Tripartite Entanglement Transformations and Tensor Rank

DOI10.1103/PhysRevLett.101.140502zbMath1228.81061arXiv0805.2977OpenAlexW2050293430WikidataQ51866832 ScholiaQ51866832MaRDI QIDQ3107626

Yaoyun Shi, Runyao Duan, Eric Chitambar

Publication date: 26 December 2011

Published in: Physical Review Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.2977

Mathematics Subject Classification ID

Quantum computation (81P68) Quantum measurement theory, state operations, state preparations (81P15)

Related Items (17)

Real and complex Waring rank of reducible cubic forms ⋮ Characterizing multipartite entanglement classes via higher-dimensional embeddings ⋮ NONDISTILLABLE ENTANGLEMENT GUARANTEES DISTILLABLE ENTANGLEMENT ⋮ Tripartite-to-bipartite entanglement transformation by stochastic local operations and classical communication and the structure of matrix spaces ⋮ Higher-order singular value decomposition and the reduced density matrices of three qubits ⋮ A family of multipartite entanglement measures ⋮ The tensor rank of tensor product of two three-qubit W states is eight ⋮ Entanglement transformation between ensembles of three-qubit GHZ-type states by LOCC ⋮ Everything you always wanted to know about LOCC (but were afraid to ask) ⋮ Entanglement manipulation beyond local operations and classical communication ⋮ Entanglement distillation from Greenberger-Horne-Zeilinger shares ⋮ Asymptotic entanglement transformation between W and GHZ states ⋮ Dimension Reduction for Polynomials over Gaussian Space and Applications ⋮ Matrix pencils and entanglement classification ⋮ Unnamed Item ⋮ Local unitary equivalence of the SLOCC class of three qubits ⋮ Entanglement classification with algebraic geometry

Cites Work

• Matrix multiplication via arithmetic progressions
• Beyond the Alder-Strassen bound.
• Gaussian elimination is not optimal
• On multiplication of 2 \(\times\) 2 matrices
• Random Bipartite Entanglement from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>W</mml:mi></mml:math>-Like States
• Multiparty entanglement in graph states
• Tensor rank is NP-complete
• Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

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