2016/08/31 by G. M. Bosyk, G. Sergioli, Giuseppe Sergioli +6
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Bipartite graph #Combinatorics #Discrete mathematics #Infimum and supremum #LOCC #Lattice (music) #Majorization #Mathematics #Multipartite entanglement #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Qubit #Squashed entanglement #State (computer science) #Statistical physics #Transformation (genetics) #quant-ph
paper · pdf · doi:10.1016/j.physa.2016.12.083
Revised manuscript close to the accepted version in Physica A (10 pages, 1 figure)
openalex publication_date 2017/01/06 · arxiv created 2017/01/11 · arxiv updated 2017/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the problem of deterministic transformations of an initial pure entangled quantum state, |ψ〉, into a target pure entangled quantum state, |ϕ〉, by using local operations and classical communication (LOCC). A celebrated result of Nielsen (1999) gives the necessary and sufficient condition that makes this entanglement transformation process possible. Indeed, this process can be achieved if and only if the majorization relation ψ≺ϕ holds, where ψ and ϕ are probability vectors obtained by taking the squares of the Schmidt coefficients of the initial and target states, respectively. In general, this condition is not fulfilled. However, one can look for an approximate entanglement transformation. Vidal et al. (2000) have proposed a deterministic transformation using LOCC in order to obtain a target state |χopt〉 most approximate to |ϕ〉 in terms of maximal fidelity between them. Here, we show a strategy to deal with approximate entanglement transformations based on the properties of the majorization lattice. More precisely, we propose as approximate target state one whose Schmidt coefficients are given by the supremum between ψ and ϕ. Our proposal is inspired on the observation that fidelity does not respect the majorization relation in general. Remarkably enough, we find that for some particular interesting cases, like two-qubit pure states or the entanglement concentration protocol, both proposals are coincident.