Choi representation of completely positive maps in brief

• URL: http://arxiv.org/abs/2402.12944v2
• Date: Sun, 26 Jan 2025 07:39:30 GMT
• Title: Choi representation of completely positive maps in brief
• Authors: G. Homa, A. Ortega, M. Koniorczyk,
• Abstract summary: The Choi representation of completely positive (CP) maps is often used in the context of quantum information and computation. It is a correspondence between CP maps and quantum states also termed as the Choi-Jamiol kowski isomorphism.
• Score: 0.0
• License:
• Abstract: The Choi representation of completely positive (CP) maps, i.e. quantum channels is often used in the context of quantum information and computation as it is easy to work with. It is a correspondence between CP maps and quantum states also termed as the Choi-Jamio\l kowski isomorphism. It is especially useful if a parametrization of the set of CP maps is needed in order to consider a general map or optimize over the set of these. Here we provide a brief introduction to this topic, focusing on certain useful calculational techniques which are presented in full detail.

Related papers

• A class of Schwarz qubit maps with diagonal unitary and orthogonal symmetries [0.0]
  A class of unital qubit maps displaying diagonal unitary and symmetries is analyzed. We provide a complete characterization of this class of maps showing intricate relation between positivity, operator Schwarz inequality, and complete positivity. Our analysis leads to generalization of seminal Fujiwara-Algoet conditions for Pauli quantum channels.
  arXiv  Detail & Related papers  (2024-04-16T20:37:16Z)
• On the Extremality of the Tensor Product of Quantum Channels [0.0]
  We investigate the preservation of extremality under the tensor product. We prove that extremality is preserved for CPT or UCP maps, but for UCPT it is not always preserved.
  arXiv  Detail & Related papers  (2023-05-09T23:00:48Z)
• Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization [46.30376601157526]
  We introduce pointwise map smoothness via the Dirichlet energy into the functional map pipeline. We propose an algorithm for optimizing it efficiently, which leads to high-quality results in challenging settings.
  arXiv  Detail & Related papers  (2022-10-05T14:07:17Z)
• Learning Implicit Feature Alignment Function for Semantic Segmentation [51.36809814890326]
  Implicit Feature Alignment function (IFA) is inspired by the rapidly expanding topic of implicit neural representations. We show that IFA implicitly aligns the feature maps at different levels and is capable of producing segmentation maps in arbitrary resolutions. Our method can be combined with improvement on various architectures, and it achieves state-of-the-art accuracy trade-off on common benchmarks.
  arXiv  Detail & Related papers  (2022-06-17T09:40:14Z)
• Order preserving maps on quantum measurements [1.2891210250935143]
  We study the equivalence classes of quantum measurements endowed with the post-processing partial order. We map this set into a simpler partially ordered set using an order preserving map and investigating the resulting image.
  arXiv  Detail & Related papers  (2022-02-01T19:50:47Z)
• Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization [105.14877281665011]
  We present SyNoRiM, a novel way to register multiple non-rigid shapes by synchronizing the maps relating learned functions defined on the point clouds. We demonstrate via extensive experiments that our method achieves a state-of-the-art performance in registration accuracy.
  arXiv  Detail & Related papers  (2021-11-25T02:37:59Z)
• Optimal radial basis for density-based atomic representations [58.720142291102135]
  We discuss how to build an adaptive, optimal numerical basis that is chosen to represent most efficiently the structural diversity of the dataset at hand. For each training dataset, this optimal basis is unique, and can be computed at no additional cost with respect to the primitive basis. We demonstrate that this construction yields representations that are accurate and computationally efficient.
  arXiv  Detail & Related papers  (2021-05-18T17:57:08Z)
• Guaranteeing Completely Positive Quantum Evolution [2.578242050187029]
  We transform an initial NCP map to a CP map through composition with the asymmetric depolarizing map. We prove that the composition can always be made CP without completely depolarizing in any direction. We show that asymmetric depolarization has many advantages over SPA in preserving the structure of the original NCP map.
  arXiv  Detail & Related papers  (2021-04-30T20:53:19Z)
• Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
  The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy. In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
  arXiv  Detail & Related papers  (2020-07-31T19:23:26Z)
• 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)
• Practical construction of positive maps which are not completely positive [0.0]
  This article introduces PnCP, a toolbox for constructing positive maps which are not completely positive. We show how this package can be applied to the problem of classifying entanglement in quantum states.
  arXiv  Detail & Related papers  (2020-01-05T07:39:44Z)

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.