Entangled three-qubit states without concurrence and three-tangle

The classification of the multipartite entanglement is an important problem in quantum information theory. We propose a class of two qubit mixed states $\sigma_{AB}= p|\chi_{1}\rangle\langle\chi_{1}|\otimes\rho_{1}+(1-p)|\chi_{2}\rangle\langle\chi_{2}|\otimes\rho_{2}$, where $|\chi_{1}\rangle=\alpha|0\rangle+\beta|1\rangle$, $|\chi_{2}\rangle=\beta|0\rangle+(-1)^{n}\alpha|1\rangle$. We have shown that the state $\sigma_{AB}$ represent a classical state when $n$ is odd while i...

We investigate the lower bound obtained from experimental data of a quantum state $\rho$, as proposed independently by G\"uhne et al. and Eisert et al. for mixed states of three qubits. The measure we consider is the convex-roof extended three-tangle. Our findings highlight an intimate relation to lower bounds obtained recently from so-called characteristic curves of a given entanglement measure. We apply the bounds to estimate the three-tangle present in recently performed e...

Exploring an analytical expression for the convex roof of the pure state squared concurrence for rank 2 mixed states the entanglement of a system of three particles under decoherence is studied, using the monogamy inequality for mixed states and the residual entanglement obtained from it. The monogamy inequality is investigated both for the concurrence and the negativity in the case of local independent phase damping channel acting on generalized GHZ states of three particles...

Invertible local transformations of a multipartite system are used to define equivalence classes in the set of entangled states. This classification concerns the entanglement properties of a single copy of the state. Accordingly, we say that two states have the same kind of entanglement if both of them can be obtained from the other by means of local operations and classical communcication (LOCC) with nonzero probability. When applied to pure states of a three-qubit system, t...

All mixed states of two qubits can be brought into normal form by the action of SLOCC operations of the kind $\rho'=(A\otimes B)\rho(A\otimes B)^\dagger$. These normal forms can be obtained by considering a Lorentz singular value decomposition on a real parameterization of the density matrix. We show that the Lorentz singular values are variationally defined and give rise to entanglement monotones, with as a special case the concurrence. Next a necessary and sufficient criter...

We present a complete analysis of multipartite entanglement of three-mode Gaussian states of continuous variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations will be quantified by a proper convex roof ...

We derive an inequality for three fermions with six single particle states which reduces to the sum of the famous Coffman-Kundu-Wootters inequalities when an embedded three qubit system is considered. We identify the quantities which are playing the role of the concurrence, the three-tangle and the invariant $\det \rho_A+\det \rho_B+\det \rho_C$ for this tripartite system. We show that this latter one is almost interchangeable with the von Neumann entropy and conjecture that ...

The quantitative assessment of the entanglement in multipartite quantum states is, apart from its fundamental importance, a practical problem. Recently there has been significant progress in developing new methods to determine certain entanglement measures. In particular, there is a method---in principle, analytical---to compute a certified lower bound for the three-tangle. The purpose of this work is to provide a manual for the implementation of this approach and to explicit...

The distribution of entanglement in a multiparty system can be described through the principles of monogamy or polygamy. Monogamy is a fundamental characteristic of entanglement that restricts its distribution among several number of parties(more than two). In this work, our aim is to explore how quantum entanglement can be distributed in accordance with monogamy relations by utilizing both the genuine multipartite entanglement measures and bipartite entanglement measures. Sp...

While the concept of entanglement for distinguishable particles is well established, defining entanglement and non-locality in systems of indistinguishable particles, which require the use of the (anti)symmetrization postulate, remains challenging, and multiple approaches have been proposed to address this issue. In this work we study the problem of detecting genuine tripartite entanglement among systems of indistinguishable bosons. A genuine entangled state is one that canno...