F eb 2 01 2 Complete set of operational measures for the characterization of 3 − qubit entanglement (original) (raw)

Entanglement Classification via Single Entanglement Measure

2021

We provide necessary and sufficient conditions for generic n-qubit states to be equivalent under Stochastic Local Operations with Classical Communication (SLOCC) using a single polynomial entanglement measure. SLOCC operations may be represented geometrically by Möbius transformations on the roots of the entanglement measure on the Bloch sphere. Moreover, we show how the roots of the 3-tangle measure classify 4-qubit generic states, and propose a method to obtain the normal form of a 4-qubit state which bypasses the possibly infinite iterative procedure.

Investigating three qubit entanglement with local measurements

In this paper we describe how three qubit entanglement can be analyzed with local measurements. For this purpose we decompose entanglement witnesses into operators which can be measured locally. Our decompositions are optimized in the number of measurement settings needed for the measurement of one witness. Our method allows to detect true threepartite entanglement and especially GHZ-states with only four measurement settings.

Application of the geometric measure of entanglement to three-qubit mixed states

2003

The geometric measure of entanglement, originated by Shimony and by Barnum and Linden, is determined for a family of tripartite mixed states consisting of aribitrary mixtures of GHZ, W, and inverted-W states. For this family of states, other measures of entanglement, such as entanglement of formation and relative entropy of entanglement, have not been determined. The results for the geometric measure of entanglement are compared with those for negativity, which are also determined. The results for the geometric measure of entanglement and the negativity provide examples of the determination of entanglement for nontrivial mixed multipartite states.

Operational classification and quantification of multipartite entangled states

Physical Review A, 2006

We formalize and extend an operational multipartite entanglement measure introduced in T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006) through the generalization of global entanglement (GE) [ D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this new measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field being thus able to detect a quantum phase transition.

Distinguishing different classes of entanglement of three-qubit pure states

The European Physical Journal D

Employing the Pauli matrices, we have constructed a set of operators, which can be used to distinguish six inequivalent classes of entanglement under SLOCC (stochastic local operation and classical communication) for three-qubit pure states. These operators have very simple structure and can be obtained from the Mermin's operator with suitable choice of directions. Moreover these operators may be implemented in an experiment to distinguish the types of entanglement present in a state. We show that the measurement of only one operator is sufficient to distinguish GHZ class from rest of the classes. It is also shown that it is possible to detect and classify other classes by performing a small number of measurements. We also show how to construct such observables in any basis. We also consider a few mixed states to investigate the usefulness of our operators. Furthermore, we consider the teleportation scheme of Lee et al. [19] and show that the partial tangles and hence teleportation fidelity can be measured. We have also shown that these partial tangles can also be used to classify genuinely entangled state, biseparable state and separable state.

Information-Theoretic Measure of Genuine Multi-Qubit Entanglement

2006

We consider pure quantum states of N qubits and study the genuine N −qubit entanglement that is shared among all the N qubits. We introduce an information-theoretic measure of genuine N -qubit entanglement based on bipartite partitions. When N is an even number, this measure is presented in a simple formula, which depends only on the purities of the partially reduced density matrices. It can be easily computed theoretically and measured experimentally. When N is an odd number, the measure can also be obtained in principle. 03.65.Ud, 73.43.Nq, 89.70.+c The nature of quantum entanglement is a fascinating topic in quantum mechanics since the famous Einstein-Podolsky-Rosen paper [1] in 1935. Recently, much interest has been focused on entanglement in quantum systems containing a large number of particles. On one hand, multipartite entanglement is valuable physical resource in large-scale quantum information processing . On the other hand, multipartite entanglement seems to play an important role in condensed matter physics [4], such as quantum phase transitions (QPT) and high temperature superconductivity . Therefore, how to characterize and quantify multipartite entanglement remains one of the central issues in quantum information theory.

The Schmidt Measure as a Tool for Quantifying Multi-Particle Entanglement

2000

We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on the full state space and is shown to be an entanglement monotone, that is, it cannot increase under local quantum operations with classical communication and under mixing. For a large class of mixed states this measure of entanglement can be calculated exactly, and it provides a detailed classification of mixed states.

An observable measure of entanglement for pure states of multi-qubit systems

Quantum information & computation

proposed a measure of multi-qubit entanglement that is a function on pure states. We find that this function can be interpreted as a physical quantity related to the average purity of the constituent qubits and show how it can be observed in an efficient manner without the need for full quantum state tomography. A possible realization is described for measuring the entanglement of a chain of atomic qubits trapped in a 3D optical lattice.