Simple Sufficient Criteria for Optimality of Entanglement Witnesses

• URL: http://arxiv.org/abs/2505.15615v2
• Date: Fri, 27 Jun 2025 12:33:53 GMT
• Title: Simple Sufficient Criteria for Optimality of Entanglement Witnesses
• Authors: Frederik vom Ende, Simon Cichy,
• Abstract summary: We introduce a novel characterization of the spanning property via entanglement-breaking channels.<n>It is slightly weaker than the spanning property, but it is a lot easier to test for -- by hand as well as numerically -- and it applies to almost all witnesses.<n>A second criterion is derived from this, where one can simply compute the expectation value of the given witness on a maximally entangled state.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: If one wants to establish optimality of a given bipartite entanglement witness, the current standard approach is to check whether it has the spanning property. Although this is not necessary for optimality, it is most often satisfied in practice, and for small enough dimensions or sufficiently structured witnesses this criterion can be checked by hand. In this work we introduce a novel characterization of the spanning property via entanglement-breaking channels, which in turn leads to a new sufficient criterion for optimality. This criterion amounts to just checking the kernel of some bipartite state. It is slightly weaker than the spanning property, but it is a lot easier to test for -- by hand as well as numerically -- and it applies to almost all witnesses which are known to have the spanning property. A second criterion is derived from this, where one can simply compute the expectation value of the given witness on a maximally entangled state. Finally, this approach implies new spectral constraints on witnesses as well as on positive maps.

Related papers

• Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states [0.0]
  We advance the applicability of the realignment criterion by deriving a condition that is both necessary and sufficient for detecting entanglement in two-qubit.<n>$X$-states have proven highly useful in entanglement studies due to their sparse structure and the ease with which entanglement-related quantities can be computed.
  arXiv  Detail & Related papers  (2025-06-30T11:03:40Z)
• Optimizing confidence in negative-partial-transpose-based entanglement criteria [0.0]
  A key requirement of any separable quantum state is that its density matrix has a positive partial transpose.<n>For continuous bipartite quantum states, violation of this condition may be tested via the hierarchy of negative-partial-transpose (NPT) based entanglement criteria.<n>Here, we develop a framework for selecting the optimal NPT-based criterion.
  arXiv  Detail & Related papers  (2025-02-26T23:26:41Z)
• On the distinguishability of geometrically uniform quantum states [8.264068966517918]
  A geometrically uniform (GU) ensemble is a uniformly weighted quantum state ensemble generated from a fixed state.<n>In this work we analyze the problem of discriminating GU ensembles from various angles.
  arXiv  Detail & Related papers  (2025-01-21T18:53:53Z)
• On the Convexity and Reliability of the Bethe Free Energy Approximation [12.02055630441676]
  We analyze when the Bethe approximation is reliable and how this can be verified. As a practical contribution we propose $textttBETHE-MIN$, a projected quasi-Newton method to efficiently find a minimum of the Bethe free energy.
  arXiv  Detail & Related papers  (2024-05-24T12:57:40Z)
• Precise Error Rates for Computationally Efficient Testing [67.30044609837749]
  We revisit the question of simple-versus-simple hypothesis testing with an eye towards computational complexity.<n>An existing test based on linear spectral statistics achieves the best possible tradeoff curve between type I and type II error rates.
  arXiv  Detail & Related papers  (2023-11-01T04:41:16Z)
• Minimax Instrumental Variable Regression and $L_2$ Convergence Guarantees without Identification or Closedness [71.42652863687117]
  We study nonparametric estimation of instrumental variable (IV) regressions. We propose a new penalized minimax estimator that can converge to a fixed IV solution. We derive a strong $L$ error rate for our estimator under lax conditions.
  arXiv  Detail & Related papers  (2023-02-10T18:08:49Z)
• Sparse random Hamiltonians are quantumly easy [105.6788971265845]
  A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state. Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
  arXiv  Detail & Related papers  (2023-02-07T10:57:36Z)
• Search for an efficient entanglement witness operator for bound entangled states in bipartite quantum systems [0.0]
  Entanglement detection problem is one of the important problem in quantum information theory. There are some powerful entanglement detection criterion such as partial transposition criterion, realignment criterion. In this work, we take an analytical approach to construct a witness operator.
  arXiv  Detail & Related papers  (2022-04-13T06:41:14Z)
• A Low Rank Promoting Prior for Unsupervised Contrastive Learning [108.91406719395417]
  We construct a novel probabilistic graphical model that effectively incorporates the low rank promoting prior into the framework of contrastive learning. Our hypothesis explicitly requires that all the samples belonging to the same instance class lie on the same subspace with small dimension. Empirical evidences show that the proposed algorithm clearly surpasses the state-of-the-art approaches on multiple benchmarks.
  arXiv  Detail & Related papers  (2021-08-05T15:58:25Z)
• An Exponential Lower Bound for Linearly-Realizable MDPs with Constant Suboptimality Gap [66.75488143823337]
  We show that an exponential sample complexity lower bound still holds even if a constant suboptimality gap is assumed. Perhaps surprisingly, this implies an exponential separation between the online RL setting and the generative model setting.
  arXiv  Detail & Related papers  (2021-03-23T17:05:54Z)
• Finite Sample Analysis of Minimax Offline Reinforcement Learning: Completeness, Fast Rates and First-Order Efficiency [83.02999769628593]
  We offer a theoretical characterization of off-policy evaluation (OPE) in reinforcement learning. We show that the minimax approach enables us to achieve a fast rate of convergence for weights and quality functions. We present the first finite-sample result with first-order efficiency in non-tabular environments.
  arXiv  Detail & Related papers  (2021-02-05T03:20:39Z)
• DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networks [45.3591788771536]
  We re-examine a continuous optimization framework dubbed NOTEARS for learning Bayesian networks. We show that the Karush-Kuhn-Tucker optimality conditions for the NOTEARS cannot be satisfied except in a trivial case. Some combinations with local search are both more accurate and more efficient than the original NOTEARS.
  arXiv  Detail & Related papers  (2020-10-18T22:59:37Z)

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.