Initial entanglement, entangling unitaries, and completely positive maps

• URL: http://arxiv.org/abs/2012.12292v2
• Date: Thu, 15 Apr 2021 15:51:10 GMT
• Title: Initial entanglement, entangling unitaries, and completely positive maps
• Abstract summary: We study the interplay between the initial correlations and the unitary applied. For almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. We obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The problem of conditions on the initial correlations between the system and the environment that lead to completely positive (CP) or not-completely positive (NCP) maps has been studied by various authors. Two lines of study may be discerned: one concerned with families of initial correlations that induce CP dynamics under the application of an arbitrary joint unitary on the system and environment; the other concerned with specific initial states that may be highly entangled. Here we study the latter problem, and highlight the interplay between the initial correlations and the unitary applied. In particular, for almost any initial entangled state, one can furnish infinitely many joint unitaries that generate CP dynamics on the system. Restricting to the case of initial, pure entangled states, we obtain the scaling of the dimension of the set of these unitaries and show that it is of zero measure in the set of all possible interaction unitaries.

Related papers

• Detecting Initial System-Environment Correlations from a Single Observable [0.0]
  We show that for a known interaction, it can be sufficient to monitor a single expectation value of the system.<n>We show that the same single-observable logic extends to an exactly solvable pure-dephasing spin--boson model with an infinite environment.
  arXiv  Detail & Related papers  (2026-02-19T19:37:36Z)
• Learning Conditional Averages [52.361762722359366]
  We introduce the problem of learning conditional averages in the PAC framework.<n>Instead of learning the target concept itself, the goal is to predict, for each instance, the average label over its neighborhood.<n>More generally, it extends PAC learning to a setting that captures learning tasks arising in several domains.
  arXiv  Detail & Related papers  (2026-02-12T13:20:29Z)
• Effect of initial intrasystem entanglement on entropy growth in generalized Jaynes-Cummings models [0.0]
  Initial intrasystem entanglement influences the entropy generated in atomic systems interacting with a photonic environment.<n>We consider ensembles of initial system states, including pure and mixed Haar-random states, ensembles with fixed average energy or fixed mixedness, and varying initial photon numbers in the environment.
  arXiv  Detail & Related papers  (2026-02-04T13:34:27Z)
• Unifying Information-Theoretic and Pair-Counting Clustering Similarity [51.660331450043806]
  Clustering similarity measures are typically organized into two principal families, pair-counting and information-theoretic.<n>Here, we develop an analytical framework that unifies these families through two complementary perspectives.
  arXiv  Detail & Related papers  (2025-11-04T21:13:32Z)
• Initial correlations in open quantum systems are always detectable [0.0]
  We show that initial correlations between the system and the environment are always detectable. We also find the condition for existence of the optimal unitary evolution, for which the entire correlation is locally detectable. On the other hand, we see that one can find cases for which initial correlations between the system and the environment always remain undetectable.
  arXiv  Detail & Related papers  (2023-11-07T10:04:40Z)
• Dynamics of inhomogeneous spin ensembles with all-to-all interactions: breaking permutational invariance [49.1574468325115]
  We investigate the consequences of introducing non-uniform initial conditions in the dynamics of spin ensembles characterized by all-to-all interactions. We find that the dynamics of the spin ensemble now spans a more expansive effective Hilbert space.
  arXiv  Detail & Related papers  (2023-09-19T16:44:14Z)
• Entanglement statistics of randomly interacting spins [62.997667081978825]
  Entanglement depends on the underlying topology of the interaction among the qubits. We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions.
  arXiv  Detail & Related papers  (2023-07-18T23:58:32Z)
• The role of initial system-environment correlations with a spin environment [0.0]
  We show that the effect of the initial correlations is, in general, very significant and non-trivial. We also extend our study to investigate the dynamics of the entanglement between two two-level systems interacting with a common spin environment.
  arXiv  Detail & Related papers  (2023-01-18T06:44:32Z)
• Initial Correlations in Open Quantum Systems: Constructing Linear Dynamical Maps and Master Equations [62.997667081978825]
  We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system. We demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure.
  arXiv  Detail & Related papers  (2022-10-24T13:43:04Z)
• Adapted projection operator technique for the treatment of initial correlations [0.0]
  We introduce a perturbative method that can be applied to any microscopic modeling of the system-environment interaction, including fully general initial correlations. Our method is further illustrated by means of two cases study, for which it reproduces the expected dynamical behavior in the long-time regime more consistently than the standard projection technique.
  arXiv  Detail & Related papers  (2021-07-28T18:01:12Z)
• 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)
• DIRV: Dense Interaction Region Voting for End-to-End Human-Object Interaction Detection [53.40028068801092]
  We propose a novel one-stage HOI detection approach based on a new concept called interaction region for the HOI problem. Unlike previous methods, our approach concentrates on the densely sampled interaction regions across different scales for each human-object pair. In order to compensate for the detection flaws of a single interaction region, we introduce a novel voting strategy.
  arXiv  Detail & Related papers  (2020-10-02T13:57:58Z)
• Bottom-Up Temporal Action Localization with Mutual Regularization [107.39785866001868]
  State-of-the-art solutions for TAL involve evaluating the frame-level probabilities of three action-indicating phases. We introduce two regularization terms to mutually regularize the learning procedure. Experiments are performed on two popular TAL datasets, THUMOS14 and ActivityNet1.3.
  arXiv  Detail & Related papers  (2020-02-18T03:59:13Z)
• Photonic dephasing dynamics and role of initial correlations [0.0]
  Dynamics of open quantum systems depends on different types of initial correlations. We derive generic master equations for the reduced dephasing dynamics of the two-photon polarization state.
  arXiv  Detail & Related papers  (2020-01-29T13:17:15Z)

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.