Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

We prove lower bounds for the entanglement of formation and the squashed entanglement for any a bipartite density matrix in terms of the conditional entropy of the bipartite state with respect to either of its partial traces, and prove that these bounds are sharp by constructing a new class of states whose entanglements can be computed, and for which the bounds are saturated.Comment: 8 pages. Version 2 includes some additional references and comment

Octopamine increases the excitability of neurons in the snail feeding system by modulation of inward sodium current but not outward potassium currents

Background: Although octopamine has long been known to have major roles as both transmitter and modulator in arthropods, it has only recently been shown to be functionally important in molluscs, playing a role as a neurotransmitter in the feeding network of the snail Lymnaea stagnalis. The synaptic potentials cannot explain all the effects of octopamine-containing neurons on the feeding network, and here we test the hypothesis that octopamine is also a neuromodulator. Results: The excitability of the B1 and B4 motoneurons in the buccal ganglia to depolarising current clamp pulses is significantly (P << 0.05) increased by (10 mu M) octopamine, whereas the B2 motoneuron becomes significantly less excitable. The ionic currents evoked by voltage steps were recorded using 2-electrode voltage clamp. The outward current of B1, B2 and B4 motoneurons had two components, a transient I-A current and a sustained I-K delayed-rectifier current, but neither was modulated by octopamine in any of these three buccal neurons. The fast inward current was eliminated in sodium - free saline and so is likely to be carried by sodium ions. 10 mu M octopamine enhanced this current by 33 and 45% in the B1 and B4 motoneurons respectively (P << 0.05), but a small reduction was seen in the B2 neuron. A Hodgkin-Huxley style simulation of the B1 motoneuron confirms that a 33% increase in the fast inward current by octopamine increases the excitability markedly. Conclusion: We conclude that octopamine is also a neuromodulator in snails, changing the excitability of the buccal neurons. This is supported by the close relationship from the voltage clamp data, through the quantitative simulation, to the action potential threshold, changing the properties of neurons in a rhythmic network. The increase in inward sodium current provides an explanation for the polycyclic modulation of the feeding system by the octopamine-containing interneurons, making feeding easier to initiate and making the feeding bursts more intense

Entropy and entanglement bounds for reduced density matrices of fermionic states

Unlike bosons, fermions always have a non-trivial entanglement. Intuitively, Slater determinantal states should be the least entangled states. To make this intuition precise we investigate entropy and entanglement of fermionic states and prove some extremal and near extremal properties of reduced density matrices of Slater determinantal states.Comment: 20 pages. This version of the paper is a substantial revision of the previous versio