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In this work, we consider an upper bound for the quantum mutual information in thermal states of a bipartite quantum system. This bound is related with the interaction energy and logarithm of the partition function of the system. We…

Quantum Physics · Physics 2015-03-20 Aleksey Fedorov , Evgeny Kiktenko

Leveraging quantum information geometry, we derive generalized quantum speed limits on the rate of change of the expectation values of observables. These bounds subsume and, for Hilbert space dimension $\geq 3$, tighten existing bounds --…

We consider estimating the magnitude of a monochromatic AC signal that couples to a two-level sensor. For any detection protocol, the precision achieved depends on the signal's frequency and can be quantified by the quantum Fisher…

Estimating mutual information (MI) is a fundamental yet challenging task in data science and machine learning. This work proposes a new estimator for mutual information. Our main discovery is that a preliminary estimate of the data…

Machine Learning · Computer Science 2024-08-20 Yanzhi Chen , Zijing Ou , Adrian Weller , Yingzhen Li

We present a new family of information-theoretic generalization bounds within the framework of conditional mutual information (CMI). Most of our results are established based on the leave-$m$-out (L$m$O) cross-validation error, with $m$…

Information Theory · Computer Science 2026-05-21 Yang Lu , Matthias Frey , Margreta Kuijper , Jingge Zhu

A possible thermalization of Fisher information is suggested for certain situations.

Mathematical Physics · Physics 2008-07-09 Robert Carroll

We propose a new information-theoretic bound on generalization error based on a combination of the error decomposition technique of Bu et al. and the conditional mutual information (CMI) construction of Steinke and Zakynthinou. In a…

Information Theory · Computer Science 2021-01-01 Ruida Zhou , Chao Tian , Tie Liu

Understanding the generalization abilities of modern machine learning algorithms has been a major research topic over the past decades. In recent years, the learning dynamics of Stochastic Gradient Descent (SGD) have been related to…

Machine Learning · Statistics 2023-12-04 Benjamin Dupuis , Paul Viallard

The data for many classification problems, such as pattern and speech recognition, follow mixture distributions. To quantify the optimum performance for classification tasks, the Shannon mutual information is a natural information-theoretic…

Signal Processing · Electrical Eng. & Systems 2022-06-22 Yijun Ding , Amit Ashok

The concept of Fisher information can be useful even in cases where the probability distributions of interest are not absolutely continuous with respect to the natural reference measure on the underlying space. Practical examples where this…

Statistics Theory · Mathematics 2018-03-28 Jeremie Houssineau , Ajay Jasra , Sumeetpal S. Singh

The probability distribution function (PDF) for prices on financial markets is derived by extremization of Fisher information. It is shown how on that basis the quantum-like description for financial markets arises and different financial…

Statistical Finance · Quantitative Finance 2015-04-16 Vadim Nastasiuk

We formulate a quantum arrival time measurement process for a Bosonic many-particle system, with the aim of extracting statistical information on single-particle properties. The arrival time is based on a dynamical multi-particle absorption…

Quantum Physics · Physics 2025-05-28 Jukka Kiukas , Andreas Ruschhaupt

Heisenberg-like and Fisher-information-based uncertainty relations which extend and generalize previous similar expressions are obtained for $N$-fermion $d$-dimensional systems. The contributions of both spatial and spin degrees of freedom…

Information Theory · Computer Science 2016-10-07 I. V. Toranzo , S. López-Rosa , R. O. Esquivel , J. S. Dehesa

We study the classical and quantum Fisher information for the Lieb-Liniger model. The Fisher information has been studied extensively when the parameter is inscribed on a quantum state by a unitary process, e.g., Mach-Zehnder or Ramsey…

Quantum Physics · Physics 2023-01-02 Jae-Gyun Baak , Uwe R. Fischer

We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the…

Quantum Physics · Physics 2024-04-02 Eoin O'Connor , Steve Campbell , Gabriel T. Landi

Generalization error bounds are critical to understanding the performance of machine learning models. In this work, we propose a new information-theoretic based generalization error upper bound applicable to supervised learning scenarios.…

Information Theory · Computer Science 2021-01-11 Gholamali Aminian , Laura Toni , Miguel R. D. Rodrigues

Mutual information has been successfully adopted in filter feature-selection methods to assess both the relevancy of a subset of features in predicting the target variable and the redundancy with respect to other variables. However,…

Machine Learning · Computer Science 2019-07-18 Mario Beraha , Alberto Maria Metelli , Matteo Papini , Andrea Tirinzoni , Marcello Restelli

We consider the problem of learning high-dimensional, nonparametric and structured (e.g. Gaussian) distributions in distributed networks, where each node in the network observes an independent sample from the underlying distribution and can…

Information Theory · Computer Science 2019-06-04 Leighton Pate Barnes , Yanjun Han , Ayfer Ozgur

Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as $T^{4}.$ We present here our interpretation of this new scaling, where the…

Quantum Physics · Physics 2017-09-13 Tuvia Gefen , Fedor Jelezko , Alex Retzker

We give two upper bounds to the mutual information in arbitrary quantum estimation strategies. The first is based on some simple Fourier properties of the estimation apparatus. The second is derived using the first but, interestingly,…

Quantum Physics · Physics 2024-09-17 Xi Lu , Wojciech Górecki , Chiara Macchiavello , Lorenzo Maccone