Measure Of Entanglement For Pure States Research Articles

An Extension of Entanglement Measures for Pure States

AbstractTo quantify the entanglement is one of the most important topics in quantum entanglement theory. An entanglement measure is built from measures for pure states. Conditions when the entanglement measure is entanglement monotone and convex are presented, as well as the interpretation of smoothed one‐shot entanglement cost. Next, a difference between the measure under the local operation and classical communication and the separability‐preserving operations is presented. Then, the relation between the convex roof extended method and the way here for the entanglement measures built from the geometric entanglement measure for pure states, as well as the concurrence for pure states in two‐qubit systems are considered. It is also shown that the measure is monogamous for system.

Quantifying entanglement of arbitrary-dimensional multipartite pure states in terms of the singular values of coefficient matrices

The entanglement quantification and classification of multipartite quantum states are two important research fields in quantum information. In this work, we study the entanglement of arbitrary-dimensional multipartite pure states by looking at the averaged partial entropies of various bipartite partitions of the system, namely, the so-called Manhattan distance ($l_1$ norm) of averaged partial entropies (MAPE), and it is proved to be an entanglement measure for pure states. We connected the MAPE with the coefficient matrices, which are important tools in entanglement classification and reexpressed the MAPE for arbitrary-dimensional multipartite pure states by the nonzero singular values of the coefficient matrices. The entanglement properties of the $n$-qubit Dicke states, arbitrary-dimensional Greenberger-Horne-Zeilinger states, and $D_3^n$ states are investigated in terms of the MAPE, and the relation between the rank of the coefficient matrix and the degree of entanglement is demonstrated for symmetric states by two examples.

Systematic generation of entanglement measures for pure states

We propose a method to generate entanglement measures systematically by using the irreducible decomposition of some copies of a state under the local unitary (LU) transformations. It is applicable to general multipartite systems. We show that there are entanglement monotones corresponding to singlet representations of the LU group. They can be evaluated efficiently in an algebraic way, and experimentally measurable by local projective measurements of the copies of the state. Nonsinglet representations are also shown to be useful to classify entanglement. Our method reproduces many well-known measures in a unified way.

ENTANGLEMENT MONOTONES AND MAXIMALLY ENTANGLED STATES IN MULTIPARTITE QUBIT SYSTEMS

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call comb in reference to the hairy-ball theorem. For qubits (i.e. spin 1/2) the combs are automatically invariant under SL (2, ℂ). This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-, five- and six-qubit entanglement.

ConstructingN-qubit entanglement monotones from antilinear operators

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call ``comb''. For qubits (or spin $1∕2$) the combs are automatically invariant under $\mathrm{SL}(2,\mathbb{C})$. This implies that the filters obtained from the combs are entanglement monotones by construction. We give alternative formulas for the concurrence and the three-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-qubit entanglement.