© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Entropy

Improving the Robustness of Entangled States by Basis Transformation

Xin-Wen Wang, Shi-Qing Tang, Yan Liu, Ji-Bing Yuan

Published Jan 13, 2019• 2 citations

Abstract

In the practical application of quantum entanglement, entangled particles usually need to be distributed to many distant parties or stored in different quantum memories. In these processes, entangled particles unavoidably interact with their surrounding environments, respectively. We here systematically investigate the entanglement-decay laws of cat-like states under independent Pauli noises with unbalanced probability distribution of three kinds of errors. We show that the robustness of cat-like entangled states is not only related to the overall noise strength and error distribution parameters, but also to the basis of qubits. Moreover, we find that whether a multi-qubit state is more robust in the computational basis or transversal basis depends on the initial entanglement and number of qubits of the state as well as the overall noise strength and error distribution parameters of the environment. However, which qubit basis is conductive to enhancing the robustness of two-qubit states is only dependent on the error distribution parameters. These results imply that one could improve the intrinsic robustness of entangled states by simply transforming the qubit basis at the right moment. This robustness-improving method does not introduce extra particles and works in a deterministic manner.

DOI: 10.3390/e21010059

Related papers

Robustness of many-qubit entanglement under general decoherence

Somshubhro Bandyopadhyay, Daniel A. Lidar

We study the robustness of the GHZ (or ``cat'') class of multi-partite states under decoherence. The noise model is described by a general completely positive map for qubits independently coupled to the environment. In particular, the robustness of N-party entanglement is studied in the large N limit when (a) the number of spatially separated subsystems is fixed but the size of each subsystem becomes macroscopic (b) the size of the subsystems is fixed while their number becomes arbitrarily large. We obtain threshold conditions for entanglement in these two cases. Among our other results, we show that the parity of an entangled state (i.e., whether it contains an even or odd number of qubits) can lead to qualitatively different robustness of entanglement under certain conditions.

•Aug 29, 2004•1 citation

Robust multipartite quantum correlations without complex encodings

Rafael Chaves, Leandro Aolita, Antonio Acín

One of the main challenges for the manipulation and storage of multipartite entanglement is its fragility under noise. We present a simple recipe for the systematic enhancement of the resistance of multipartite entanglement against any local noise with a privileged direction in the Bloch sphere. For the case of exact local dephasing along any given basis, and for all noise strengths, our prescription grants full robustness: Even states with exponentially decaying entanglement are mapped to states whose entanglement is constant. In contrast to previous techniques resorting to complex logical-qubit encodings, such enhancement is attained simply by performing local-unitary rotations before the noise acts. The scheme is therefore highly experimentally friendly, as it brings no overhead of extra physical qubits to encode logical ones. In addition, we show that, apart from entanglement, the resiliences of the relative entropy of quantumness and the usefulness as resources for practical tasks such as metrology and nonlocality-based protocols are equivalently enhanced.

arXiv:1112.2645•Physical Review A•Aug 2, 2012•22 citations

Robustness of multiqubit entanglement in the independent decoherence model

Somshubhro Bandyopadhyay, Daniel A. Lidar

We study the robustness of the Greenberger-Horne-Zeilinger (``cat'') class of multipartite states under decoherence. The noise model is described by a general completely positive map for qubits independently coupled to the environment. In particular, the robustness of $N$-party entanglement is studied in the large $N$ limit when (a) the number of spatially separated subsystems is fixed but the size of each subsystem becomes large and (b) the size of the subsystems is fixed while their number becomes arbitrarily large. We obtain conditions for entanglement in these two cases. Among our other results, we show that the parity of an entangled state (i.e., whether it contains an even or odd number of qubits) can lead to qualitatively different robustness of entanglement under certain conditions.

arXiv:quant-ph/0408174•Physical Review A•Oct 31, 2005•38 citations

Single-copy entanglement purification: a robust approach for diverse noise sources

Sajede Harraz, Shuang Cong

Effectively managing various types of decoherence is crucial for leveraging entanglement in quantum information processing and quantum computing. In this paper, we propose purification circuits that deterministically produce a maximally entangled state from a single copy of an imperfect entangled pair affected by various noise sources. Unlike conventional methods, our approach eliminates the need for multiple copies of the entangled state, pre-purification operations, and imposes no restrictions on the initial entanglement fidelity of the imperfect pair. Our method utilizes ancilla qubits and CNOT gates to address errors from Pauli X and Z (bit flip and phase flip), as well as combinations of these errors that create general mixed entangled states and amplitude-damped entangled states. Our analysis shows that noisy CNOT gates impact fidelity minimally, with only the final two gates being critical. We validate our approach through mathematical analysis and practical implementation in Qiskit, demonstrating its effectiveness and robustness.

EPJ Quantum Technology•Apr 1, 2025•1 citation

Manipulation of entanglement localization under quantum noises and its application to entanglement distribution

Xin-Wen Wang, Shi-Qing Tang, Ji-Bing Yuan +1 more

The effect of quantum noise on entanglement localization is investigated. We show that the optimal strategy for reducing a multiparticle entangled state to a two-particle one via local measurements in the noise-free case is different from that in a noisy environment, and explore the best von Neumann measurement on one of three qubits of a triple Greenberger-Horne-Zeilinger state for extracting a two-qubit entangled state in the presence of local amplitude noises. We also demonstrate that the idea of entanglement localization can be utilized to improve the quality of bipartite entanglement distributing through noisy quantum channels. These results might shed a new light on entanglement manipulations and transformations.

•Feb 9, 2014•0 citations

Robustness of Entanglement During Decoherence

Kwang-Il Kim, Bao‐Kui Zhao, Hong-Mei Li +1 more

Finding the most robust entangled states during the whole process of decoherence is a particularly fundamental problem for quantum physics and quantum information processing. In this paper, the decoherence process of two-qubit system under two individual identical decoherence channels is investigated systematically. We find that although the robustness of two-qubit states with same initial entanglement is usually different, the Bell-like states are always the most robust entangled states during decoherence. That is to say, affected by the same amount of noise, the remain entanglement of an arbitrary two-qubit state is not more than that of a Bell-like state with the same initial entanglement.

Communications in Theoretical Physics•Nov 1, 2014•6 citations

In the practical application of quantum entanglement, entangled particles usually need to be distributed to many distant parties or stored in different quantum memories. In these processes, entangled particles unavoidably interact with their surrounding environments, respectively. We here systematically investigate the entanglement-decay laws of cat-like states under independent Pauli noises with unbalanced probability distribution of three kinds of errors. We show that the robustness of cat-like entangled states is not only related to the overall noise strength and error distribution parameters, but also to the basis of qubits. Moreover, we find that whether a multi-qubit state is more robust in the computational basis or transversal basis depends on the initial entanglement and number of qubits of the state as well as the overall noise strength and error distribution parameters of the environment. However, which qubit basis is conductive to enhancing the robustness of two-qubit states is only dependent on the error distribution parameters. These results imply that one could improve the intrinsic robustness of entangled states by simply transforming the qubit basis at the right moment. This robustness-improving method does not introduce extra particles and works in a deterministic manner.

We study the robustness of the GHZ (or ``cat'') class of multi-partite states under decoherence. The noise model is described by a general completely positive map for qubits independently coupled to the environment. In particular, the robustness of N-party entanglement is studied in the large N limit when (a) the number of spatially separated subsystems is fixed but the size of each subsystem becomes macroscopic (b) the size of the subsystems is fixed while their number becomes arbitrarily large. We obtain threshold conditions for entanglement in these two cases. Among our other results, we show that the parity of an entangled state (i.e., whether it contains an even or odd number of qubits) can lead to qualitatively different robustness of entanglement under certain conditions.

One of the main challenges for the manipulation and storage of multipartite entanglement is its fragility under noise. We present a simple recipe for the systematic enhancement of the resistance of multipartite entanglement against any local noise with a privileged direction in the Bloch sphere. For the case of exact local dephasing along any given basis, and for all noise strengths, our prescription grants full robustness: Even states with exponentially decaying entanglement are mapped to states whose entanglement is constant. In contrast to previous techniques resorting to complex logical-qubit encodings, such enhancement is attained simply by performing local-unitary rotations before the noise acts. The scheme is therefore highly experimentally friendly, as it brings no overhead of extra physical qubits to encode logical ones. In addition, we show that, apart from entanglement, the resiliences of the relative entropy of quantumness and the usefulness as resources for practical tasks such as metrology and nonlocality-based protocols are equivalently enhanced.

We study the robustness of the Greenberger-Horne-Zeilinger (``cat'') class of multipartite states under decoherence. The noise model is described by a general completely positive map for qubits independently coupled to the environment. In particular, the robustness of

N

-party entanglement is studied in the large

N

limit when (a) the number of spatially separated subsystems is fixed but the size of each subsystem becomes large and (b) the size of the subsystems is fixed while their number becomes arbitrarily large. We obtain conditions for entanglement in these two cases. Among our other results, we show that the parity of an entangled state (i.e., whether it contains an even or odd number of qubits) can lead to qualitatively different robustness of entanglement under certain conditions.

Effectively managing various types of decoherence is crucial for leveraging entanglement in quantum information processing and quantum computing. In this paper, we propose purification circuits that deterministically produce a maximally entangled state from a single copy of an imperfect entangled pair affected by various noise sources. Unlike conventional methods, our approach eliminates the need for multiple copies of the entangled state, pre-purification operations, and imposes no restrictions on the initial entanglement fidelity of the imperfect pair. Our method utilizes ancilla qubits and CNOT gates to address errors from Pauli X and Z (bit flip and phase flip), as well as combinations of these errors that create general mixed entangled states and amplitude-damped entangled states. Our analysis shows that noisy CNOT gates impact fidelity minimally, with only the final two gates being critical. We validate our approach through mathematical analysis and practical implementation in Qiskit, demonstrating its effectiveness and robustness.

The effect of quantum noise on entanglement localization is investigated. We show that the optimal strategy for reducing a multiparticle entangled state to a two-particle one via local measurements in the noise-free case is different from that in a noisy environment, and explore the best von Neumann measurement on one of three qubits of a triple Greenberger-Horne-Zeilinger state for extracting a two-qubit entangled state in the presence of local amplitude noises. We also demonstrate that the idea of entanglement localization can be utilized to improve the quality of bipartite entanglement distributing through noisy quantum channels. These results might shed a new light on entanglement manipulations and transformations.

Finding the most robust entangled states during the whole process of decoherence is a particularly fundamental problem for quantum physics and quantum information processing. In this paper, the decoherence process of two-qubit system under two individual identical decoherence channels is investigated systematically. We find that although the robustness of two-qubit states with same initial entanglement is usually different, the Bell-like states are always the most robust entangled states during decoherence. That is to say, affected by the same amount of noise, the remain entanglement of an arbitrary two-qubit state is not more than that of a Bell-like state with the same initial entanglement.