Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Shuxue de shijian yu renshi

The Reduction Criteria for States in Infinite Dimensional Multipartite Quantum Systems

Wang Yin-zh

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In quantum information theory,quantum entangled state is a class very important resource.Detecting entanglement for states is a extremely important problem.In 2001,Nielsen M A proposed a reduction criterion,then William Hall proposed a different reduction criterion for multipartite finite dimensional systems in 2005.In this paper,we generalized above two reduction criteria to infinite dimensional multipartite quantum systems.Two class reduction criteria axe obtained for states in infinite dimensional multipartite quantum systems.

Related papers

The generalized partial transposition criterion for infinite-dimensional quantum systems

Siqing YanYu GuoJinchuan Hou

The positive partial transposition (PPT) criterion and the realignment criterion constitute two of the most important criteria for detecting entanglement. The general- ized partial transposition (GPT) criterion which contains the PPT criterion and the realignment criterion as special cases, provides a necessary condition for a multipartite state to be separable. Here we extend the GPT criterion to the infinite- dimensional multipartite (bipartite) case and show that it includes multipartite (bipartite) PPT criterion and multipartite (bipartite) realignment criterion as special cases as well.

•Jan 1, 2014•0 citations

Efficient k-separability criteria for mixed multipartite quantum states

Ting Gao, Yan Hong, Yao Lu +1 more

We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient $k$-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish $n-1$ different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti W states, and mixtures thereof. They detect $k$-nonseparable $n$-partite quantum states which have previously not been identified. Here $k=2,3,\cdots,n$. No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most $\mathcal{O}(n^2)$ local measurements.

arXiv:1204.2864•Europhysics Letters (EPL)•Oct 1, 2013•49 citations

Quantum entanglement in finite-dimensional Hilbert spaces

Szilárd Szalay

In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and if it is, then how much entanglement is carried by that? These questions introduce the topics of separability criteria and entanglement measures, both of which are based on the issue of classification of multipartite entanglement. In this dissertation, after reviewing these three fundamental topics for finite dimensional Hilbert spaces, I present my contribution to knowledge. My main result is the elaboration of the partial separability classification of mixed states of quantum systems composed of arbitrary number of subsystems of Hilbert spaces of arbitrary dimensions. This problem is simple for pure states, however, for mixed states it has not been considered in full detail yet. I give not only the classification but also necessary and sufficient criteria for the classes, which make it possible to determine to which class a mixed state belongs. Moreover, these criteria are given by the vanishing of quantities measuring entanglement. Apart from these, I present some side results related to the entanglement of mixed states. These results are obtained in the learning phase of my studies and give some illustrations and examples.

arXiv:1302.4654•Feb 19, 2013•6 citations

On the reduction criterion for random quantum states

Maria Anastasia Jivulescu, Nicolae Lupa, Ion Nechita

In this paper, we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems. We first obtain an explicit formula for the moments of a random quantum state to which the reduction criterion has been applied. We show that the empirical eigenvalue distribution of this random matrix converges strongly to a limit that we compute, in three different asymptotic regimes. We then employ tools from free probability theory to study the asymptotic positivity of the reduction operators. Finally, we compare the reduction criterion with other entanglement criteria, via thresholds.

arXiv:1402.4292•Journal of Mathematical Physics•Nov 1, 2014•9 citations

Detecting high-dimensional multipartite entanglement via some classes of measurements

Lu Liu, Ting Gao, Fengli Yan

Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and present some criteria detecting entanglement of arbitrary high dimensional multi-qudit systems and multipartite systems of subsystems with different dimensions. It is proved that these criteria can detect the k -nonseparability ( k is even) of multipartite qudit systems and arbitrary high dimensional multipartite systems of m subsystems with different dimensions. We show that they are more efficient and wider of application range than the previous ones. They provide experimental implementation in detecting entanglement without full quantum state tomography.

arXiv:1512.02853•Chinese Physics B•Feb 1, 2018•13 citations

Approximation of multipartite quantum states and the relative entropy of entanglement

Максим Евгеньевич Широков

Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We prove several results about analytical properties of the multipartite relative entropy of entanglement and its regularization (the lower semicontinuity on wide class of states, the uniform continuity under the energy constraints, etc.). We establish a finite-dimensional approximation property for the relative entropy of entanglement and its regularization that allows to generalize to the infinite-dimensional case the results proved in the finite-dimensional settings.

arXiv:2103.12111•Mar 22, 2021•3 citations
In quantum information theory,quantum entangled state is a class very important resource.Detecting entanglement for states is a extremely important problem.In 2001,Nielsen M A proposed a reduction criterion,then William Hall proposed a different reduction criterion for multipartite finite dimensional systems in 2005.In this paper,we generalized above two reduction criteria to infinite dimensional multipartite quantum systems.Two class reduction criteria axe obtained for states in infinite dimensional multipartite quantum systems.
The positive partial transposition (PPT) criterion and the realignment criterion constitute two of the most important criteria for detecting entanglement. The general- ized partial transposition (GPT) criterion which contains the PPT criterion and the realignment criterion as special cases, provides a necessary condition for a multipartite state to be separable. Here we extend the GPT criterion to the infinite- dimensional multipartite (bipartite) case and show that it includes multipartite (bipartite) PPT criterion and multipartite (bipartite) realignment criterion as special cases as well.
We investigate classification and detection of entanglement of multipartite quantum states in a very general setting, and obtain efficient kkk-separability criteria for mixed multipartite states in arbitrary dimensional quantum systems. These criteria can be used to distinguish n−1n-1n−1 different classes of multipartite inseparable states and can detect many important multipartite entangled states such as GHZ states, W states, anti W states, and mixtures thereof. They detect kkk-nonseparable nnn-partite quantum states which have previously not been identified. Here k=2,3,⋯ ,nk=2,3,\cdots,nk=2,3,⋯,n. No optimization or eigenvalue evaluation is needed, and our criteria can be evaluated by simple computations involving components of the density matrix. Most importantly, they can be implemented in today's experiments by using at most O(n2)\mathcal{O}(n^2)O(n2) local measurements.
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and if it is, then how much entanglement is carried by that? These questions introduce the topics of separability criteria and entanglement measures, both of which are based on the issue of classification of multipartite entanglement. In this dissertation, after reviewing these three fundamental topics for finite dimensional Hilbert spaces, I present my contribution to knowledge. My main result is the elaboration of the partial separability classification of mixed states of quantum systems composed of arbitrary number of subsystems of Hilbert spaces of arbitrary dimensions. This problem is simple for pure states, however, for mixed states it has not been considered in full detail yet. I give not only the classification but also necessary and sufficient criteria for the classes, which make it possible to determine to which class a mixed state belongs. Moreover, these criteria are given by the vanishing of quantities measuring entanglement. Apart from these, I present some side results related to the entanglement of mixed states. These results are obtained in the learning phase of my studies and give some illustrations and examples.
In this paper, we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems. We first obtain an explicit formula for the moments of a random quantum state to which the reduction criterion has been applied. We show that the empirical eigenvalue distribution of this random matrix converges strongly to a limit that we compute, in three different asymptotic regimes. We then employ tools from free probability theory to study the asymptotic positivity of the reduction operators. Finally, we compare the reduction criterion with other entanglement criteria, via thresholds.
Mutually unbiased bases, mutually unbiased measurements and general symmetric informationally complete measurements are three related concepts in quantum information theory. We investigate multipartite systems using these notions and present some criteria detecting entanglement of arbitrary high dimensional multi-qudit systems and multipartite systems of subsystems with different dimensions. It is proved that these criteria can detect the k -nonseparability ( k is even) of multipartite qudit systems and arbitrary high dimensional multipartite systems of m subsystems with different dimensions. We show that they are more efficient and wider of application range than the previous ones. They provide experimental implementation in detecting entanglement without full quantum state tomography.
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We prove several results about analytical properties of the multipartite relative entropy of entanglement and its regularization (the lower semicontinuity on wide class of states, the uniform continuity under the energy constraints, etc.). We establish a finite-dimensional approximation property for the relative entropy of entanglement and its regularization that allows to generalize to the infinite-dimensional case the results proved in the finite-dimensional settings.