Reduced State Uniquely Defines Groverian Measure of Original Pure State

Abstract

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.

title is changed, proofs are generalized to qudits and simplified, new analytic and numeric results are presented, new references are added, PRA version

References in corpus (1)

• Analytic Expressions for Geometric Measure of Three Qubit States

Cited by in corpus (10)

• Multiqubit symmetric states with high geometric entanglement
• The maximally entangled symmetric state in terms of the geometric measure
• Maximally entangled three-qubit states via geometric measure of entanglement
• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
• Mixed-State Entanglement and Quantum Teleportation through Noisy Channels
• The Communication Value of a Quantum Channel
• Geometric Measure of Entanglement and Shared Quantum States
• Exploring Non-Multiplicativity in the Geometric Measure of Entanglement
• Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement
• Role of Three-Qubit Mixed-States Entanglement in Teleportation Scheme