A Necessary and Sufficient Entanglement Criterion of N-qubit System Based on Correlation Tensor

• URL: http://arxiv.org/abs/2205.05323v1
• Date: Wed, 11 May 2022 08:01:28 GMT
• Title: A Necessary and Sufficient Entanglement Criterion of N-qubit System Based on Correlation Tensor
• Authors: Feng-Lin Wu and Si-Yuan Liu and Wen-Li Yang and Shao-Ming Fei and Heng Fan
• Abstract summary: We propose a necessary and sufficient entanglement criterion for general N-qubit systems. Our results pave the way to solve the entanglement-separability criterion for more general cases.
• Score: 18.123649659460465
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Great advances have been achieved in studying characteristics of entanglement for fundamentals of quantum mechanics and quantum information processing. However, even for N-qubit systems, the problem of entanglement criterion has not been well solved. In this Letter, using the method of state decomposition and high order singular value decomposition (HOSVD), we propose a necessary and sufficient entanglement criterion for general N-qubit systems. As an example, we apply our method to study the multi-qubit W state with white noise. We not only obtain the separability critical point, which is tight and thus better than known results, but also the separate states ensemble for decomposition. More examples are presented to show our criterion is accurate, which is tighter than the well-known positive partial transpose criterion. For two-qubit case, we can provide an entanglement measurer which gives similar results with concurrence up to a factor. Our results pave the way to solve the entanglement-separability criterion for more general cases.

Related papers

• SQ Lower Bounds for Non-Gaussian Component Analysis with Weaker Assumptions [50.20087216230159]
  We study the complexity of Non-Gaussian Component Analysis (NGCA) in the Statistical Query model. We prove near-optimal SQ lower bounds for NGCA under the moment-matching condition only.
  arXiv  Detail & Related papers  (2024-03-07T18:49:32Z)
• Quantum Soft Covering and Decoupling with Relative Entropy Criterion [11.987004396261241]
  We prove covering lemmas by deriving one-shot bounds on the rates in terms of smooth min-entropies and smooth max-divergences. We present a one-shot quantum decoupling theorem with relative entropy criterion.
  arXiv  Detail & Related papers  (2024-02-16T22:31:38Z)
• Asymptotic Quantum State Discrimination for Mixtures of Unitarily Related States [0.0]
  Quantum state discrimination is a prominent problem in quantum communication theory. We first present an approach to QSD in the case of countable mixtures. We then outline an analogous approach to uncountable mixtures, presenting some conjectures that mirror the results presented for the cases of countable mixtures.
  arXiv  Detail & Related papers  (2024-02-07T22:24:12Z)
• Multi-Label Quantification [78.83284164605473]
  Quantification, variously called "labelled prevalence estimation" or "learning to quantify", is the supervised learning task of generating predictors of the relative frequencies of the classes of interest in unsupervised data samples. We propose methods for inferring estimators of class prevalence values that strive to leverage the dependencies among the classes of interest in order to predict their relative frequencies more accurately.
  arXiv  Detail & Related papers  (2022-11-15T11:29:59Z)
• Bounding entanglement dimensionality from the covariance matrix [1.8749305679160366]
  High-dimensional entanglement has been identified as an important resource in quantum information processing. Most widely used methods for experiments are based on fidelity measurements with respect to highly entangled states. Here, instead, we consider covariances of collective observables, as in the well-known Covariance Matrix Criterion.
  arXiv  Detail & Related papers  (2022-08-09T17:11:44Z)
• Quantitative characterization of several entanglement detection criteria [0.0]
  We show that reduction, majorization, and the R'enyi-entropy-based criteria are very ineffective compared to the positive partial transpose. In the case of the R'enyi-entropy-based criterion, we show that the ratio of detectable entanglement increases with the order of the R'enyi entropy.
  arXiv  Detail & Related papers  (2022-07-05T13:48:23Z)
• Clipped Stochastic Methods for Variational Inequalities with Heavy-Tailed Noise [64.85879194013407]
  We prove the first high-probability results with logarithmic dependence on the confidence level for methods for solving monotone and structured non-monotone VIPs. Our results match the best-known ones in the light-tails case and are novel for structured non-monotone problems. In addition, we numerically validate that the gradient noise of many practical formulations is heavy-tailed and show that clipping improves the performance of SEG/SGDA.
  arXiv  Detail & Related papers  (2022-06-02T15:21:55Z)
• Average-case Speedup for Product Formulas [69.68937033275746]
  Product formulas, or Trotterization, are the oldest and still remain an appealing method to simulate quantum systems. We prove that the Trotter error exhibits a qualitatively better scaling for the vast majority of input states. Our results open doors to the study of quantum algorithms in the average case.
  arXiv  Detail & Related papers  (2021-11-09T18:49:48Z)
• Exact Recovery in the General Hypergraph Stochastic Block Model [92.28929858529679]
  This paper investigates fundamental limits of exact recovery in the general d-uniform hypergraph block model (d-HSBM) We show that there exists a sharp threshold such that exact recovery is achievable above the threshold and impossible below it.
  arXiv  Detail & Related papers  (2021-05-11T03:39:08Z)
• Fractional norms and quasinorms do not help to overcome the curse of dimensionality [62.997667081978825]
  Using of the Manhattan distance and even fractional quasinorms lp can help to overcome the curse of dimensionality in classification problems. A systematic comparison shows that the difference of the performance of kNN based on lp for p=2, 1, and 0.5 is statistically insignificant.
  arXiv  Detail & Related papers  (2020-04-29T14:30:12Z)
• Entanglement as upper bounded for the nonlocality of a general two-qubit system [16.676050048472963]
  We systematically investigate the relationship between entanglement and nonlocality of a general two-qubit system. We find that the nonlocality of two different two-qubit states can be optimally stimulated by the same nonlocality test setting.
  arXiv  Detail & Related papers  (2020-04-17T16:42:27Z)

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.