Quantum Information Dimension and Geometric Entropy
- URL: http://arxiv.org/abs/2111.06374v2
- Date: Tue, 12 Mar 2024 13:53:54 GMT
- Title: Quantum Information Dimension and Geometric Entropy
- Authors: Fabio Anza and James P. Crutchfield
- Abstract summary: We introduce two analysis tools, inspired by Renyi's information theory, to characterize and quantify fundamental properties of geometric quantum states.
We recount their classical definitions, information-theoretic meanings, and physical interpretations, and adapt them to quantum systems via the geometric approach.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Geometric quantum mechanics, through its differential-geometric underpinning,
provides additional tools of analysis and interpretation that bring quantum
mechanics closer to classical mechanics: state spaces in both are equipped with
symplectic geometry. This opens the door to revisiting foundational questions
and issues, such as the nature of quantum entropy, from a geometric
perspective. Central to this is the concept of geometric quantum state -- the
probability measure on a system's space of pure states. This space's continuity
leads us to introduce two analysis tools, inspired by Renyi's information
theory, to characterize and quantify fundamental properties of geometric
quantum states: the quantum information dimension that is the rate of geometric
quantum state compression and the dimensional geometric entropy that monitors
information stored in quantum states. We recount their classical definitions,
information-theoretic meanings, and physical interpretations, and adapt them to
quantum systems via the geometric approach. We then explicitly compute them in
various examples and classes of quantum system. We conclude commenting on
future directions for information in geometric quantum mechanics.
Related papers
- Geometric methods in quantum information and entanglement variational principle [0.0]
We first make a survey of the most important settings in which geometrical methods have proven useful to quantum information theory.
We then lay down a general framework for an action principle for quantum resources like entanglement, coherence, and anti-flatness.
arXiv Detail & Related papers (2024-03-19T19:06:55Z) - A Geometry of entanglement and entropy [0.7373617024876725]
We provide a comprehensive overview of entanglement, highlighting its crucial role in quantum mechanics.
We discuss various methods for quantifying and characterizing entanglement through a geometric perspective.
An example of entanglement as an indispensable resource for the task of state teleportation is presented at the end.
arXiv Detail & Related papers (2024-02-24T18:26:32Z) - Quantifying High-Order Interdependencies in Entangled Quantum States [43.70611649100949]
We introduce the Q-information: an information-theoretic measure capable of distinguishing quantum states dominated by synergy or redundancy.
We show that quantum systems need at least four variables to exhibit high-order properties.
Overall, the Q-information sheds light on novel aspects of the internal organisation of quantum systems and their time evolution.
arXiv Detail & Related papers (2023-10-05T17:00:13Z) - Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
We explore the applicability of quantum-data learning to practical problems in high-energy physics.
We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states.
The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
arXiv Detail & Related papers (2023-06-29T18:00:01Z) - Generalized quantum geometric tensor for excited states using the path
integral approach [0.0]
The quantum geometric tensor encodes the parameter space geometry of a physical system.
We first provide a formulation of the quantum geometrical tensor in the path integral formalism that can handle both the ground and excited states.
We then generalize the quantum geometric tensor to incorporate variations of the system parameters and the phase-space coordinates.
arXiv Detail & Related papers (2023-05-19T08:50:46Z) - Geometric and holonomic quantum computation [1.4644151041375417]
Quantum gates based on geometric phases and quantum holonomies possess built-in resilience to certain kinds of errors.
This review provides an introduction to the topic as well as gives an overview of the theoretical and experimental progress for constructing geometric and holonomic quantum gates.
arXiv Detail & Related papers (2021-10-07T16:31:54Z) - A thorough introduction to non-relativistic matrix mechanics in
multi-qudit systems with a study on quantum entanglement and quantum
quantifiers [0.0]
This article provides a deep and abiding understanding of non-relativistic matrix mechanics.
We derive and analyze the respective 1-qubit, 1-qutrit, 2-qubit, and 2-qudit coherent and incoherent density operators.
We also address the fundamental concepts of quantum nondemolition measurements, quantum decoherence and, particularly, quantum entanglement.
arXiv Detail & Related papers (2021-09-14T05:06:47Z) - Probing Topological Spin Liquids on a Programmable Quantum Simulator [40.96261204117952]
We use a 219-atom programmable quantum simulator to probe quantum spin liquid states.
In our approach, arrays of atoms are placed on the links of a kagome lattice and evolution under Rydberg blockade creates frustrated quantum states.
The onset of a quantum spin liquid phase of the paradigmatic toric code type is detected by evaluating topological string operators.
arXiv Detail & Related papers (2021-04-09T00:18:12Z) - Quantum Entropic Causal Inference [30.939150842529052]
We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles.
We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links.
arXiv Detail & Related papers (2021-02-23T15:51:34Z) - Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer.
We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
arXiv Detail & Related papers (2020-11-12T18:49:11Z) - Preferred basis, decoherence and a quantum state of the Universe [77.34726150561087]
We review a number of issues in foundations of quantum theory and quantum cosmology.
These issues can be considered as a part of the scientific legacy of H.D. Zeh.
arXiv Detail & Related papers (2020-06-28T18:07:59Z)
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.