2019/08/31 by Christopher Eltschka, Jens Siewert
Computer Science · Physics and Astronomy · #Multipartite #Multipartite entanglement #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum discord #Quantum entanglement #Quantum many-body systems #Quantum system #Tensor product #W state #quant-ph
paper · pdf · doi:10.22331/q-2020-02-10-229
published as Quantum 4, 229 (2020) · 11 pages, 1 figure, accepted for publication in Quantum
openalex created_date 2019/08/22 · arxiv created 2020/02/06 · openalex publication_date 2020/02/10 · arxiv updated 2020/02/12 · openalex updated_date 2026/08/05
The existence of correlations between the parts of a quantum system on the one hand, and entanglement between them on the other, are different properties. Yet, one intuitively would identify strong<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-party correlations with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-party entanglement in an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-partite quantum state. If the local systems are qubits, this intuition is confirmed: The state with the strongest<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-party correlations is the Greenberger-Horne-Zeilinger (GHZ) state, which does have genuine multipartite entanglement. However, for high-dimensional local systems the state with strongest<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-party correlations may be a tensor product of Bell states, that is, partially separable. We show this by introducing several novel tools for handling the Bloch representation.