Quantifying entanglement from the geometric perspective
- URL: http://arxiv.org/abs/2505.01394v2
- Date: Tue, 27 May 2025 20:56:30 GMT
- Title: Quantifying entanglement from the geometric perspective
- Authors: Lisa T. Weinbrenner, Otfried Gühne,
- Abstract summary: We present a review on the geometric measure of entanglement, being a quantifier based on the distance of a state to the nearest separable state.<n>We explain basic properties, existing methods to compute it, its operational interpretations, as well as scaling and complexity issues.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of quantifying the amount of entanglement in a quantum state. We present a review on the geometric measure of entanglement, being a quantifier based on the distance of a state to the nearest separable state. We explain basic properties, existing methods to compute it, its operational interpretations, as well as scaling and complexity issues. We point out intimate relations to fundamental problems in mathematics concerning eigenvalues and norms of tensors. Consequently, the geometric measure of entanglement provides a playground where physical intuition and mathematical rigor benefit from each other.
Related papers
- Quantum information elements in Quantum Gravity states and processes [0.0]
We discuss basic features of quantum gravity states and processes, common to a number of related quantum gravity formalisms.<n>We show how entanglement is a seed of topological and geometric properties, and how a pre-geometric, discrete notion of quantum causality can be implemented.
arXiv Detail & Related papers (2025-02-28T17:03:09Z) - 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) - Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders [9.617349193925188]
Entanglement constitutes one of the key concepts in quantum mechanics and serves as an indispensable tool in the understanding of quantum many-body systems.
We perform extensive numerical investigations of extensive entanglement properties of coupled quantum spin chains.
arXiv Detail & Related papers (2023-11-03T04:06:20Z) - SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction,
and Machine Learning [11.861283136635837]
We show that in the presence of SU(d) symmetry, the local conserved quantities would exhibit residual values even at $t rightarrow infty$.
We also show that SU(d)-symmetric unitaries can be used to constructally optimal codes.
We derive an overpartameterization threshold via the quantum neural kernel.
arXiv Detail & Related papers (2023-09-28T16:12:31Z) - Quantification of Entanglement and Coherence with Purity Detection [16.01598003770752]
Entanglement and coherence are fundamental properties of quantum systems, promising to power near future quantum technologies.
Here, we demonstrate quantitative bounds to operationally useful entanglement and coherence.
Our research offers an efficient means of verifying large-scale quantum information processing.
arXiv Detail & Related papers (2023-08-14T11:03:40Z) - Unraveling the Mystery of Quantum Measurement with A New Space-Time Approach to Relativistic Quantum Mechanics [9.116661570248171]
Quantum measurement is a fundamental concept in the field of quantum mechanics.
Despite its significance, four fundamental issues continue to pose significant challenges to the broader application of quantum measurement.
We employ a new space-time approach to relativistic quantum mechanics to address these issues systematically.
arXiv Detail & Related papers (2023-06-01T13:25:08Z) - A Mechanical Implementation and Diagrammatic Calculation of Entangled
Basis States [0.0]
We give for the first time a diagrammatic calculational tool of quantum entanglement.
When two or more particles are correlated in a certain way, no matter how far apart they are in space, their states remain correlated.
Our results seem to advocate the idea that quantum entanglement generates the extra dimensions of the gravitational theory.
arXiv Detail & Related papers (2021-12-20T00:31:48Z) - Quantum Information Dimension and Geometric Entropy [0.0]
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.
arXiv Detail & Related papers (2021-11-11T18:40:49Z) - A Theoretical Framework for Learning from Quantum Data [15.828697880068704]
We propose a theoretical foundation for learning classical patterns from quantum data.
We present a quantum counterpart of the well-known PAC framework.
We establish upper bounds on the quantum sample complexity quantum concept classes.
arXiv Detail & Related papers (2021-07-13T21:39:47Z) - Relating the topology of Dirac Hamiltonians to quantum geometry: When
the quantum metric dictates Chern numbers and winding numbers [0.0]
We establish relations between the quantum metric and the topological invariants of generic Dirac Hamiltonians.
We show that topological indices are bounded by the quantum volume determined by the quantum metric.
This work suggests unexplored topological responses and metrological applications in a broad class of quantum-engineered systems.
arXiv Detail & Related papers (2021-06-01T21:10:48Z) - Operational Resource Theory of Imaginarity [48.7576911714538]
We show that quantum states are easier to create and manipulate if they only have real elements.
As an application, we show that imaginarity plays a crucial role for state discrimination.
arXiv Detail & Related papers (2020-07-29T14:03:38Z) - Cost of quantum entanglement simplified [13.683637401785505]
We introduce an entanglement measure that has a precise information-theoretic meaning as the exact cost required to prepare an entangled state.
Our results bring key insights into the fundamental entanglement structure of arbitrary quantum states, and they can be used directly to assess and quantify the entanglement produced in quantum-physical experiments.
arXiv Detail & Related papers (2020-07-28T14:36:23Z) - 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.