Quantify entanglement by concurrence hierarchy. (English) Zbl 1068.81011

Fan, Heng; Matsumoto, Keiji; Imai, Hiroshi

J. Phys. A, Math. Gen. 36, No. 14, 4151-4158 (2003).

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.

MSC:

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