Power and limitations of distributed quantum state purification

• URL: http://arxiv.org/abs/2509.08691v1
• Date: Wed, 10 Sep 2025 15:33:18 GMT
• Title: Power and limitations of distributed quantum state purification
• Authors: Benchi Zhao, Yu-Ao Chen, Xuanqiang Zhao, Chengkai Zhu, Giulio Chiribella, Xin Wang,
• Abstract summary: Quantum state purification has applications in quantum communication and computation with imperfect devices.<n>We systematically study distributed quantum state purification under local operations and classical communication.<n>We show that single-state purification is achievable, and we provide an explicit analytical LOCC protocol for individual target states.
• Score: 8.17540482298122
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum state purification, which mitigates noise by exploiting multiple noisy copies of unknown states, has applications in quantum communication and computation with imperfect devices. Despite its importance, the fundamental capabilities and limitations of purification in distributed quantum systems remain largely unexplored. Here, we systematically study distributed quantum state purification under local operations and classical communication (LOCC). We prove that no nontrivial two-to-one LOCC purification protocol exists for three fundamental sets: all pure states, all maximally entangled states, and the four Bell states. This no-go theorem demonstrates that no LOCC protocol can reduce noise for every state within these sets, even probabilistically. In stark contrast, we show that single-state purification is achievable, and we provide an explicit analytical LOCC protocol for individual target states. For arbitrary state sets, we develop an optimization-based algorithm that systematically designs LOCC purification protocols, demonstrating its efficacy through concrete examples. These results delineate the fundamental boundaries of LOCC-based purification and provide practical strategies for noise reduction in distributed quantum information processing.

Related papers

• Optimality of universal conclusive entanglement purification protocols [75.52645767671567]
  We establish fundamental limits for conclusive protocols distilling perfect Bell states from a pure two-qubit states.<n>We prove that a known protocol achieves these bounds, confirming its optimality.
  arXiv  Detail & Related papers  (2025-09-11T13:04:17Z)
• Carrier-Assisted Entanglement Purification [7.610551500789847]
  Entanglement distillation enables the purification of noisy entangled states shared among distant nodes by local operations and classical communication.<n>We present an entanglement purification protocol via quantum communication, namely a carrier-assisted entanglement purification protocol.<n>We show that the protocol, when single-qubit transmission is noiseless, can purify a noisy entangled state shared by parties.
  arXiv  Detail & Related papers  (2025-09-09T08:51:17Z)
• No-Go Theorems for Universal Quantum State Purification via Classically Simulable Operations [5.213969622428918]
  We investigate the limitations of classically simulable operations for quantum state purification.<n>We prove that neither deterministic nor probabilistic protocols using only classically simulable operations can achieve universal purification.<n>Our findings highlight the indispensable role of non-stabilizer resources and the inherent limitations of classically simulable operations in quantum state purification.
  arXiv  Detail & Related papers  (2025-04-10T17:03:10Z)
• Protocols and Trade-Offs of Quantum State Purification [4.732131350249]
  We introduce a general state purification framework designed to achieve the highest fidelity with a specified probability. For i.i.d. quantum states under depolarizing noise, our framework can replicate the purification protocol proposed by Barenco and al. We prove the protocols' optimality for two copies of noisy states with any dimension and confirm its optimality for higher numbers of copies and dimensions.
  arXiv  Detail & Related papers  (2024-04-01T14:34:45Z)
• Performance of entanglement purification including maximally entangled mixed states [0.0]
  Entanglement between distant quantum systems is a critical resource for implementing quantum communication. We propose an entanglement purification protocol based on two entangling two-qubit operations. Two variants of the core protocol are introduced and shown to be more practical in certain scenarios.
  arXiv  Detail & Related papers  (2024-02-06T18:34:34Z)
• Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement [41.94295877935867]
  We introduce and develop the framework of Gibbs-preserving local operations and classical communication.<n>We focus on systems with fully degenerate local Hamiltonians, where local cooling aligns with the extraction of local purity.<n>Our findings open doors to various practical applications, including techniques for entanglement detection and estimation.
  arXiv  Detail & Related papers  (2023-11-20T14:58:31Z)
• Retrieving non-linear features from noisy quantum states [11.289924445850328]
  In this paper, we analyze the feasibility and efficiency of extracting high-order moments from noisy states. We first show that there exists a quantum protocol capable of accomplishing this task if and only if the underlying noise channel is invertible. Our work contributes to a deeper understanding of how quantum noise could affect high-order information extraction and provides guidance on how to tackle it.
  arXiv  Detail & Related papers  (2023-09-20T15:28:18Z)
• Suppressing Amplitude Damping in Trapped Ions: Discrete Weak Measurements for a Non-unitary Probabilistic Noise Filter [62.997667081978825]
  We introduce a low-overhead protocol to reverse this degradation. We present two trapped-ion schemes for the implementation of a non-unitary probabilistic filter against amplitude damping noise. This filter can be understood as a protocol for single-copy quasi-distillation.
  arXiv  Detail & Related papers  (2022-09-06T18:18:41Z)
• Quantum communication complexity beyond Bell nonlocality [87.70068711362255]
  Efficient distributed computing offers a scalable strategy for solving resource-demanding tasks. Quantum resources are well-suited to this task, offering clear strategies that can outperform classical counterparts. We prove that a new class of communication complexity tasks can be associated to Bell-like inequalities.
  arXiv  Detail & Related papers  (2021-06-11T18:00:09Z)
• Heterogeneous Multipartite Entanglement Purification for Size-Constrained Quantum Devices [68.8204255655161]
  Purifying entanglement resources after their imperfect generation is an indispensable step towards using them in quantum architectures. Here we depart from the typical purification paradigm for multipartite states explored in the last twenty years. We find that smaller sacrificial' states, like Bell pairs, can be more useful in the purification of multipartite states than additional copies of these same states.
  arXiv  Detail & Related papers  (2020-11-23T19:00:00Z)
• Entanglement purification by counting and locating errors with entangling measurements [62.997667081978825]
  We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble.
  arXiv  Detail & Related papers  (2020-11-13T19:02:33Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.