2014/06/30 by Maria Anastasia Jivulescu, Nicolae Lupa, Ion Nechita +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Combinatorics #Computer science #Discrete mathematics #Eigenvalues and eigenvectors #Mathematics #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Qubit #Reduction (mathematics) #Set (abstract data type) #Simple (philosophy) #Spectral line #Spectrum (functional analysis) #Transpose #msc:15B48 #msc:81P45 #quant-ph
paper · pdf · doi:10.1016/j.laa.2014.11.031
published as Lin. Alg. Appl. 469, 276-304 (2015) · Linear Algebra and its Applications (2015)
arxiv created 2014/11/29 · openalex publication_date 2014/12/06 · arxiv updated 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We study the problem of whether all bipartite quantum states having a prescribed spectrum remain positive under the reduction map applied to one subsystem. We provide necessary and sufficient conditions, in the form of a family of linear inequalities, which the spectrum has to verify. Our conditions become explicit when one of the two subsystems is a qubit, as well as for further sets of states. Finally, we introduce a family of simple entanglement criteria for spectra, closely related to the reduction and positive partial transpose criteria, which also provide new insight into the set of spectra that guarantee separability or positivity of the partial transpose.