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:quant-ph/0001084 · Physical Review Letters

Distillation of Greenberger-Horne-Zeilinger States by Selective Information Manipulation

Oliver Cohen, Todd A. Brun

Published Jun 19, 2000• 26 citations
arXivHTMLPDF

Abstract

Methods for distilling Greenberger-Horne-Zeilinger (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique has two stages which we call primary and secondary distillations. Primary distillation produces a GHZ state with some probability, so that when applied to an ensemble of systems a certain percentage is discarded. Secondary distillation produces further GHZs from the discarded systems. These protocols are developed with the help of an approach to quantum information theory based on absolutely selective information, which has other potential applications.

DOI
10.1103/physrevlett.84.5908

Related papers

Practical scheme for efficient distillation of GHZ states

Áron Rozgonyi, Gábor Széchenyi, Orsolya Kálmán +1 more

We develop an efficient local operation and classical communication (LOCC) scheme for the distillation of Greenberger-Horne-Zeilinger (GHZ) states from tripartite systems subjected to both coherent and incoherent errors. The proposed method employs an iterative process that applies a postselection-based non-linear transformation to increase the entanglement of 3-qubit states. In contrast to traditional distillation protocols that require an exponential number of initial states as a resource, our method achieves subexponential convergence towards a pure GHZ state. The proposed scheme is practical in the sense that it employs a small set of relatively simple unitary operations and projective measurements in the computational basis. We systematically develop a double-iteration protocol by providing a mathematical framework for the transformation processes involved, emphasizing the role of unitary operations in correcting arbitrary small errors in the initial states. Through analytical derivations and numerical simulations, we demonstrate the protocol's ability to progressively eliminate noise and improve fidelity over subsequent iterations. Significantly, our protocol not only corrects for small arbitrary distortions in the GHZ states but also maintains operational simplicity, making it feasible for practical quantum computing applications.

arXiv:2501.12268•Jan 21, 2025•0 citations

Distillation of the Greenberger-Horne-Zeilinger state from arbitrary tripartite states

Yi-Na Mo, Chuan‐Feng Li, Guang‐Can Guo

We present a method of distillation of Greenberger-Horne-Zeilinger states from arbitrary tripartite pure states by local operations and classical communication. We go further to discuss the various results we get and calculate the efficiency of the protocol.

Physical Review A•Jan 4, 2002•2 citations

Distilling a Greenberger-Horne-Zeilinger State From an Arbitrary Pure State of Three Qubits

Li-Xiang Cen, Shun-Jin Wang

We present a general algorithm to achieve local operators which can produce the GHZ state for an arbitrary given three-qubit state. Thus the distillation process of the state can be realized optimally. The algorithm is shown to be sufficient for the three-qubit state on account of the fact that any state for which this distillation algorithm is invalid cannot be distilled to the GHZ state by any local actions. Moreover, an analytical result of distillation operations is achieved for the general state of three qubits.

arXiv:quant-ph/0012022•Dec 5, 2000•0 citations

GHZ Distillation using Quantum LDPC Codes

Narayanan Rengaswamy, Ankur Raina, Nithin Raveendran +1 more

Entanglement distribution is a critical task in quantum networks. Since the distributed entanglement can suffer from noise in the channel, it is necessary to develop methods that distill higher quality entanglement from the shared noisy entangled states. In this work, we propose a protocol to distill multi-qubit Greenberger-Horne-Zeilinger (GHZ) states among the nodes of a network using quantum error correcting codes. The method builds upon a Bell state distillation protocol by Wilde et at. (2007) that we recently generalized to 3-qubit GHZ states. The key technical result that enables our protocol shows how measuring a Pauli operator, or in general a set of code stabilizers, on one subsystem of a multipartite GHZ state affects the other subsystems. The design and analysis of the protocol is driven by the stabilizer formalism for measurements, and we provide discussions to elucidate the steps of the protocol. A similar approach can be applied to distill other multipartite entangled states as long as they are stabilizer states.

International Symposium on Turbo Codes and Iterative Information Processing•Sep 4, 2023•0 citations

Training iterated protocols for distillation of GHZ states with variational quantum algorithms

Áron Rozgonyi, Gábor Széchenyi, Orsolya Kálmán +1 more

We present optimized distillation schemes for preparing Greenberger-Horne-Zeilinger (GHZ) states. Our approach relies on training variational quantum circuits with white noise affected GHZ states as inputs. Optimizing for a single iteration of the scheme, we find that it is possible to achieve an increased fidelity to the GHZ state, although further iterations decrease the fidelity. The same scheme, acting on coherently distorted pure-state inputs, is effective only in certain special cases. We show that radically different results can be achieved, however, when one optimizes for the output after two iterations of the protocol. In this case, the obtained schemes are more effective in distilling GHZ states from inputs affected by white noise. Moreover, they can also correct several types of coherent pure-state errors.

arXiv:2311.04646•Physics Letters A•Feb 2, 2024•5 citations

Distillation of Greenberger–Horne–Zeilinger States by Combinatorial Methods

Péter Vrana, Matthias Christandl

We prove a lower bound on the rate of Greenberger-Horne-Zeilinger states distillable from pure multipartite states by local operations and classical communication (LOCC). Our proof is based on a modification of a combinatorial argument used in the fast matrix multiplication algorithm of Coppersmith and Winograd. Previous use of methods from algebraic complexity in quantum information theory concerned transformations with stochastic LOCC (SLOCC), resulting in an asymptotically vanishing success probability. In contrast, our new protocol works with an asymptotically vanishing error.

arXiv:1805.09096•IEEE Transactions on Information Theory•Apr 1, 2019•6 citations
Methods for distilling Greenberger-Horne-Zeilinger (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique has two stages which we call primary and secondary distillations. Primary distillation produces a GHZ state with some probability, so that when applied to an ensemble of systems a certain percentage is discarded. Secondary distillation produces further GHZs from the discarded systems. These protocols are developed with the help of an approach to quantum information theory based on absolutely selective information, which has other potential applications.
We develop an efficient local operation and classical communication (LOCC) scheme for the distillation of Greenberger-Horne-Zeilinger (GHZ) states from tripartite systems subjected to both coherent and incoherent errors. The proposed method employs an iterative process that applies a postselection-based non-linear transformation to increase the entanglement of 3-qubit states. In contrast to traditional distillation protocols that require an exponential number of initial states as a resource, our method achieves subexponential convergence towards a pure GHZ state. The proposed scheme is practical in the sense that it employs a small set of relatively simple unitary operations and projective measurements in the computational basis. We systematically develop a double-iteration protocol by providing a mathematical framework for the transformation processes involved, emphasizing the role of unitary operations in correcting arbitrary small errors in the initial states. Through analytical derivations and numerical simulations, we demonstrate the protocol's ability to progressively eliminate noise and improve fidelity over subsequent iterations. Significantly, our protocol not only corrects for small arbitrary distortions in the GHZ states but also maintains operational simplicity, making it feasible for practical quantum computing applications.
We present a general algorithm to achieve local operators which can produce the GHZ state for an arbitrary given three-qubit state. Thus the distillation process of the state can be realized optimally. The algorithm is shown to be sufficient for the three-qubit state on account of the fact that any state for which this distillation algorithm is invalid cannot be distilled to the GHZ state by any local actions. Moreover, an analytical result of distillation operations is achieved for the general state of three qubits.
Entanglement distribution is a critical task in quantum networks. Since the distributed entanglement can suffer from noise in the channel, it is necessary to develop methods that distill higher quality entanglement from the shared noisy entangled states. In this work, we propose a protocol to distill multi-qubit Greenberger-Horne-Zeilinger (GHZ) states among the nodes of a network using quantum error correcting codes. The method builds upon a Bell state distillation protocol by Wilde et at. (2007) that we recently generalized to 3-qubit GHZ states. The key technical result that enables our protocol shows how measuring a Pauli operator, or in general a set of code stabilizers, on one subsystem of a multipartite GHZ state affects the other subsystems. The design and analysis of the protocol is driven by the stabilizer formalism for measurements, and we provide discussions to elucidate the steps of the protocol. A similar approach can be applied to distill other multipartite entangled states as long as they are stabilizer states.
We present optimized distillation schemes for preparing Greenberger-Horne-Zeilinger (GHZ) states. Our approach relies on training variational quantum circuits with white noise affected GHZ states as inputs. Optimizing for a single iteration of the scheme, we find that it is possible to achieve an increased fidelity to the GHZ state, although further iterations decrease the fidelity. The same scheme, acting on coherently distorted pure-state inputs, is effective only in certain special cases. We show that radically different results can be achieved, however, when one optimizes for the output after two iterations of the protocol. In this case, the obtained schemes are more effective in distilling GHZ states from inputs affected by white noise. Moreover, they can also correct several types of coherent pure-state errors.
We prove a lower bound on the rate of Greenberger-Horne-Zeilinger states distillable from pure multipartite states by local operations and classical communication (LOCC). Our proof is based on a modification of a combinatorial argument used in the fast matrix multiplication algorithm of Coppersmith and Winograd. Previous use of methods from algebraic complexity in quantum information theory concerned transformations with stochastic LOCC (SLOCC), resulting in an asymptotically vanishing success probability. In contrast, our new protocol works with an asymptotically vanishing error.