Multipartite entanglement in 2 x 2 x n quantum systems

We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum system, for example the 4-qubit system distributed over 3 parties, under local filtering operations. We show that there exist nine essentially different classes of states, and they give rise to a five-graded partially ordered structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W classes of 3 qubits. In particular, all 2 x 2 x n-states can be deterministically prepared from one maximally entangled state, and some applications like entanglement swapping are discussed.Comment: 9 pages, 3 eps figure

Asymptotic entanglement capacity of the Ising and anisotropic Heisenberg interactions

We compute the asymptotic entanglement capacity of the Ising interaction ZZ, the anisotropic Heisenberg interaction XX + YY, and more generally, any two-qubit Hamiltonian with canonical form K = a XX + b YY. We also describe an entanglement assisted classical communication protocol using the Hamiltonian K with rate equal to the asymptotic entanglement capacity.Comment: 5 pages, 1 figure; minor corrections, conjecture adde

Normal forms and entanglement measures for multipartite quantum states

A general mathematical framework is presented to describe local equivalence classes of multipartite quantum states under the action of local unitary and local filtering operations. This yields multipartite generalizations of the singular value decomposition. The analysis naturally leads to the introduction of entanglement measures quantifying the multipartite entanglement (as generalizations of the concurrence and the 3-tangle), and the optimal local filtering operations maximizing these entanglement monotones are obtained. Moreover a natural extension of the definition of GHZ-states to e.g. $2\times 2\times N$ systems is obtained.Comment: Proof of uniqueness of normal form adde

A bipartite class of entanglement monotones for N-qubit pure states

We construct a class of algebraic invariants for N-qubit pure states based on bipartite decompositions of the system. We show that they are entanglement monotones, and that they differ from the well know linear entropies of the sub-systems. They therefore capture new information on the non-local properties of multipartite systems.Comment: 6 page

Genralized Robustness of Entanglement

The robustness of entanglement results of Vidal and Tarrach considered the problem whereby an entangled state is mixed with a separable state so that the overall state becomes non-entangled. In general it is known that there are also cases when entangled states are mixed with other entangled states and where the sum is separable. In this paper, we treat the more general case where entangled states can be mixed with any states so that the resulting mixture is unentangled. It is found that entangled pure states for this generalized case have the same robustness as the restricted case of Vidal and Tarrach.Comment: Final version. Editorial changes and references added to independent wor

Quantum entanglement theory in the presence of superselection rules

Superselection rules severly constrain the operations which can be implemented on a distributed quantum system. While the restriction to local operations and classical communication gives rise to entanglement as a nonlocal resource, particle number conservation additionally confines the possible operations and should give rise to a new resource. In [Phys. Rev. Lett. 92, 087904 (2004), quant-ph/0310124] we showed that this resource can be quantified by a single additional number, the superselection induced variance (SiV) without changing the concept of entanglement. In this paper, we give the results on pure states in greater detail; additionally, we provide a discussion of mixed state nonlocality with superselection rules where we consider both formation and distillation. Finally, we demonstrate that SiV is indeed a resource, i.e., that it captures how well a state can be used to overcome the restrictions imposed by the superselection rule.Comment: 16 pages, 5 figure

A new family of matrix product states with Dzyaloshinski-Moriya interactions

We define a new family of matrix product states which are exact ground states of spin 1/2 Hamiltonians on one dimensional lattices. This class of Hamiltonians contain both Heisenberg and Dzyaloshinskii-Moriya interactions but at specified and not arbitrary couplings. We also compute in closed forms the one and two-point functions and the explicit form of the ground state. The degeneracy structure of the ground state is also discussed.Comment: 15 pages, 1 figur

Charge qubit entanglement in double quantum dots

We study entanglement of charge qubits in a vertical tunnel-coupled double quantum dot containing two interacting electrons. Exact diagonalization is used to compute the negativity characterizing entanglement. We find that entanglement can be efficiently generated and controlled by sidegate voltages, and describe how it can be detected. For large enough tunnel coupling, the negativity shows a pronounced maximum at an intermediate interaction strength within the Wigner molecule regime.Comment: revised version of the manuscript, as published in EPL, 7 pages, 4 figure

Amino acid metabolism conflicts with protein diversity

The twenty protein coding amino acids are found in proteomes with different relative abundances. The most abundant amino acid, leucine, is nearly an order of magnitude more prevalent than the least abundant amino acid, cysteine. Amino acid metabolic costs differ similarly, constraining their incorporation into proteins. On the other hand, sequence diversity is necessary for protein folding, function and evolution. Here we present a simple model for a cost-diversity trade-off postulating that natural proteomes minimize amino acid metabolic flux while maximizing sequence entropy. The model explains the relative abundances of amino acids across a diverse set of proteomes. We found that the data is remarkably well explained when the cost function accounts for amino acid chemical decay. More than one hundred proteomes reach comparable solutions to the trade-off by different combinations of cost and diversity. Quantifying the interplay between proteome size and entropy shows that proteomes can get optimally large and diverse

Classification of qubit entanglement: SL(2,C) versus SU(2) invariance

The role of SU(2) invariants for the classification of multiparty entanglement is discussed and exemplified for the Kempe invariant I_5 of pure three-qubit states. It is found to being an independent invariant only in presence of both W-type entanglement and threetangle. In this case, constant I_5 admits for a wide range of both threetangle and concurrences. Furthermore, the present analysis indicates that an SL^3 orbit of states with equal tangles but continuously varying I_5 must exist. This means that I_5 provides no information on the entanglement in the system in addition to that contained in the tangles (concurrences and threetangle) themselves. Together with the numerical evidence that I_5 is an entanglement monotone this implies that SU(2) invariance or the monotone property are too weak requirements for the characterization and quantification of entanglement for systems of three qubits, and that SL(2,C) invariance is required. This conclusion can be extended to general multipartite systems (including higher local dimension) because the entanglement classes of three-qubit systems appear as subclasses.Comment: 9 pages, 10 figures, revtex