2017/12/06 by Yue Dai, Wen‐Long You, Wenlong You +2 · 8 citations
Computer Science · Mathematics · Physics and Astronomy · #Coherence (philosophical gambling strategy) #Combinatorics #Concurrence #Geometry #Mathematics #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum mechanics #Regular polygon #Statistics #Triangle inequality #quant-ph
paper · pdf · doi:10.1103/physreva.96.062308
published in Physical Review A 96(6) (American Physical Society) · 6 pages, 2 figures
openalex publication_date 2017/12/06 · arxiv created 2018/04/11 · arxiv updated 2018/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We provide detailed proofs of triangle inequalities in coherence measures and entanglement concurrence. If a rank-2 state \ensuremath\varrho can be expressed as a convex combination of two pure states, i.e., \ensuremath\varrho=p1|\ensuremathψ1\ensuremath⟩\ensuremath⟨\ensuremathψ1|+p2|\ensuremathψ2\ensuremath⟩\ensuremath⟨\ensuremathψ2|, a triangle inequality can be established as |E(|\mathrm\ensuremathΨ1\ensuremath⟩)\ensuremath-E(|\mathrm\ensuremathΨ2\ensuremath⟩)|\ensuremath≤E(\ensuremath\varrho)\ensuremath≤E(|\mathrm\ensuremathΨ1\ensuremath⟩)+E(|\mathrm\ensuremathΨ2\ensuremath⟩), where |\mathrm\ensuremathΨ1\ensuremath⟩=√p1|\ensuremathψ1\ensuremath⟩ and |\mathrm\ensuremathΨ2\ensuremath⟩=√p2|\ensuremathψ2\ensuremath⟩; E can be considered either coherence measures or entanglement concurrence. This inequality displays mathematical beauty for its similarity to the triangle inequality in plane geometry. An illustrative example is given after the proof.