Construction of a Family of Positive But Not Completely Positive Map For the Detection of Bound Entangled States

• URL: http://arxiv.org/abs/2104.13308v2
• Date: Tue, 30 Nov 2021 15:39:15 GMT
• Title: Construction of a Family of Positive But Not Completely Positive Map For the Detection of Bound Entangled States
• Authors: Richa Rohira, Shreya Sanduja, Satyabrata Adhikari
• Abstract summary: We construct a family of map which is shown to be positive when imposing certain condition on the parameters. After tuning the parameters, we found that the map still remain positive but it is not completely positive.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct a family of map which is shown to be positive when imposing certain condition on the parameters. Then we show that the constructed map can never be completely positive. After tuning the parameters, we found that the map still remain positive but it is not completely positive. We then use the positive but not completely positive map in the detection of bound entangled state and negative partial transpose entangled states.

Related papers

• Your Negative May not Be True Negative: Boosting Image-Text Matching with False Negative Elimination [62.18768931714238]
  We propose a novel False Negative Elimination (FNE) strategy to select negatives via sampling. The results demonstrate the superiority of our proposed false negative elimination strategy.
  arXiv  Detail & Related papers  (2023-08-08T16:31:43Z)
• A minimal completion theorem and almost everywhere equivalence for Completely Positive maps [0.0]
  It is shown that whenever such a completion is feasible there exists a unique minimal completion. This theorem is used to show that under some very general conditions a completely positive map almost everywhere equivalent to a quasi-pure map is actually equal to that map.
  arXiv  Detail & Related papers  (2023-06-28T06:25:40Z)
• The Forward-Forward Algorithm: Some Preliminary Investigations [91.3755431537592]
  The Forward-Forward algorithm replaces the forward and backward passes of backpropagation by two forward passes. If the positive and negative passes could be separated in time, the negative passes could be done offline.
  arXiv  Detail & Related papers  (2022-12-27T02:54:46Z)
• Rethinking Rotation in Self-Supervised Contrastive Learning: Adaptive Positive or Negative Data Augmentation [50.21289052547294]
  We propose a novel augmentation strategy, adaptive Positive or Negative Data Augmentation (PNDA) In PNDA, an original and its rotated image are a positive pair if they are semantically close and a negative pair if they are semantically different. Our experiments showed that PNDA improves the performance of contrastive learning.
  arXiv  Detail & Related papers  (2022-10-23T09:37:47Z)
• Counterexamples to the extendibility of positive unital norm-one maps [5.926203312586108]
  Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete positivity is replaced by positivity is known to be false. Here we provide three counterexamples showing that positive norm-one unital maps defined on an operator subsystem cannot be extended to a positive map on the full matrix algebra.
  arXiv  Detail & Related papers  (2022-04-19T11:40:41Z)
• Learning Sound Localization Better From Semantically Similar Samples [79.47083330766002]
  Existing audio-visual works employ contrastive learning by assigning corresponding audio-visual pairs from the same source as positives while randomly mismatched pairs as negatives. Our key contribution is showing that hard positives can give similar response maps to the corresponding pairs. We demonstrate the effectiveness of our approach on VGG-SS and SoundNet-Flickr test sets.
  arXiv  Detail & Related papers  (2022-02-07T08:53:55Z)
• New examples of entangled states on $\mathbb{C}^3 \otimes \mathbb{C}^3$ [0.0]
  We use the Buckley-vSivic method for simultaneous construction of families of positive maps on $3 times 3$ self-adjoint matrices. We obtain entanglement witnesses that are indecomposable and belong to extreme rays of the cone of positive maps. The constructed states as well as the method of their construction offer some valuable insights for quantum information theory.
  arXiv  Detail & Related papers  (2021-12-23T15:29:06Z)
• Interpolating between positive and completely positive maps: a new hierarchy of entangled states [0.0]
  A new class of positive maps is introduced. It interpolates between positive and completely positive maps. It gives rise to a new characterization of entangled states.
  arXiv  Detail & Related papers  (2021-04-28T15:32:11Z)
• Rethinking Ranking-based Loss Functions: Only Penalizing Negative Instances before Positive Ones is Enough [55.55081785232991]
  We argue that only penalizing negative instances before positive ones is enough, because the loss only comes from them. Instead of following the AP-based loss, we propose a new loss, namely Penalizing Negative instances before Positive ones (PNP) PNP-D may be more suitable for real-world data, which usually contains several local clusters for one class.
  arXiv  Detail & Related papers  (2021-02-09T04:30:15Z)
• Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps [91.3755431537592]
  We show that any positive product of a qubit map with itself is decomposable. We characterize the cone of decomposable ququart Pauli diagonal maps.
  arXiv  Detail & Related papers  (2020-06-25T16:39:32Z)
• Strict Positivity and $D$-Majorization [0.0]
  We first investigate the notion of strict positivity, that is, linear maps which map positive definite states to something positive definite again. We show that strict positivity is decided by the action on any full-rank state, and that the image of non-strictly positive maps lives inside a lower-dimensional subalgebra.
  arXiv  Detail & Related papers  (2020-04-12T13:42:27Z)

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.