@article{038c8cc1e72b4926a687fb6cd373d156,

title = "Bounds on mixed state entanglement",

abstract = "In the general framework of d1 x d2 mixed states, we derive an explicit bound for bipartite negative partial transpose (NPT) entanglement based on the mixedness characterization of the physical system. The derived result is very general, being based only on the assumption of finite dimensionality. In addition, it turns out to be of experimental interest since some purity-measuring protocols are known. Exploiting the bound in the particular case of thermal entanglement, a way to connect thermodynamic features to the monogamy of quantum correlations is suggested, and some recent results on the subject are given a physically clear explanation.",

keywords = "Entanglement, Negativity",

author = "Bruno Leggio and Anna Napoli and Hiromichi Nakazato and Antonino Messina",

note = "Funding Information: d=211,andconsidering the natural bipartition into the HN acknowledges partial support by a Grant-in-Aid where Ei is the i-th energy level of the system and Z is its partition function, β being the inverse two-levelsystemand the spin chain, one has dm = 2 and for Scientific Research (C) (No.22540292), JSPS, Japan. Funding Information: HN was partly supported byWaseda University Grant for Special Research Projects (Project number: 2019C-256). Funding Information: In this paper we derived a bound on the degree of information storable as bipartite quantum Appendix: Proof of Lemma 1. – Let us first no- entanglement within an open d-dimensional quantum system in terms of its linear entropy. Our result is quite general, holding for arbitrary bipartitions of an also arbitrary s2ystem. Indeed, our work concerns any bipartite quantum system of finite dimension. Examples may include coupled quantum dots, interacting atoms or m(soeleeceuqlueast,idoinfsfer(e9n)-t(1d3e)g)r.eeNs ootfifcreeefdurotmheorftphhaottobnotsh, oAr s(ut)perconducting circuits, but this is a very limited list of examples of typical experimenta↵l realization of quantum systems that are easy to manipulate. The same is true for the states considered: our results apply to any quantum state of finite-sized bipartite quantum systems. As a matter of fact, as shown in this paper, all we need to specify Fig.2:Negativityofreducedstateoftheistwtheo ulpuritytracoldofatsuchoms states, which is well-defined for any quantum state. We emphasize that our result (fullline),boundQ1(dottedline)andbouisndexperimentallyQ2 (dashed line)appreciable in view1 ofA quiteB recently proposed protocols aimed at measuring the versusquadraticinteraction parameter . The otherparame-d tershavebeenfixedaskBT=2,⌧=3anpurityd k = 1of. a state of a quantum system. Inspired by the seminal paper of Popescu, Short, and Winter [29], our conclusions highlight the interplay between quantum entanglement inside a thermalized system The function l(A, B) at the extremal points of its domain and its physical properties. Our results are of interest not only for quantum information researchers, (corresponding to a pure and a maximally mixed state) but also for the growing cross-community of theoreticians and experimentalists investigating the satisfies (23). For a maximally mixed state, calling n↵ (n ) subtleunderlyinglinkthbetweene numberquantumof ↵ (featur) clesassandeigethermodynamics.nvalues (n↵ + n = d), one gets A = n↵/d2 and B = n /d2 and thus l = d2n↵1 0 Author Contributions: Conceptualization, B.L., A.N., H.N. and A.M.; Formal analysis, B.L., A.N., H.N. and A.M.; Writing—original draft, B.L.; Writing—review and editing, A.N., H.N. and A.M. All authors have read and agreed tothepublishedversionp-5 of the manuscript. Funding: HN was partly supported by Waseda University Grant for Special Research Projects (Project number: 2019C-256). Publisher Copyright: {\textcopyright} 2019 by the authors.",

year = "2020",

month = jan,

day = "1",

doi = "10.3390/e22010062",

language = "English",

volume = "22",

pages = "62",

journal = "Entropy",

issn = "1099-4300",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "1",

}