Multipartite entanglement in fermionic systems via a geometric measure

We study multipartite entanglement in a system consisting of indistinguishable fermions. Specifically, we have proposed a geometric entanglement measure for N spin-1/2 fermions distributed over 2L modes (single particle states). The measure is defined on the 2L qubit space isomorphic to the Fock space for 2L single particle states. This entanglement measure is defined for a given partition of 2L modes containing m >= 2 subsets. Thus this measure applies to m <= 2L partite fermionic system where L is any finite number, giving the number of sites. The Hilbert spaces associated with these subsets may have different dimensions. Further, we have defined the local quantum operations with respect to a given partition of modes. This definition is generic and unifies different ways of dividing a fermionic system into subsystems. We have shown, using a representative case, that the geometric measure is invariant under local unitaries corresponding to a given partition. We explicitly demonstrate the use of the measure to calculate multipartite entanglement in some correlated electron systems. To the best of our knowledge, there is no usable entanglement measure of m > 3 partite fermionic systems in the literature, so that this is the first measure of multipartite entanglement for fermionic systems going beyond the bipartite and tripartite cases.Comment: 25 pages, 8 figure

Sub-lethal toxicity of chlorpyrifos on Common carp, Cyprinus carpio (Linnaeus, 1758): Biochemical response

Chlorpyrifos, an organophosphate pesticide, is widely used to control pests in agriculture farms and orchards of fruit trees. In this study, the fish were exposed to sub-lethal concentrations of chlorpyrifos which were determined based on numerical value of 96 h LC50. Blood was sampled after 10, 20 and 30 days and biochemical parameters including glucose, total protein, albumin, globulin, triglyceride and cholesterol levels, and aspartate aminotransferase (AST), alanine aminotransferase (ALT), lactate dehydrogenase (LDH), creatine kinase (CK), alkaline phosphatase (ALP) and acetylcholinsetrase (AChE) activities were measured. Behavioral changes in the fish were also recorded during the experiment. Unbalanced swimming, swimming in the surface water and hyperglycemia, increased blood triglyceride, and increased levels of AST, LDH and CK activities as well as decreased levels of AChE activity were important changes that were observed in the specimens exposed to chlorpyrifos during experimental periods. The most important alterations in the blood biochemical parameters were measured in the specimens exposed to 40 µg/L chlorpyrifos on the 20th and 30th day of the trial. In conclusion, results of the present study indicated that exposure to sub-lethal concentrations of chlorpyrifos as low as 40 µg/L may cause biochemical and behavioral changes in Cyprinus carpio

Entanglement Capacity of Nonlocal Hamiltonians : A Geometric Approach

We develop a geometric approach to quantify the capability of creating entanglement for a general physical interaction acting on two qubits. We use the entanglement measure proposed by us for $N$-qubit pure states (PRA \textbf{77}, 062334 (2008)). Our procedure reproduces the earlier results (PRL \textbf{87}, 137901 (2001)). The geometric method has the distinct advantage that it gives an experimental way to monitor the process of optimizing entanglement production.Comment: 8 pages, 1 figure