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:0707.2710 · Physical Review A

Local cloning of genuinely entangled states of three qubits

Sujit K. Choudhary, Guruprasad Kar, Samir Kunkri, Ramij Rahaman, Anirban Roy

Published Dec 19, 2007• 3 citations
arXivHTMLPDF

Abstract

We discuss the (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancilla under local operation and classical communication. Whereas any two orthogonal Greenberger-Horne-Zeilinger (GHZ) states taken from the canonical GHZ basis can be cloned with the help of a known GHZ state, surprisingly we find that no two $W$ states can be cloned by using any known three qubit (possibly entangled) state as a blank copy.

DOI
10.1103/physreva.76.062312

Related papers

Local cloning of entangled qubits

Sujit K. Choudhary, Samir Kunkri, Ramij Rahaman +1 more

We discuss the exact cloning of orthogonal but entangled qubits under local operations and classical communication. The amount of entanglement necessary in a blank copy is obtained for various cases. Surprisingly, this amount is more than 1 ebit for certain sets of two nonmaximal but equally entangled states of two qubits. To clone any three Bell states, at least ${\text{log}}_{2}\text{ }3$ ebit is necessary.

arXiv:0706.2459•Physical Review A•Nov 7, 2007•6 citations

Broadcasting of Entanglement in Three-Particle Greenberger-Horne-Zeilinger State via Quantum Copying

Zhao-Yang Tong, Kuang Le-Man

We introduce entanglement measures to describe entanglement in a three-particle system and apply it to studying broadcasting of entanglement in the three-particle Greenberger-Horne-Zeilinger (GHZ) state. The results show that the entanglement of the three-qubit GHZ state can be partially broadcasted with the help of local or non-local copying processes. It is found that non-local cloning is much more efficient than local cloning for the broadcasting of entanglement.

arXiv:quant-ph/0005070•Chinese Physics Letters•Jul 1, 2000•8 citations

Assisted cloning of a class of unknown three-qubit GHZ state

Shi Shou-Hua

A protocol for probabilistic cloning of a class of three-qubit Greenberger-Horne-Zeilinger (GHZ) state and its orthogonal complement state by using three maximally two-qubit entangled states as the quantum channel is proposed.In this protocol,Bob(the state receiver) can receive the unknown state via usual teleportation process.With the assistance of Victor(the state preparer), Alice(the state sender) can produce the perfect copies and complement copies of an unknown state. A protocol for the teleportation is given by using non-maximally entangled states as quantum channel,and the clones and complement clones of unknown state also can be obtained by Alice with assistance offered by the state preparer.

Chinese Journal of Quantum Electronics•Jan 1, 2009•0 citations

Local Conversion of Greenberger-Horne-Zeilinger States to Approximate W States

Philip John Walther, Kevin J. Resch, Anton Zeilinger

Genuine 3-qubit entanglement comes in two different inconvertible types represented by the Greenberger-Horne-Zeilinger (GHZ) state and the $W$ state. We describe a specific method based on local positive operator valued measures and classical communication that can convert the ideal $N$-qubit GHZ state to a state arbitrarily close to the ideal $N$-qubit $W$ state. We then experimentally implement this scheme in the 3-qubit case and characterize the input and the final state using 3-photon quantum state tomography.

arXiv:quant-ph/0506190•Physical Review Letters•Jun 22, 2005•80 citations

Local copying of orthogonal entangled quantum states

Fabio Anselmi, Anthony Chefles, Martin Bodo Plenio

In classical information theory one can, in principle, produce a perfect copy of any input state. In quantum information theory, the no cloning theorem prohibits exact copying of non-orthogonal states. Moreover, if we wish to copy multiparticle entangled states and can perform only local operations and classical communication (LOCC), then further restrictions apply. We investigate the problem of copying orthogonal, entangled quantum states with an entangled blank state under the restriction to LOCC. Throughout, the subsystems have finite dimension D . We show that if all of the states to be copied are non-maximally entangled, then novel LOCC copying procedures based on entanglement catalysis are possible. We then study in detail the LOCC copying problem where both the blank state and at least one of the states to be copied are maximally entangled. For this to be possible, we find that all the states to be copied must be maximally entangled. We obtain a necessary and sufficient condition for LOCC copying under these conditions. For two orthogonal, maximally entangled states, we provide the general solution to this condition. We use it to show that for D = 2, 3, any pair of orthogonal, maximally entangled states can be locally copied using a maximally entangled blank state. However, we also show that for any D which is not prime, one can construct pairs of such states for which this is impossible.

arXiv:quant-ph/0407168•New Journal of Physics•Nov 13, 2004•27 citations

Is It Possible To Clone Using An Arbitrary Blank State?

Roy, A, Ujjwal Sen, Sen, U

We show that using a fixed cloning machine, whether deterministic inexact or probabilistic exact, one can take an arbitrary blank state. Quantum information cannot be cloned. There cannot exist a machine which can produce two (or more) exact copies of an arbitrary state in a deterministic manner [1]. Replication is not allowed even when the input state is taken at random from a given set of two non-orthogonal states [2]. It has been further shown that probabilistic cloning is not possible if the input state is from a given linearly dependent set [3]. Henceforth we deal explicitly with qubits although all the results can be extended to higher dimensions. Although exact cloning is not possible, one can approximately clone an arbitrary input state [4, 5, 6]. In this scheme a fixed state is taken as the blank state, depending on which and the initial machine state, the cloning operation is constructed. We extend this operation such that any arbitrary (pure or mixed) state taken as the blank copy can do the job. The optimal universal 1 → 2 inexact qubit cloner of Brußet al.[5] takes an arbitrary qubit |ψ 〉 〈ψ | = 1 2 (I + − → s. − → σ) along with a fixed blank qubit |b 〉 and a machine state |M 〉 as input. An entangled state of the three qubits is produced as the output such that the reduced density matrices of the first two qubits are two similar approximate copies ρ = 1 2 (I + η− → s. − → σ) of |ψ 〉 〈ψ | with η = 2 3. The unitary operator realizing this process is defined on the combined Hilbert space of the input qubit, the blank qubit and machine by U ′ √ √

•Jan 1, 2001•1 citation
We discuss the (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancilla under local operation and classical communication. Whereas any two orthogonal Greenberger-Horne-Zeilinger (GHZ) states taken from the canonical GHZ basis can be cloned with the help of a known GHZ state, surprisingly we find that no two WWW states can be cloned by using any known three qubit (possibly entangled) state as a blank copy.
We discuss the exact cloning of orthogonal but entangled qubits under local operations and classical communication. The amount of entanglement necessary in a blank copy is obtained for various cases. Surprisingly, this amount is more than 1 ebit for certain sets of two nonmaximal but equally entangled states of two qubits. To clone any three Bell states, at least log2 3{\text{log}}_{2}\text{ }3log2​ 3 ebit is necessary.
A protocol for probabilistic cloning of a class of three-qubit Greenberger-Horne-Zeilinger (GHZ) state and its orthogonal complement state by using three maximally two-qubit entangled states as the quantum channel is proposed.In this protocol,Bob(the state receiver) can receive the unknown state via usual teleportation process.With the assistance of Victor(the state preparer), Alice(the state sender) can produce the perfect copies and complement copies of an unknown state. A protocol for the teleportation is given by using non-maximally entangled states as quantum channel,and the clones and complement clones of unknown state also can be obtained by Alice with assistance offered by the state preparer.
Genuine 3-qubit entanglement comes in two different inconvertible types represented by the Greenberger-Horne-Zeilinger (GHZ) state and the WWW state. We describe a specific method based on local positive operator valued measures and classical communication that can convert the ideal NNN-qubit GHZ state to a state arbitrarily close to the ideal NNN-qubit WWW state. We then experimentally implement this scheme in the 3-qubit case and characterize the input and the final state using 3-photon quantum state tomography.
In classical information theory one can, in principle, produce a perfect copy of any input state. In quantum information theory, the no cloning theorem prohibits exact copying of non-orthogonal states. Moreover, if we wish to copy multiparticle entangled states and can perform only local operations and classical communication (LOCC), then further restrictions apply. We investigate the problem of copying orthogonal, entangled quantum states with an entangled blank state under the restriction to LOCC. Throughout, the subsystems have finite dimension D . We show that if all of the states to be copied are non-maximally entangled, then novel LOCC copying procedures based on entanglement catalysis are possible. We then study in detail the LOCC copying problem where both the blank state and at least one of the states to be copied are maximally entangled. For this to be possible, we find that all the states to be copied must be maximally entangled. We obtain a necessary and sufficient condition for LOCC copying under these conditions. For two orthogonal, maximally entangled states, we provide the general solution to this condition. We use it to show that for D = 2, 3, any pair of orthogonal, maximally entangled states can be locally copied using a maximally entangled blank state. However, we also show that for any D which is not prime, one can construct pairs of such states for which this is impossible.
We show that using a fixed cloning machine, whether deterministic inexact or probabilistic exact, one can take an arbitrary blank state. Quantum information cannot be cloned. There cannot exist a machine which can produce two (or more) exact copies of an arbitrary state in a deterministic manner [1]. Replication is not allowed even when the input state is taken at random from a given set of two non-orthogonal states [2]. It has been further shown that probabilistic cloning is not possible if the input state is from a given linearly dependent set [3]. Henceforth we deal explicitly with qubits although all the results can be extended to higher dimensions. Although exact cloning is not possible, one can approximately clone an arbitrary input state [4, 5, 6]. In this scheme a fixed state is taken as the blank state, depending on which and the initial machine state, the cloning operation is constructed. We extend this operation such that any arbitrary (pure or mixed) state taken as the blank copy can do the job. The optimal universal 1 → 2 inexact qubit cloner of Brußet al.[5] takes an arbitrary qubit |ψ 〉 〈ψ | = 1 2 (I + − → s. − → σ) along with a fixed blank qubit |b 〉 and a machine state |M 〉 as input. An entangled state of the three qubits is produced as the output such that the reduced density matrices of the first two qubits are two similar approximate copies ρ = 1 2 (I + η− → s. − → σ) of |ψ 〉 〈ψ | with η = 2 3. The unitary operator realizing this process is defined on the combined Hilbert space of the input qubit, the blank qubit and machine by U ′ √ √