Entanglement and entropy in multipartite systems: a useful approach
- URL: http://arxiv.org/abs/2307.05205v2
- Date: Thu, 15 Feb 2024 14:08:15 GMT
- Title: Entanglement and entropy in multipartite systems: a useful approach
- Authors: A. Bernal, J. A. Casas and J.M. Moreno
- Abstract summary: We show how the notion of concurrence vector, re-expressed in a particularly useful form, provides new insights and computational tools.
The approach is also useful to derive sufficient conditions for genuine entanglement in generic multipartite systems.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Quantum entanglement and quantum entropy are crucial concepts in the study of
multipartite quantum systems. In this work we show how the notion of
concurrence vector, re-expressed in a particularly useful form, provides new
insights and computational tools for the analysis of both. In particular, using
this approach for a general multipartite pure state, one can easily prove known
relations in an easy way and to build up new relations between the concurrences
associated with the different bipartitions. The approach is also useful to
derive sufficient conditions for genuine entanglement in generic multipartite
systems that are computable in polynomial time. From an entropy-of-entanglement
perspective, the approach is powerful to prove properties of the Tsallis-$2$
entropy, such as the subadditivity, and to derive new ones, e.g. a modified
version of the strong subadditivity which is always fulfilled; thanks to the
purification theorem these results hold for any multipartite state, whether
pure or mixed.
Related papers
- Quantum Conditional Entropies [7.988085110283119]
We introduce a comprehensive family of conditional entropies that reveals a unified structure underlying all previously studied forms of quantum conditional R'enyi entropies.
This new family satisfies a range of desiderata, including data processing inequalities, additivity under tensor products, duality relations, chain rules, concavity or convexity, and various parameter monotonicity relations.
We expect this family of entropies, along with our generalized chain rules, to find applications in quantum cryptography and information theory.
arXiv Detail & Related papers (2024-10-29T12:03:10Z) - Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold.
The established relation can be applied to various quantum optimization problems.
arXiv Detail & Related papers (2024-08-19T09:15:54Z) - One-Shot Min-Entropy Calculation And Its Application To Quantum Cryptography [21.823963925581868]
We develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state.
It gives an alternative tight finite-data analysis for the well-known BB84 quantum key distribution protocol.
It provides a security proof for a novel source-independent continuous-variable quantum random number generation protocol.
arXiv Detail & Related papers (2024-06-21T15:11:26Z) - Gaussian Entanglement Measure: Applications to Multipartite Entanglement
of Graph States and Bosonic Field Theory [50.24983453990065]
An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers.
We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states.
By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
arXiv Detail & Related papers (2024-01-31T15:50:50Z) - The polygon relation and subadditivity of entropic measures for discrete and continuous multipartite entanglement [0.6759148939470331]
We study the relationship between the polygon relation and the subadditivity of entropy.
Our work provides a better understanding of the rich structure of multipartite states.
arXiv Detail & Related papers (2024-01-04T05:09:37Z) - Probing multipartite entanglement through persistent homology [6.107978190324034]
We propose a study of multipartite entanglement through persistent homology.
persistent homology is a tool used in topological data analysis.
We show that persistence barcodes provide more fine-grained information than its topological summary.
arXiv Detail & Related papers (2023-07-14T17:24:33Z) - Multipartite entanglement theory with entanglement-nonincreasing
operations [91.3755431537592]
We extend the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication.
We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states.
arXiv Detail & Related papers (2023-05-30T12:53:56Z) - Entanglement monogamy via multivariate trace inequalities [12.814476856584346]
We derive variational formulas for relative entropies based on restricted measurements of multipartite quantum systems.
We give direct, matrix-analysis-based proofs for the faithfulness of squashed entanglement.
arXiv Detail & Related papers (2023-04-28T14:36:54Z) - Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees.
Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation.
We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
arXiv Detail & Related papers (2022-03-30T02:02:16Z) - Genuine Network Multipartite Entanglement [62.997667081978825]
We argue that a source capable of distributing bipartite entanglement can, by itself, generate genuine $k$-partite entangled states for any $k$.
We provide analytic and numerical witnesses of genuine network entanglement, and we reinterpret many past quantum experiments as demonstrations of this feature.
arXiv Detail & Related papers (2020-02-07T13:26:00Z)
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.