interaction-based model. The application of the Matryoshka GHZ-Bell states for n-qubit teleportation is reviewed and an extension to more general Matryoshka ExhS-Bell states is posited. An example of Matryoshka ExhS-Bell states is given in the form of the genuinely entangled seven-qubit Xin-Wei Zha state. Generation, characterisation and application of this seven-qubit resource state in theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation are presented.
Multipartite entanglement is a resource for application in disparate protocols, of computing, communication and cryptography. In this paper, generation, characterisation and application of a genuine genuinely entangled seven-qubit resource state is studied. Theoretical schemes for quantum teleportation of arbitrary one, two and three qubits states, bidirectional teleportation of arbitrary two qubit states and probabilistic circular controlled teleportation as well as three schemes for undertaking tripartite quantum state sharing are presented.
Abstract By blending the ideas of controlled teleportation, bidirectional teleportation and remote implementation of quantum operations, we investigate the bidirectional transmission of quantum operations under the control of one supervisor. Firstly, we provide a method for generating a class of multi-particle entangled states, including five-particle and seven-particle entangled states, using a nine-particle entangled state as an example. Then using our constructed five-particle entangled state as a quantum channel, we propose a new controlled bidirectional protocol for remotely implementing partially known quantum operations (PUQOs for short) of one qubit within the two restricted sets satisfying specific conditions. Subsequently, exploiting a nine-particle entangled state as the quantum channel, we extend it to the case of two-qubit quantum operations which come from eight restricted sets. Replacing two PUQO of two qubits by a PUQO of one qubit and a PUQO of two qubits, we put forward another new asymmetric controlled bidirectional protocol for remotely implementing PKQOs via a seven-particle entangled state as the quantum channel. In these protocols, by using universal recovered operations performed by the receivers, the senders can simultaneously exchange their PUQOs as long as the controller collaborates, where each PUQO acts on the corresponding unknown state owned by the remote recipient.
This dissertation consists of three sections. In the first section, we discuss the generation \nof arbitrary two-qubit entangled states and present three generation methods. \nThe first method is based on the interaction of an atom with classical and quantized \ncavity fields. The second method is based on the interaction of two coupled two-level \natoms with a laser field. In the last method, we use two spin-1/2 systems which \ninteract with a tuned radio frequency pulse. Using those methods we have generated \ntwo qubit arbitrary entangled states which is widely used in quantum computing and \nquantum information. In the second section, we discuss a possible experimental implementation \nof quantum walk which is based on the passage of an atom through a \nhigh-Q cavity. The chirality is determined by the atomic states and the displacement \nis characterized by the photon number inside the cavity. Our scheme makes quantum \nwalk possible in a cavity QED system and the results could be widely used on \nquantum computer. In the last section, we investigate the properties of teleporting \nan arbitrary superposition of entangled Dicke states of any number of atoms (qubits) \nbetween two distant cavities. We also studied teleporting continuous variables of an \noptical field. Teleportation of Dicke states relies on adiabatic passage using multiatom \ndark states in each cavity and a conditional detection of photons leaking out of both cavities. In the continuous variables teleportation scheme we first reformulate \nthe protocol of quantum teleportation of arbitrary input optical field states in \nthe density matrix form, and established the relation between the P-function of the \ninput and output states. We then present a condition involving squeeze parameter \nand detection efficiency under which the P-function of the output state becomes the \nQ function of the input state such that any nonclassical features in the input state \nwill be eliminated in the teleported state. Based on the research in this section we \nhave made it possible of arbitrary atomic Dicke states teleportation from one cavity \nto another, and this teleortation will play an essential role in quantum communication. \nSince quantum properties is so important in quantum communication, the \ncondition we give in this section to distinguish classical and quantum teleportation is \nalso important.
Abstract We investigate bidirectional teleportation that works in a fair and efficient manner. Two explicit protocols are proposed to realize bidirectional teleportation with a controller. One is a symmetric protocol for two-qubit states. The other is an asymmetric protocol for single- and two-qubit states. We then devise a universal protocol for arbitrary n 1 - and n 2 -qubit states via a (2 n 1 + 2 n 2 + 1)-qubit entangled state, where n 1 ≤ n 2 . The receiver only needs to perform the single-qubit recovery operation, which is derived by a general expression. Moreover, a (2 n 1 + 1)-bit classical communication cost can be saved within the controller’s broadcast channel by the use of network coding technology.