Approximation of multipartite quantum states: revised version with new
applications
- URL: http://arxiv.org/abs/2401.02388v1
- Date: Thu, 4 Jan 2024 17:59:01 GMT
- Title: Approximation of multipartite quantum states: revised version with new
applications
- Authors: M.E.Shirokov
- Abstract summary: We show that for any multipartite state with finite energy the infimum in the definition of the relative entropy of $pi$-entanglement can be taken over the set of finitely-decomposable $pi$-separable states with finite energy.
We also show that for any multipartite state with finite energy the infimum in the definition of the relative entropy of $pi$-entanglement can be taken over the set of finitely-decomposable $pi$-separable states with finite energy.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Special approximation technique for analysis of different characteristics of
states of multipartite infinite-dimensional quantum systems is proposed and
applied to the study of the relative entropy of $\pi$-entanglement and its
regularisation.
In particular, by using this technique we obtain simple sufficient conditions
for local continuity (convergence) of the regularized relative entropy of
$\pi$-entanglement.
We establish a finite-dimensional approximation property for the relative
entropy of entanglement and its regularization that allows us to generalize to
the infinite-dimensional case the results proved in the finite-dimensional
settings.
We also show that for any multipartite state with finite energy the infimum
in the definition of the relative entropy of $\pi$-entanglement can be taken
over the set of finitely-decomposable $\pi$-separable states with finite
energy.
Related papers
- 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) - Entanglement cost for infinite-dimensional physical systems [6.6908747077585105]
We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state.
This generalizes a result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems.
arXiv Detail & Related papers (2024-01-17T19:12:10Z) - An Analysis of On-the-fly Determinization of Finite-state Automata [65.268245109828]
We establish an abstraction of on-the-fly determinization of finite-state automata and demonstrate how it can be applied to bound the automatons.
A special case of our findings is that automata with many non-deterministic transitions almost always admit a determinization of complexity.
arXiv Detail & Related papers (2023-08-27T11:51:27Z) - Entanglement and entropy in multipartite systems: a useful approach [0.0]
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.
arXiv Detail & Related papers (2023-07-11T12:20:30Z) - Convergence of Dynamics on Inductive Systems of Banach Spaces [68.8204255655161]
Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from quantum theory at large action, and continuum quantum field theory arising from renormalization group fixed points.
We present a flexible modeling tool for the limit of theories: soft inductive limits constituting a generalization of inductive limits of Banach spaces.
arXiv Detail & Related papers (2023-06-28T09:52:20Z) - Renormalized von Neumann entropy with application to entanglement in
genuine infinite dimensional systems [0.0]
Von Neumann quantum entropy is finite and continuous in general, infinite dimensional case.
The renormalized quantum entropy is defined by the explicit use of the Fredholm determinants theory.
Several features of majorization theory are preserved under then introduced renormalization as it is proved in this paper.
arXiv Detail & Related papers (2022-11-10T12:56:07Z) - Maximum entropy quantum state distributions [58.720142291102135]
We go beyond traditional thermodynamics and condition on the full distribution of the conserved quantities.
The result are quantum state distributions whose deviations from thermal states' get more pronounced in the limit of wide input distributions.
arXiv Detail & Related papers (2022-03-23T17:42:34Z) - Neural-Network Quantum States for Periodic Systems in Continuous Space [66.03977113919439]
We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of periodicity.
For one-dimensional systems we find very precise estimations of the ground-state energies and the radial distribution functions of the particles.
In two dimensions we obtain good estimations of the ground-state energies, comparable to results obtained from more conventional methods.
arXiv Detail & Related papers (2021-12-22T15:27:30Z) - Attainability and lower semi-continuity of the relative entropy of
entanglement, and variations on the theme [8.37609145576126]
The relative entropy of entanglement $E_Rite is defined as the distance of a multi-part quantum entanglement from the set of separable states as measured by the quantum relative entropy.
We show that this state is always achieved, i.e. any state admits a closest separable state, even in dimensions; also, $E_Rite is everywhere lower semi-negative $lambda_$quasi-probability distribution.
arXiv Detail & Related papers (2021-05-17T18:03:02Z) - Approximation of multipartite quantum states and the relative entropy of
entanglement [0.0]
We prove several results about analytical properties of the multipartite relative entropy of entanglement and its regularization.
We establish a finite-dimensional approximation property for the relative entropy of entanglement and its regularization.
arXiv Detail & Related papers (2021-03-22T18:12:24Z) - Catalytic Transformations of Pure Entangled States [62.997667081978825]
Entanglement entropy is the von Neumann entropy of quantum entanglement of pure states.
The relation between entanglement entropy and entanglement distillation has been known only for the setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open.
Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving results an operational meaning also in entangled single-copy setup.
arXiv Detail & Related papers (2021-02-22T16:05:01Z)
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.