Multi-stage emplacement of the Götemar Pluton, SE Sweden: new evidence inferred from field observations and microfabric analysis, including cathodoluminescence microscopy

The emplacement of the Mesoproterozoic Götemar Pluton into Paleoproterozoic granitoid host rocks of the Transscandinavian Igneous Belt is re-examined by microfabric analysis, including cathodoluminescence microscopy. Field data on the pluton-host rock system are used to strengthen the model. The Götemar Pluton, situated on the Baltic Shield of SE Sweden, is a horizontally zoned tabular structure that was constructed by the intrusion of successive pulses of magma with different crystal/melt ratios, at an estimated crustal depth of 4–8 km. Initial pluton formation involved magma ascent along a vertical dike, which was arrested at a mechanical discontinuity within the granitoid host rocks; this led to the formation of an initial sill. Subsequent sill stacking and their constant inflation resulted in deformation and reheating of existing magma bodies, which also raised the pluton roof. This multi-stage emplacement scenario is indicated by complex dike relationships and the occurrence of several generations of quartz (Si-metasomatism). The sills were charged by different domains of a heterogeneous magma chamber with varying crystal/melt ratios. Ascent or emplacement of magma with a high crystal/melt ratio is indicated by syn-magmatic deformation of phenocrysts. Complex crystallization fabrics (e.g. oscillatory growth zoning caused by high crystal defect density, overgrowth and replacement features, resorbed and corroded crystal cores, rapakivi structure) are mostly related to processes within the main chamber, that is repeated magma mixing or water influx

Tripartite entanglement and quantum relative entropy

We establish relations between tripartite pure state entanglement and additivity properties of the bipartite relative entropy of entanglement. Our results pertain to the asymptotic limit of local manipulations on a large number of copies of the state. We show that additivity of the relative entropy would imply that there are at least two inequivalent types of asymptotic tripartite entanglement. The methods used include the application of some useful lemmas that enable us to analytically calculate the relative entropy for some classes of bipartite states.Comment: 7 pages, revtex, no figures. v2: discussion about recent results, 2 refs. added. Published versio

Conditional q-Entropies and Quantum Separability: A Numerical Exploration

We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's and Tsallis' measures constitute particular instances of these entropies. We perform a systematic numerical survey of the space of mixed states of two-qubit systems in order to determine, as a function of the degree of mixture, and for different values of the entropic parameter q, the volume in state space occupied by those states characterized by positive values of the relative entropy. Similar calculations are performed for qubit-qutrit systems and for composite systems described by Hilbert spaces of larger dimensionality. We pay particular attention to the limit case q --> infinity. Our numerical results indicate that, as the dimensionalities of both subsystems increase, composite quantum systems tend, as far as their relative q-entropies are concerned, to behave in a classical way

Parallel transport in an entangled ring

This paper defines a notion of parallel transport in a lattice of quantum particles, such that the transformation associated with each link of the lattice is determined by the quantum state of the two particles joined by that link. We focus particularly on a one-dimensional lattice--a ring--of entangled rebits, which are binary quantum objects confined to a real state space. We consider states of the ring that maximize the correlation between nearest neighbors, and show that some correlation must be sacrificed in order to have non-trivial parallel transport around the ring. An analogy is made with lattice gauge theory, in which non-trivial parallel transport around closed loops is associated with a reduction in the probability of the field configuration. We discuss the possibility of extending our result to qubits and to higher dimensional lattices.Comment: 31 pages, no figures; v2 includes a new example of a qubit rin

On 1-qubit channels

The entropy H_T(rho) of a state rho with respect to a channel T and the Holevo capacity of the channel require the solution of difficult variational problems. For a class of 1-qubit channels, which contains all the extremal ones, the problem can be significantly simplified by associating an Hermitian antilinear operator theta to every channel of the considered class. The concurrence of the channel can be expressed by theta and turns out to be a flat roof. This allows to write down an explicit expression for H_T. Its maximum would give the Holevo (1-shot) capacity.Comment: 12 pages, several printing or latex errors correcte

Frontier between separability and quantum entanglement in a many spin system

We discuss the critical point $x_c$ separating the quantum entangled and separable states in two series of N spins S in the simple mixed state characterized by the matrix operator $\rho=x|\tilde{\phi}><\tilde{\phi}| + \frac{1-x}{D^N} I_{D^N}$ where $x \in [0,1]$, $D =2S+1$, ${\bf I}_{D^N}$ is the $D^N \times D^N$ unity matrix and $|\tilde {\phi}>$ is a special entangled state. The cases x=0 and x=1 correspond respectively to fully random spins and to a fully entangled state. In the first of these series we consider special states $|\tilde{\phi}>$ invariant under charge conjugation, that generalizes the N=2 spin S=1/2 Einstein-Podolsky-Rosen state, and in the second one we consider generalizations of the Weber density matrices. The evaluation of the critical point $x_c$ was done through bounds coming from the partial transposition method of Peres and the conditional nonextensive entropy criterion. Our results suggest the conjecture that whenever the bounds coming from both methods coincide the result of $x_c$ is the exact one. The results we present are relevant for the discussion of quantum computing, teleportation and cryptography.Comment: 4 pages in RevTeX forma