Reduced State Uniquely Defines Groverian Measure of Original Pure State

Details Reduced State Uniquely Defines Groverian Measure of Original Pure State Reduced State Uniquely Defines Groverian Measure of Original Pure State

2007-09-27

arxiv.org/abs/0709.4292v2

Phys. Rev. A 77, 062317 (2008)

Physics

Quantum Physics

title is changed, proofs are generalized to qudits and simplified, new analytic and numeric results are presented, new referen

Scientific paper

10.1103/PhysRevA.77.062317

Groverian and Geometric entanglement measures of the n-party pure state are expressed by the (n-1)-party reduced state density operator directly. This main theorem derives several important consequences. First, if two pure n-qudit states have reduced states of (n-1)-qudits, which are equivalent under local unitary(LU) transformations, then they have equal Groverian and Geometric entanglement measures. Second, both measures have an upper bound for pure states. However, this upper bound is reached only for two qubit systems. Third, it converts effectively the nonlinear eigenvalue problem for three qubit Groverian measure into linear eigenvalue equations. Some typical solutions of these linear equations are written explicitly and the features of the general solution are discussed in detail.

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