The number of product vectors and their partial conjugates in a pair of spaces

2013/09/17 by Joohan Na, Na, Joohan
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1309.4177

12 pages

openalex publication_date 2013/09/17 · arxiv created 2013/09/24 · arxiv updated 2013/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D and E be subspaces of the tensor product of the finite-dimensional Hilbert spaces ℂ^m ⊗ ℂⁿ. We show that the number of product vectors in D with their partial conjugates in E is uniformly bounded depending only on m and n whenever it is finite. We also give an upper bound in qubit-qunit case which we expect to be sharp.

Citations

• Separable states with unique decompositions
• Separability Criterion for Density Matrices

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