Analytic Expressions for Geometric Measure of Three Qubit States
arXiv:0710.0571 · doi:10.1103/PhysRevA.77.022325
Abstract
A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to derive the analytic expressions of the geometric entanglement measure in the wide range of the three qubit systems, including the general class of W-states and states which are symmetric under permutation of two qubits. The nearest separable states are not necessarily unique and highly entangled states are surrounded by the one-parametric set of equally distant separable states. A possibility for the physical applications of the various three qubit states to quantum teleportation and superdense coding is suggested from the aspect of the entanglement.
6 pages, no figure, PRA version
References in corpus (25)
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Mixed State Entanglement and Quantum Error Correction
- Quantum Mechanics helps in searching for a needle in a haystack
- Three qubits can be entangled in two inequivalent ways
- Concentrating Partial Entanglement by Local Operations
- Distributed Entanglement
- Efficient classical simulation of slightly entangled quantum computations
- Quantifying Entanglement
- Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolski-Rosen Channels
- Entanglement Measures and Purification Procedures
- Conditions for a class of entanglement transformations
- Geometric measure of entanglement and applications to bipartite and multipartite quantum states
- On the role of entanglement in quantum computational speed-up
- Generalized Schmidt decomposition and classification of three-quantum-bit states
- Perfect Teleportation and Superdense Coding With W-States
- Thermodynamics and the Measure of Entanglement
- Limits for entanglement measures
- The Entanglement of Formation for Isotropic States
- Monotones and invariants for multi-particle quantum states
- Non-local properties of multi-particle density matrices
- Approximate transformations and robust manipulation of bipartite pure state entanglement
- An entanglement monotone derived from Grover's algorithm
- Characterization of pure quantum states of multiple qubits using the Groverian entanglement measure
- Connecting the generalized robustness and the geometric measure of entanglement
- Entangled Quantum States Generated by Shor's Factoring Algorithm
Cited by in corpus (27)
- Entanglement detection
- The geometric measure of entanglement for symmetric states
- GHZ versus W : Quantum Teleportation through Noisy Channels
- Multiqubit symmetric states with high geometric entanglement
- Geometric measure of entanglement for pure multipartite states
- Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
- Maximally entangled three-qubit states via geometric measure of entanglement
- Additivity and non-additivity of multipartite entanglement measures
- Entanglement and Discord of superposition of Greenberger-Horne-Zeilinger states
- Classification of Entanglement in Symmetric States
- Reduced State Uniquely Defines Groverian Measure of Original Pure State
- Duality and the geometric measure of entanglement of general multiqubit W states
- Easy implementable algorithm for the geometric measure of entanglement
- Mixed-State Entanglement and Quantum Teleportation through Noisy Channels
- Geometric Measure of Entanglement and Shared Quantum States
- Entanglement of Periodic States, the Quantum Fourier Transform and Shor's Factoring Algorithm
- Multipartite entanglement in fermionic systems via a geometric measure
- Universal behavior of the geometric entanglement measure of many-qubit W states
- Entanglement detection from interference fringes in atom-photon systems
- Geometric entanglement in the Laughlin wave function
- Toward an understanding of entanglement for generalized n-qubit W-states
- Nonstrict inequality for Schmidt coefficients of three-qubit states
- Effect of Phase Factor in the Geometric Entanglement Measure of Three-Qubit States
- Absolutely maximally entangled pure states of multipartite quantum systems
- Role of Three-Qubit Mixed-States Entanglement in Teleportation Scheme
- Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems
- Entanglement of formation for qubit-qudit system using partition of qudit sytem into a set of qubit system