Efficient verification of Affleck-Kennedy-Lieb-Tasaki states

• URL: http://arxiv.org/abs/2206.15307v1
• Date: Thu, 30 Jun 2022 14:24:37 GMT
• Title: Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Authors: Tianyi Chen, Yunting Li, and Huangjun Zhu
• Abstract summary: Affleck-Kennedy-Lieb-Tasaki (AKLT) states are an important class of many-body quantum states. We propose a general approach for constructing efficient verification protocols for AKLT states on arbitrary graphs.
• Score: 14.158567687044409
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Affleck-Kennedy-Lieb-Tasaki (AKLT) states are an important class of many-body quantum states that are useful in quantum information processing, including measurement-based quantum computation in particular. Here we propose a general approach for constructing efficient verification protocols for AKLT states on arbitrary graphs with local spin measurements. Our verification protocols build on bond verification protocols and matching covers (including edge coloring) of the underlying graphs, which have a simple geometric and graphic picture. We also provide rigorous performance guarantee that is required for practical applications. With our approach, most AKLT states of wide interest, including those defined on 1D and 2D lattices, can be verified with a constant sample cost, which is independent of the system size and is dramatically more efficient than all previous approaches. As an illustration, we construct concrete verification protocols for AKLT states on various lattices and on arbitrary graphs up to five vertices.

Related papers

• Multi-user QKD using quotient graph states derived from continuous-variable dual-rail cluster states [0.0]
  Multipartite entangled states are fundamental resources for multi-user quantum cryptographic tasks. We introduce a novel protocol for generating three user conference keys using a CV dual-rail cluster state.
  arXiv  Detail & Related papers  (2024-12-18T20:35:12Z)
• Tower of Structured Excited States from Measurements [0.07673339435080445]
  We introduce a log-depth protocol leveraging quantum phase estimation to measure a global observable. We demonstrate its capability to prepare towers of structured excited states that are useful in quantum metrology. Our results expand the utility of measurement-based approaches to accessing highly entangled states in quantum many-body systems.
  arXiv  Detail & Related papers  (2024-11-26T01:07:46Z)
• Noisy certification of continuous variables graph states [1.534667887016089]
  We show how CV graph states can be efficiently verified and certified even in a noisy and imperfect setting. We then discuss how our findings impact the usability of states obtained after the protocol for different applications.
  arXiv  Detail & Related papers  (2024-06-06T09:42:58Z)
• 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)
• Robust and efficient verification of graph states in blind measurement-based quantum computation [52.70359447203418]
  Blind quantum computation (BQC) is a secure quantum computation method that protects the privacy of clients. It is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension.
  arXiv  Detail & Related papers  (2023-05-18T06:24:45Z)
• Efficient verification of arbitrary entangled states with homogeneous local measurements [0.874274295147112]
  Quantum state verification (QSV) is the task of relying on local measurements to verify that a given quantum device produces the desired target state. We present a systematic strategy to tackle this problem by considering the locality of what we initiate as the choice-independent measurement protocols. We show the explicit procedures of the protocol design using standard Pauli projections, demonstrating the superiority of our method for attaining better QSV strategies.
  arXiv  Detail & Related papers  (2022-08-01T18:32:56Z)
• Data post-processing for the one-way heterodyne protocol under composable finite-size security [62.997667081978825]
  We study the performance of a practical continuous-variable (CV) quantum key distribution protocol. We focus on the Gaussian-modulated coherent-state protocol with heterodyne detection in a high signal-to-noise ratio regime. This allows us to study the performance for practical implementations of the protocol and optimize the parameters connected to the steps above.
  arXiv  Detail & Related papers  (2022-05-20T12:37:09Z)
• Machine-Learning-Derived Entanglement Witnesses [55.76279816849472]
  We show a correspondence between linear support vector machines (SVMs) and entanglement witnesses. We use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target entangled states.
  arXiv  Detail & Related papers  (2021-07-05T22:28:02Z)
• Sample-efficient device-independent quantum state verification and certification [68.8204255655161]
  Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing. We develop a systematic approach to device-independent verification of quantum states free of IID assumptions in the finite copy regime. We show that device-independent verification can be performed with optimal sample efficiency.
  arXiv  Detail & Related papers  (2021-05-12T17:48:04Z)
• 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)
• Verification of graph states in an untrusted network [0.0]
  We consider verification of graph states generated by an untrusted source and shared between a network of possibly dishonest parties. This has implications in certifying the application of graph states for various distributed tasks. We present a protocol which is globally efficient for a large family of useful graph states.
  arXiv  Detail & Related papers  (2020-07-26T13:17:21Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

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.