{"title":"Majorization-based entanglement criterion for fermion systems using the von Neumann entropy","authors":"Y. Akbari-Kourbolagh, E. Rezazadeh-Dizaji","doi":"10.1140/epjd/s10053-024-00905-8","DOIUrl":null,"url":null,"abstract":"<p>We use the Schur concavity of the von Neumann entropy and introduce a majorization-based entanglement criterion for the states of systems consisting of identical fermions. This criterion is in the form of an inequality between the von Neumann entropies of the total density matrix and the single-particle reduced density matrix which have to be satisfied by the separable states of such systems, and therefore, its violation indicates the entanglement. Our criterion is an improved version of the one introduced by Zander et al. (in Eur. Phys. J. D <b>66</b>: 14, 2012). To illustrate its utility, we use the criterion to various illustrative instances of the families of mixed states and find that when the single-particle Hilbert spaces are of dimension four, the criterion indicates all the entangled states within the families under consideration.</p>","PeriodicalId":789,"journal":{"name":"The European Physical Journal D","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The European Physical Journal D","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1140/epjd/s10053-024-00905-8","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"OPTICS","Score":null,"Total":0}
引用次数: 0
Abstract
We use the Schur concavity of the von Neumann entropy and introduce a majorization-based entanglement criterion for the states of systems consisting of identical fermions. This criterion is in the form of an inequality between the von Neumann entropies of the total density matrix and the single-particle reduced density matrix which have to be satisfied by the separable states of such systems, and therefore, its violation indicates the entanglement. Our criterion is an improved version of the one introduced by Zander et al. (in Eur. Phys. J. D 66: 14, 2012). To illustrate its utility, we use the criterion to various illustrative instances of the families of mixed states and find that when the single-particle Hilbert spaces are of dimension four, the criterion indicates all the entangled states within the families under consideration.
摘要 我们利用冯-诺依曼熵的舒尔凹性，为由相同费米子组成的系统的状态引入了一个基于大化的纠缠准则。该判据的形式是总密度矩阵的冯-诺依曼熵与单粒子还原密度矩阵的冯-诺依曼熵之间的不等式，此类系统的可分离态必须满足该不等式，因此，违反该不等式表明存在纠缠。我们的标准是赞德等人（Eur. Phys. J. D. 66: 14, 2012）提出的标准的改进版。为了说明它的效用，我们将该准则用于混合态族的各种说明性实例，并发现当单粒子希尔伯特空间的维数为四时，该准则可指示所考虑的族中的所有纠缠态。
期刊介绍：
The European Physical Journal D (EPJ D) presents new and original research results in:
Atomic Physics;
Molecular Physics and Chemical Physics;
Atomic and Molecular Collisions;
Clusters and Nanostructures;
Plasma Physics;
Laser Cooling and Quantum Gas;
Nonlinear Dynamics;
Optical Physics;
Quantum Optics and Quantum Information;
Ultraintense and Ultrashort Laser Fields.
The range of topics covered in these areas is extensive, from Molecular Interaction and Reactivity to Spectroscopy and Thermodynamics of Clusters, from Atomic Optics to Bose-Einstein Condensation to Femtochemistry.
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