Quantify entanglement by concurrence hierarchy. (English) Zbl 1068.81011

Summary: We define the concurrence hierarchy as \(d- 1\) independent invariants under local unitary transformations in \(d\)-level quantum system. The first one is the original concurrence defined by W. Wootters [Phys. Rev. Lett. 80, 2245 (1998)] and S. Hill and W. Wootters [Phys. Rev. Lett. 78, 5022–5025 (1997)] in a two-level quantum system and generalized to the \(d\)-level pure quantum state case. We propose to use this concurrence hierarchy as a measurement of entanglement. This measurement does not increase under local quantum operations and classical communication.


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