Entropic time-energy uncertainty relations: An algebraic approach

• URL: http://arxiv.org/abs/2001.00799v1
• Date: Fri, 3 Jan 2020 11:59:34 GMT
• Title: Entropic time-energy uncertainty relations: An algebraic approach
• Authors: Christian Bertoni, Yuxiang Yang, Joseph M. Renes
• Abstract summary: We address uncertainty relations between time and energy or, more precisely, between measurements of an observable $G$ and the displacement $r$ of the $G$-generated evolution $e-ir G$. We derive lower bounds on the entropic uncertainty in two frequently considered scenarios, which can be illustrated as two different guessing games in which the role of the guessers are fixed or not.
• Score: 9.881112657341788
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We address entropic uncertainty relations between time and energy or, more precisely, between measurements of an observable $G$ and the displacement $r$ of the $G$-generated evolution $e^{-ir G}$. We derive lower bounds on the entropic uncertainty in two frequently considered scenarios, which can be illustrated as two different guessing games in which the role of the guessers are fixed or not. In particular, our bound for the first game improves the previous result by Coles et al.. Our derivation uses as a subroutine a recently proposed novel algebraic method, which can in general be used to derive a wider class of entropic uncertainty principles.

Related papers

• Variance-Aware Regret Bounds for Stochastic Contextual Dueling Bandits [53.281230333364505]
  This paper studies the problem of contextual dueling bandits, where the binary comparison of dueling arms is generated from a generalized linear model (GLM) We propose a new SupLinUCB-type algorithm that enjoys computational efficiency and a variance-aware regret bound $tilde Obig(dsqrtsum_t=1Tsigma_t2 + dbig)$. Our regret bound naturally aligns with the intuitive expectation in scenarios where the comparison is deterministic, the algorithm only suffers from an $tilde O(d)$ regret.
  arXiv  Detail & Related papers  (2023-10-02T08:15:52Z)
• Coherent states for generalized uncertainty relations as Tsallis probability amplitudes: new route to non-extensive thermostatistics [0.0]
  We study coherent states associated to a generalized uncertainty principle (GUP) We argue that this combination of coherent states with Tsallis entropy offers a natural conceptual framework allowing to study GUP in terms of non-extensive thermodynamics.
  arXiv  Detail & Related papers  (2023-08-23T18:16:15Z)
• The Shrinkage-Delinkage Trade-off: An Analysis of Factorized Gaussian Approximations for Variational Inference [3.167685495996986]
  We consider two popular ways to measure the uncertainty deficit of variational inference (VI) We prove that $q$ always underestimates both the componentwise variance and the entropy of $p$. We study various manifestations of this trade-off, notably one where, as the dimension of the problem grows, the per-component entropy gap becomes vanishingly small.
  arXiv  Detail & Related papers  (2023-02-17T22:21:47Z)
• A Primal-Dual Approach to Solving Variational Inequalities with General Constraints [54.62996442406718]
  Yang et al. (2023) recently showed how to use first-order gradient methods to solve general variational inequalities. We prove the convergence of this method and show that the gap function of the last iterate of the method decreases at a rate of $O(frac1sqrtK)$ when the operator is $L$-Lipschitz and monotone.
  arXiv  Detail & Related papers  (2022-10-27T17:59:09Z)
• Non-Abelian symmetry can increase entanglement entropy [62.997667081978825]
  We quantify the effects of charges' noncommutation on Page curves. We show analytically and numerically that the noncommuting-charge case has more entanglement.
  arXiv  Detail & Related papers  (2022-09-28T18:00:00Z)
• Benign Underfitting of Stochastic Gradient Descent [72.38051710389732]
  We study to what extent may gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit training data. We analyze the closely related with-replacement SGD, for which an analogous phenomenon does not occur and prove that its population risk does in fact converge at the optimal rate.
  arXiv  Detail & Related papers  (2022-02-27T13:25:01Z)
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts [0.0]
  In a $d$ dimensional system and two mutually unbiased measurements, the sum of two information entropies is lower bounded by $ln d$. It has recently been shown that projective measurements subject to operational mutual unbiasedness can also be constructed in a continuous domain. Here we consider the whole family of R'enyi entropies applied to these discretized observables and prove that such a scheme does also admit the uncertainty relation mentioned above.
  arXiv  Detail & Related papers  (2021-07-26T18:48:26Z)
• R\'enyi divergence inequalities via interpolation, with applications to generalised entropic uncertainty relations [91.3755431537592]
  We investigate quantum R'enyi entropic quantities, specifically those derived from'sandwiched' divergence. We present R'enyi mutual information decomposition rules, a new approach to the R'enyi conditional entropy tripartite chain rules and a more general bipartite comparison.
  arXiv  Detail & Related papers  (2021-06-19T04:06:23Z)
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme [8.37609145576126]
  The relative entropy of entanglement $E_Rite is defined as the distance of a multi-part quantum entanglement from the set of separable states as measured by the quantum relative entropy. We show that this state is always achieved, i.e. any state admits a closest separable state, even in dimensions; also, $E_Rite is everywhere lower semi-negative $lambda_$quasi-probability distribution.
  arXiv  Detail & Related papers  (2021-05-17T18:03:02Z)
• Super fast rates in structured prediction [88.99819200562784]
  We show how we can leverage the fact that discrete problems are essentially predicting a discrete output when continuous problems are predicting a continuous value. We first illustrate it for predictors based on nearest neighbors, generalizing rates known for binary classification to any discrete problem within the framework of structured prediction. We then consider kernel ridge regression where we improve known rates in $n-1/4$ to arbitrarily fast rates, depending on a parameter characterizing the hardness of the problem.
  arXiv  Detail & Related papers  (2021-02-01T10:50:04Z)
• Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy [0.0]
  We present a novel generalization of the Heisenberg uncertainty principle. The result is an exact generalized uncertainty principle valid at all energy scales. We study the implications of this new model on some quantum mechanical applications and on the black hole thermodynamics.
  arXiv  Detail & Related papers  (2020-10-12T17:46:39Z)

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.