Majorization theory for quasiprobabilities

• URL: http://arxiv.org/abs/2507.22986v1
• Date: Wed, 30 Jul 2025 18:00:03 GMT
• Title: Majorization theory for quasiprobabilities
• Authors: Twesh Upadhyaya, Zacharie Van Herstraeten, Jack Davis, Oliver Hahn, Nikolaos Koukoulekidis, Ulysse Chabaud,
• Abstract summary: Majorization theory is a powerful tool to compare the disorder in distributions.<n>We introduce a notion of majorization for continuous quasiprobability distributions over infinite measure spaces.<n>We give several applications of our results in the context of quantum resource theories.
• Score: 0.49478969093606673
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Majorization theory is a powerful mathematical tool to compare the disorder in distributions, with wide-ranging applications in many fields including mathematics, physics, information theory, and economics. While majorization theory typically focuses on probability distributions, quasiprobability distributions provide a pivotal framework for advancing our understanding of quantum mechanics, quantum information, and signal processing. Here, we introduce a notion of majorization for continuous quasiprobability distributions over infinite measure spaces. Generalizing a seminal theorem by Hardy, Littlewood, and P\'olya, we prove the equivalence of four definitions for both majorization and relative majorization in this setting. We give several applications of our results in the context of quantum resource theories, obtaining new families of resource monotones and no-goes for quantum state conversions. A prominent example we explore is the Wigner function in quantum optics. More generally, our results provide an extensive majorization framework for assessing the disorder of integrable functions over infinite measure spaces.

Related papers

• Connecting classical finite exchangeability to quantum theory [45.76759085727843]
  Exchangeability is a fundamental concept in probability theory and statistics.<n>It allows to model situations where the order of observations does not matter.<n>It is well known that both theorems do not hold for finitely exchangeable sequences.
  arXiv  Detail & Related papers  (2023-06-06T17:15:19Z)
• A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
  We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
  arXiv  Detail & Related papers  (2023-05-19T13:15:48Z)
• Quasiprobability distribution of work in the quantum Ising model [0.0]
  We try to clarify the genuinely quantum features of the process by studying the work quasiprobability for an Ising model in a transverse field. We examine the critical features related to a quantum phase transition and the role of the initial quantum coherence as useful resource.
  arXiv  Detail & Related papers  (2023-02-22T10:07:49Z)
• Advantages of quantum mechanics in the estimation theory [0.0]
  In quantum theory, the situation with operators is different due to its non-commutativity nature. We formulate, with complete generality, the quantum estimation theory for Gaussian states in terms of their first and second moments.
  arXiv  Detail & Related papers  (2022-11-13T18:03:27Z)
• Theory of Quantum Generative Learning Models with Maximum Mean Discrepancy [67.02951777522547]
  We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs) We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution. Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
  arXiv  Detail & Related papers  (2022-05-10T08:05:59Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• An introductory review on resource theories of generalized nonclassical light [0.0]
  Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. Generalized quantum optical framework strives to bring in several prosperous contemporary ideas.
  arXiv  Detail & Related papers  (2021-03-23T05:10:44Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• Framework for resource quantification in infinite-dimensional general probabilistic theories [6.308539010172309]
  Resource theories provide a general framework for the characterization of properties of physical systems in quantum mechanics and beyond. We introduce methods for the quantification of resources in general probabilistic theories (GPTs) We show that a given resource state enables in channel discrimination tasks over all resourceless states. We demonstrate applications of the robustness to several resources of physical relevance: optical nonclassicality, entanglement, genuine non-Gaussianity, and coherence.
  arXiv  Detail & Related papers  (2020-09-23T18:00:20Z)
• Towards correlation self-testing of quantum theory in the adaptive Clauser-Horne-Shimony-Holt game [1.0878040851638]
  Correlation self-testing of a theory addresses the question of whether we can identify the set of correlations realisable in a theory from its performance in a particular information processing task. This is the first step towards a general solution that could rule out all theories in which the set of realisable correlations does not coincide with the quantum set.
  arXiv  Detail & Related papers  (2020-09-10T18:04:13Z)
• Perfect Discrimination in Approximate Quantum Theory of General Probabilistic Theories [51.7367238070864]
  We define larger measurement classes that are smoothly connected with the class of POVMs via a parameter. We give a sufficient condition of perfect discrimination, which shows a significant improvement beyond the class of POVMs.
  arXiv  Detail & Related papers  (2020-04-10T08:45:20Z)

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.