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

Laser Physics

Construction of a 4-uniform 12-qubit entangled state based on recurrence relations

Ziyao Wang, Jingjing Wang, Yang Liu, Angdi Lu, Zhao Zhang, Junling Che

Published Jul 1, 2025• 0 citations
Publisher

Abstract

Abstract The quantification of quantum entangled states is essential for developing entanglement resources, and this process has profound implications for advancing quantum computing and quantum communication. To address the challenge of quantifying such systems beyond 10 qubits, we present a method for constructing high-dimensional k-uniform states using a 9-qubit entangled state and recurrence relations. By incrementally increasing the number of qubits, we construct 10-, 11-, and 12-qubit entangled states and verify their uniformity using reduced density matrices. We demonstrate for the first time that the 12-qubit state is 4-uniform as all 4-qubit subsystems exhibit maximal mixedness. Compared to conventional designs, our recurrence-relation-based approach emphasizes intrinsic multiqubit correlations, offering a direct method for quantifying high-dimensional entanglement. The 4-uniform state offers distinct advantages for quantum error correction and fault-tolerant computation, laying a foundation for large-scale quantum information systems.

DOI
10.1088/1555-6611/adebee

Related papers

Construct maximally seven-qubit entangled state via Brown state

Yazhou Yue, Erdun Minze, Yuanzheng Liu +1 more

It is worth studying recurrence relation of multi-qubit states due to its benefits to the criterion and measurement of quantum entanglement. Recently, Huang et al. presented an expand recurrence relation of multi-qubit state. Using this expand recurrence relation and Brown state, we construct a new seven-qubit maximally entangled states of 32 and 3 balanced purities equal to 1/8 and 1/4, whose averaged subsystem purity is equal to 19/140. We found that the marginal density matrices for subsystems of 1 and 2 qubits all completely mixed in these states.

International Journal of Modern Physics B•Sep 22, 2022•1 citation

Quantifying entanglement in a 68-billion dimensional quantum system

James Schneeloch, Christopher C. Tison, Michael L. Fanto +2 more

Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Achieving a quantum advantage requires scaling quantum systems to sizes that can support a large amount of entanglement. Because real-world systems are varied and imperfect, the quantum resources they provide must be characterized before use. However, exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which requires an intractable number of measurements even for modestly sized systems. Here we demonstrate a new method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only 6,456 measurements are needed to certify an entanglement-of-formation of $7.11 \pm .04$ ebits shared between spatially-entangled photon pairs. With a Hilbert space exceeding 68 billion dimensions, this is 10-million-fold fewer measurements than traditional approaches. The procedure does not computationally recover an underlying state and allows straightforward error analysis. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.

•Apr 12, 2018•0 citations

Entanglement Quantification via Determinantal Polynomials

PAULO SÉRGIO DE ANDRADE

Entanglement, a fundamental resource in quantum information science, underpins many quantum technologies, including quantum computation and cryptography. Quantifying entanglement is a critical challenge, especially for mixed states and higher-dimensional systems, where existing measures often face computational complexities or lack analytical closed-form expressions. This paper introduces a novel approach to entanglement quantification utilizing determinantal polynomials. We propose a framework where entanglement properties of quantum states, particularly their degree and type, can be characterized and potentially measured through the analysis of determinants derived from state representations, such as density matrices and their partial transposes. By constructing specific polynomial functions whose roots or coefficients are directly linked to entanglement measures or criteria, we aim to provide a more tractable and potentially analytical pathway for quantifying entanglement. The methodology leverages advanced concepts from linear algebra and algebraic geometry, connecting the algebraic properties of quantum states to their entanglement features. This work discusses the theoretical underpinnings, provides illustrative examples for low-dimensional systems, and explores the potential of this method to overcome some limitations of current entanglement measures, offering a new perspective on the algebraic structure of entanglement.

•Nov 24, 2025•0 citations

Constructing seven ququarts absolutely maximally entangled state via recurrence relation

Haiqing Huang, Irfan Ahmed, Da Zhang +2 more

Abstract Recently, Che and Wu (2019 Int. J. Theor. Phys. 58 584–90) presented a recurrence relation of multi-qubit states. Inspired by this, we present the recurrence relation of ququart maximally entangled states. Further, via the recurrence relation of six ququarts maximally entangled states, a seven ququarts absolutely maximally entangled state can be constructed. We also show this state is the three-uniform state of seven ququarts states.

Laser Physics•Dec 14, 2020•2 citations

Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms

Iris Cong, Harry Levine, Alexander Keesling +3 more

Neutral-atom arrays have recently emerged as a promising platform for quantum information processing.One important remaining roadblock for the large-scale application of these systems is the ability to perform error-corrected quantum operations.To entangle the qubits in these systems, atoms are typically excited to Rydberg states, which could decay or give rise to various correlated errors that cannot be addressed directly through traditional methods of fault-tolerant quantum computation.In this work, we provide the first complete characterization of these sources of error in a neutral-atom quantum computer and propose hardware-efficient, fault-tolerant quantum computation schemes that mitigate them.Notably, we develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace.These advances allow us to significantly reduce the resource cost for fault-tolerant quantum computation compared to existing, general-purpose schemes.Our protocols can be implemented in the near term using state-of-the-art neutral-atom platforms with qubits encoded in both alkali and alkaline-earth atoms.

arXiv:2105.13501•Physical Review X•Jun 1, 2022•144 citations

Stabilizer Entanglement Distillation and Efficient Fault-Tolerant Encoders

Yu Bo Shi, Ashlesha Patil, Saikat Guha

Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement distillation protocol to higher-rate n -to- ( n − 1 ) protocols that can correct any single-qubit errors. These protocols are evaluated through numerical simulations focusing on fidelity and yield. We also outline a method to adapt any classical error-correcting code for entanglement distillation, where the code can correct both bit-flip and phase-flip errors by incorporating Hadamard gates. (2) We propose a constant-depth decoder for stabilizer codes that transforms logical states into physical ones using single-qubit measurements. This decoder is applied to entanglement distillation protocols, reducing circuit depth and enabling protocols derived from high-performance quantum error-correcting codes. We demonstrate this by evaluating the circuit complexity for entanglement distillation protocols based on surface codes and quantum convolutional codes. (3) Our stabilizer entanglement distillation techniques advance quantum computing. We propose a fault-tolerant protocol for constant-depth encoding and decoding of arbitrary states in surface codes, with potential extensions to more general quantum low-density parity-check codes. This protocol is feasible with state-of-the-art reconfigurable atom arrays and surpasses the limits of conventional logarithmic depth encoders. Overall, our study integrates stabilizer formalism, measurement-based quantum computing, and entanglement distillation, advancing both quantum communication and computing.

arXiv:2408.06299•PRX Quantum•Mar 4, 2025•10 citations
Abstract The quantification of quantum entangled states is essential for developing entanglement resources, and this process has profound implications for advancing quantum computing and quantum communication. To address the challenge of quantifying such systems beyond 10 qubits, we present a method for constructing high-dimensional k-uniform states using a 9-qubit entangled state and recurrence relations. By incrementally increasing the number of qubits, we construct 10-, 11-, and 12-qubit entangled states and verify their uniformity using reduced density matrices. We demonstrate for the first time that the 12-qubit state is 4-uniform as all 4-qubit subsystems exhibit maximal mixedness. Compared to conventional designs, our recurrence-relation-based approach emphasizes intrinsic multiqubit correlations, offering a direct method for quantifying high-dimensional entanglement. The 4-uniform state offers distinct advantages for quantum error correction and fault-tolerant computation, laying a foundation for large-scale quantum information systems.
It is worth studying recurrence relation of multi-qubit states due to its benefits to the criterion and measurement of quantum entanglement. Recently, Huang et al. presented an expand recurrence relation of multi-qubit state. Using this expand recurrence relation and Brown state, we construct a new seven-qubit maximally entangled states of 32 and 3 balanced purities equal to 1/8 and 1/4, whose averaged subsystem purity is equal to 19/140. We found that the marginal density matrices for subsystems of 1 and 2 qubits all completely mixed in these states.
Entanglement is the powerful and enigmatic resource central to quantum information processing, which promises capabilities in computing, simulation, secure communication, and metrology beyond what is possible for classical devices. Achieving a quantum advantage requires scaling quantum systems to sizes that can support a large amount of entanglement. Because real-world systems are varied and imperfect, the quantum resources they provide must be characterized before use. However, exactly quantifying the entanglement of an unknown system requires completely determining its quantum state, a task which requires an intractable number of measurements even for modestly sized systems. Here we demonstrate a new method for rigorously quantifying high-dimensional entanglement from extremely limited data. We improve an entropic, quantitative entanglement witness to operate directly on compressed experimental data acquired via an adaptive, multilevel sampling procedure. Only 6,456 measurements are needed to certify an entanglement-of-formation of 7.11±.047.11 \pm .047.11±.04 ebits shared between spatially-entangled photon pairs. With a Hilbert space exceeding 68 billion dimensions, this is 10-million-fold fewer measurements than traditional approaches. The procedure does not computationally recover an underlying state and allows straightforward error analysis. Our technique offers a universal method for quantifying entanglement in any large quantum system shared by two parties.
Entanglement, a fundamental resource in quantum information science, underpins many quantum technologies, including quantum computation and cryptography. Quantifying entanglement is a critical challenge, especially for mixed states and higher-dimensional systems, where existing measures often face computational complexities or lack analytical closed-form expressions. This paper introduces a novel approach to entanglement quantification utilizing determinantal polynomials. We propose a framework where entanglement properties of quantum states, particularly their degree and type, can be characterized and potentially measured through the analysis of determinants derived from state representations, such as density matrices and their partial transposes. By constructing specific polynomial functions whose roots or coefficients are directly linked to entanglement measures or criteria, we aim to provide a more tractable and potentially analytical pathway for quantifying entanglement. The methodology leverages advanced concepts from linear algebra and algebraic geometry, connecting the algebraic properties of quantum states to their entanglement features. This work discusses the theoretical underpinnings, provides illustrative examples for low-dimensional systems, and explores the potential of this method to overcome some limitations of current entanglement measures, offering a new perspective on the algebraic structure of entanglement.
Neutral-atom arrays have recently emerged as a promising platform for quantum information processing.One important remaining roadblock for the large-scale application of these systems is the ability to perform error-corrected quantum operations.To entangle the qubits in these systems, atoms are typically excited to Rydberg states, which could decay or give rise to various correlated errors that cannot be addressed directly through traditional methods of fault-tolerant quantum computation.In this work, we provide the first complete characterization of these sources of error in a neutral-atom quantum computer and propose hardware-efficient, fault-tolerant quantum computation schemes that mitigate them.Notably, we develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace.These advances allow us to significantly reduce the resource cost for fault-tolerant quantum computation compared to existing, general-purpose schemes.Our protocols can be implemented in the near term using state-of-the-art neutral-atom platforms with qubits encoded in both alkali and alkaline-earth atoms.
Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement distillation protocol to higher-rate n -to- ( n − 1 ) protocols that can correct any single-qubit errors. These protocols are evaluated through numerical simulations focusing on fidelity and yield. We also outline a method to adapt any classical error-correcting code for entanglement distillation, where the code can correct both bit-flip and phase-flip errors by incorporating Hadamard gates. (2) We propose a constant-depth decoder for stabilizer codes that transforms logical states into physical ones using single-qubit measurements. This decoder is applied to entanglement distillation protocols, reducing circuit depth and enabling protocols derived from high-performance quantum error-correcting codes. We demonstrate this by evaluating the circuit complexity for entanglement distillation protocols based on surface codes and quantum convolutional codes. (3) Our stabilizer entanglement distillation techniques advance quantum computing. We propose a fault-tolerant protocol for constant-depth encoding and decoding of arbitrary states in surface codes, with potential extensions to more general quantum low-density parity-check codes. This protocol is feasible with state-of-the-art reconfigurable atom arrays and surpasses the limits of conventional logarithmic depth encoders. Overall, our study integrates stabilizer formalism, measurement-based quantum computing, and entanglement distillation, advancing both quantum communication and computing.