Related papers: Mutual Information Bounded by Fisher Information

Mutual Information Bounded by Fisher Information

URL: http://arxiv.org/abs/2403.10248v2
Date: Wed, 17 Jul 2024 12:05:30 GMT
Title: Mutual Information Bounded by Fisher Information
Authors: Wojciech Górecki, Xi Lu, Chiara Macchiavello, Lorenzo Maccone,
Abstract summary: We derive a general upper bound to mutual information in terms of the Fisher information. We then generalize them to the quantum case, where they bound the Holevo information in terms of the quantum Fisher information.
Score: 1.9865335779110387
License: http://creativecommons.org/licenses/by/4.0/
Abstract: We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the literature (e.g.~the van Trees inequality) that are useful also for cases where the latter ones give trivial bounds. We then generalize them to the quantum case, where they bound the Holevo information in terms of the quantum Fisher information. We illustrate the usefulness of our bounds with a case study in quantum phase estimation. Here, they allow us to adapt to mutual information (useful for global strategies where the prior plays an important role) the known and highly nontrivial bounds for the Fisher information in the presence of noise. The results are also useful in the context of quantum communication, both for continuous and discrete alphabets.

Related papers

Improved bounds on quantum uncommon information [2.812395851874055]
In quantum information theory, quantum uncommon information is the minimal amount of entanglement required for the quantum communication task of quantum state exchange. We develop a subspace exchange strategy that leverages a common subspace of two parties to identify the unnecessary qubits for exchange. Our bounds provide more precise estimations for the quantum uncommon information.
arXiv Detail & Related papers (2024-06-21T06:02:41Z)
Number of bits returned by a quantum estimation [1.9865335779110387]
We give two upper bounds to the mutual information in arbitrary quantum estimation strategies. We illustrate the usefulness of these bounds by characterizing the quantum phase estimation algorithm in the presence of noise.
arXiv Detail & Related papers (2024-03-26T03:08:00Z)
Efficient algorithms for quantum information bottleneck [64.67104066707309]
We propose a new and general algorithm for the quantum generalisation of information bottleneck. Our algorithm excels in the speed and the definiteness of convergence compared with prior results. Notably, we discover that a quantum system can achieve strictly better performance than a classical system of the same size regarding quantum information bottleneck.
arXiv Detail & Related papers (2022-08-22T14:20:05Z)
Generalized Wigner-Yanase Skew Information and the Affiliated Inequality [0.0]
A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. We find in this work an exact skew information inequality for qubit system, which may regard as the information counterpart of the uncertainty relation.
arXiv Detail & Related papers (2022-05-14T07:01:19Z)
Shannon theory beyond quantum: information content of a source [68.8204255655161]
We extend the definition of information content to operational probabilistic theories. We prove relevant properties as the subadditivity, and the relation between purity and information content of a state.
arXiv Detail & Related papers (2021-12-23T16:36:06Z)
A Bayesian Framework for Information-Theoretic Probing [51.98576673620385]
We argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations encode exactly the same information about a target task as the original sentences. This paper proposes a new framework to measure what we term Bayesian mutual information.
arXiv Detail & Related papers (2021-09-08T18:08:36Z)
Fisher information universally identifies quantum resources [0.0]
We show that the classical as well as the quantum definitions of the Fisher information faithfully identify resourceful quantum states in general quantum resource theories. This shows that all quantum resources confer an advantage in metrology, and establishes the Fisher information as a universal tool to probe the resourcefulness of quantum states.
arXiv Detail & Related papers (2021-04-05T04:12:31Z)
Tracing Information Flow from Open Quantum Systems [52.77024349608834]
We use photons in a waveguide array to implement a quantum simulation of the coupling of a qubit with a low-dimensional discrete environment. Using the trace distance between quantum states as a measure of information, we analyze different types of information transfer.
arXiv Detail & Related papers (2021-03-22T16:38:31Z)
Quantum information spreading in a disordered quantum walk [50.591267188664666]
We design a quantum probing protocol using Quantum Walks to investigate the Quantum Information spreading pattern. We focus on the coherent static and dynamic disorder to investigate anomalous and classical transport. Our results show that a Quantum Walk can be considered as a readout device of information about defects and perturbations occurring in complex networks.
arXiv Detail & Related papers (2020-10-20T20:03:19Z)
Quantum noise protects quantum classifiers against adversaries [120.08771960032033]
Noise in quantum information processing is often viewed as a disruptive and difficult-to-avoid feature, especially in near-term quantum technologies. We show that by taking advantage of depolarisation noise in quantum circuits for classification, a robustness bound against adversaries can be derived. This is the first quantum protocol that can be used against the most general adversaries.
arXiv Detail & Related papers (2020-03-20T17:56:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.