Model inspired by population genetics to study fragmentation of brittle plates

We use a model whose rules were inspired by population genetics, the random capability growth model, to describe the statistical details observed in experiments of fragmentation of brittle platelike objects, and in particular the existence of (i) composite scaling laws, (ii) small critical exponents \tau associated with the power-law fragment-size distribution, and (iii) the typical pattern of cracks. The proposed computer simulations do not require numerical solutions of the Newton's equations of motion, nor several additional assumptions normally used in discrete element models. The model is also able to predict some physical aspects which could be tested in new experiments of fragmentation of brittle systems.Comment: We have modified the text in order to make the description of the model more clear. One Figure (Figure 1) was introduced showing the steps of the dynamics of colonization. Twelve references were adde

Conservation law for distributed entanglement of formation and quantum discord

We present a direct relation, based upon a monogamic principle, between entanglement of formation (EOF) and quantum discord (QD), showing how they are distributed in an arbitrary tripartite pure system. By extending it to a paradigmatic situation of a bipartite system coupled to an environment, we demonstrate that the EOF and the QD obey a conservation relation. By means of this relation we show that in the deterministic quantum computer with one pure qubit the protocol has the ability to rearrange the EOF and the QD, which implies that quantum computation can be understood on a different basis as a coherent dynamics where quantum correlations are distributed between the qubits of the computer. Furthermore, for a tripartite mixed state we show that the balance between distributed EOF and QD results in a stronger version of the strong subadditivity of entropy.Comment: Published versio

State reconstruction of finite dimensional compound systems via local projective measurements and one-way classical communication

For a finite dimensional discrete bipartite system, we find the relation between local projections performed by Alice, and Bob post-selected state dependence on the global state submatrices. With this result the joint state reconstruction problem for a bipartite system can be solved with strict local projections and one-way classical communication. The generalization to multipartite systems is straightforward.Comment: 4 pages, 1 figur