Functional co-monotony of processes with applications to peacocks and barrier options

We show that several general classes of stochastic processes satisfy a functional co-monotony principle, including processes with independent increments, Brownian diffusions, Liouville processes. As a first application, we recover some recent results about peacock processes obtained by Hirsch et al. which were themselves motivated by a former work of Carr et al. about the sensitivity of Asian Call options with respect to their volatility and residual maturity (seniority). We also derive semi-universal bounds for various barrier options.Comment: 27 page

Tight lower bound to the geometric measure of quantum discord

Dakic, Vedral and Brukner [Physical Review Letters \tf{105},190502 (2010)] gave a geometric measure of quantum discord in a bipartite quantum state as the distance of the state from the closest classical quantum (or zero discord) state and derived an explicit formula for a two qubit state. Further, S.Luo and S.Fu [Physical Review A \tf{82}, 034302 (2010)] obtained a generic form of this geometric measure for a general bipartite state and established a lower bound. In this brief report we obtain a rigorous lower bound to the geometric measure of quantum discord in a general bipartite state which dominates that obtained by S.Luo and S.Fu.Comment: 10 pages,2 figures. In the previous versions, a constraint was ignored while optimizing the second term in Eq.(5), in which case, only a lower bound on the geometric discord can be obtained. The title is also consequently changed. Accepted in Phys.Rev.

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

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

An Experimentally accessible geometric measure for entanglement in NN-qubit pure states

We present a multipartite entanglement measure for $N$-qubit pure states, using the norm of the correlation tensor which occurs in the Bloch representation of the state. We compute this measure for several important classes of $N$-qubit pure states such as GHZ states, W states and their superpositions. We compute this measure for interesting applications like one dimensional Heisenberg antiferromagnet. We use this measure to follow the entanglement dynamics of Grover's algorithm. We prove that this measure possesses almost all the properties expected of a good entanglement measure, including monotonicity. Finally, we extend this measure to $N$-qubit mixed states via convex roof construction and establish its various properties, including its monotonicity. We also introduce a related measure which has all properties of the above measure and is also additive.Comment: 23 pages, 6 figures, presented in part at ISCQI (Bhubaneswar, India), comments are welcom

Separability and Entanglement of Quantum States Based on Covariance Matrices

We investigate the separability of quantum states based on covariance matrices. Separability criteria are presented for multipartite states. The lower bound of concurrence proposed in Phys. Rev. A. 75, 052320 (2007) is improved by optimizing the local orthonormal observables.Comment: 11 page

Geometric measure of quantum discord and total quantum correlations in a N-partite quantum state

Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. \textbf{88}, 017901 (2001)], is a measure of the discrepancy between quantum versions of two classically equivalent expressions for mutual information and is found to be useful in quantification and application of quantum correlations in mixed states. It is viewed as a key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. An early step toward the quantification of quantum discord in a quantum state was by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105,190502 (2010)] who introduced a geometric measure of quantum discord and derived an explicit formula for any two-qubit state. Recently, Luo and Fu [Phys. Rev. A \textbf{82}, 034302 (2010)] introduced a generic form of the geometric measure of quantum discord for a bipartite quantum state. We extend these results and find generic forms of the geometric measure of quantum discord and total quantum correlations in a general N-partite quantum state. Further, we obtain computable exact formulas for the geometric measure of quantum discord and total quantum correlations in a N-qubit quantum state. The exact formulas for the $N$-qubit quantum state are experimentally implementable.Comment: 18 pages, 3 figure

Protection of Stem Cell-Derived Lymphocytes in a Primate AIDS Gene Therapy Model after In Vivo Selection

Background: There is currently no effective AIDS vaccine, emphasizing the importance of developing alternative therapies. Recently, a patient was successfully transplanted with allogeneic, naturally resistant CCR5-negative (CCR5 delta 32) cells, setting the stage for transplantation of naturally resistant, or genetically modified stem cells as a viable therapy for AIDS. Hematopoietic stem cell (HSC) gene therapy using vectors that express various anti-HIV transgenes has also been attempted in clinical trials, but inefficient gene transfer in these studies has severely limited the potential of this approach. Here we evaluated HSC gene transfer of an anti-HIV vector in the pigtailed macaque (Macaca nemestrina) model, which closely models human transplantation. Methods and Findings: We used lentiviral vectors that inhibited both HIV-1 and simian immunodeficiency virus (SIV)/HIV-1 (SHIV) chimera virus infection, and also expressed a P140K mutant methylguanine methyltransferase (MGMT) transgene to select gene-modified cells by adding chemotherapy drugs. Following transplantation and MGMT-mediated selection we demonstrated transgene expression in over 7% of stem-cell derived lymphocytes. The high marking levels allowed us to demonstrate protection from SHIV in lymphocytes derived from gene-modified macaque long-term repopulating cells that expressed an HIV-1 fusion inhibitor. We observed a statistically significant 4-fold increase of gene-modified cells after challenge of lymphocytes from one macaque that received stem cells transduced with an anti-HIV vector (p<0.02, Student's t-test), but not in lymphocytes from a macaque that received a control vector. We also established a competitive repopulation assay in a second macaque for preclinical testing of promising anti-HIV vectors. The vectors we used were HIV-based and thus efficiently transduce human cells, and the transgenes we used target HIV-1 genes that are also in SHIV, so our findings can be rapidly translated to the clinic. Conclusions: Here we demonstrate the ability to select protected HSC-derived lymphocytes in vivo in a clinically relevant nonhuman primate model of HIV/SHIV infection. This approach can now be evaluated in human clinical trials in AIDS lymphoma patients. In this patient setting, chemotherapy would not only kill malignant cells, but would also increase the number of MGMTP140K-expressing HIV-resistant cells. This approach should allow for high levels of HIV-protected cells in AIDS patients to evaluate AIDS gene therapy

The most common Chinese rhesus macaque MHC class I molecule shares peptide binding repertoire with the HLA-B7 supertype

Of the two rhesus macaque subspecies used for AIDS studies, the Simian immunodeficiency virus-infected Indian rhesus macaque (Macaca mulatta) is the most established model of HIV infection, providing both insight into pathogenesis and a system for testing novel vaccines. Despite the Chinese rhesus macaque potentially being a more relevant model for AIDS outcomes than the Indian rhesus macaque, the Chinese-origin rhesus macaques have not been well-characterized for their major histocompatibility complex (MHC) composition and function, reducing their greater utilization. In this study, we characterized a total of 50 unique Chinese rhesus macaques from several varying origins for their entire MHC class I allele composition and identified a total of 58 unique complete MHC class I sequences. Only nine of the sequences had been associated with Indian rhesus macaques, and 28/58 (48.3%) of the sequences identified were novel. From all MHC alleles detected, we prioritized Mamu-A1*02201 for functional characterization based on its higher frequency of expression. Upon the development of MHC/peptide binding assays and definition of its associated motif, we revealed that this allele shares peptide binding characteristics with the HLA-B7 supertype, the most frequent supertype in human populations. These studies provide the first functional characterization of an MHC class I molecule in the context of Chinese rhesus macaques and the first instance of HLA-B7 analogy for rhesus macaques