Conditions for compatibility of quantum state assignments

Suppose N parties describe the state of a quantum system by N possibly different density operators. These N state assignments represent the beliefs of the parties about the system. We examine conditions for determining whether the N state assignments are compatible. We distinguish two kinds of procedures for assessing compatibility, the first based on the compatibility of the prior beliefs on which the N state assignments are based and the second based on the compatibility of predictive measurement probabilities they define. The first procedure leads to a compatibility criterion proposed by Brun, Finkelstein, and Mermin [BFM, Phys. Rev. A 65, 032315 (2002)]. The second procedure leads to a hierarchy of measurement-based compatibility criteria which is fundamentally different from the corresponding classical situation. Quantum mechanically none of the measurement-based compatibility criteria is equivalent to the BFM criterion.Comment: REVTEX 4, 19 pages, 1 postscript figur

A novel mutation in isoform 3 of the plasma membrane Ca2+ pump impairs cellular Ca2+ homeostasis in a patient with cerebellar ataxia and laminin subunit 1\u3b1 mutations.

The particular importance of Ca2+ signaling to neurons demands its precise regulation within their cytoplasm. Isoform 3 of the plasma membrane Ca2+ ATPase (the PMCA3 pump), which is highly expressed in brain and cerebellum, plays an important role in the regulation of neuronal Ca2+. A genetic defect of the function of the PMCA3 pump has been described in one family with X-linked congenital cerebellar ataxia. Here we describe a novel mutation of the PMCA3 pump (ATP2B3) in a patient with global developmental delay, generalized hypotonia and cerebellar ataxia. The mutation (a R482H replacement) impairs the Ca2+ ejection function of the pump. It reduces the ability of the pump expressed in model cells to control Ca2+ transients generated by cell stimulation and impairs its Ca2+ extrusion function under conditions of low resting cytosolic Ca2+ as well. In silico analysis of the structural effect of the mutation suggests a reduced stabilization of the portion of the pump surrounding the mutated residue in the Ca2+-bound state. The patient also carries two missense mutations in LAMA1, encoding for laminin subunit 1\u3b1. On the basis of the family pedigree of the patient, the presence of both PMCA3 and LAMA1 mutations appears to be necessary for the development of the disease. Considering the observed defect in cellular Ca2+ homeostasis and the previous finding that PMCAs act as digenic modulators in Ca2+-linked pathologies, the PMCA3 dysfunction along with LAMA1 mutations could act synergistically to cause the neurological phenotype

Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication

We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement. A similar, general condition is also shown for pure and mixed states. These results offer a rare operational interpretation for three abstractly defined distance like measures of multipartite entanglement.Comment: 4 pages, 1 figure. Title changed in accordance with jounral request. Major changes to the paper. Intro rewritten to make motivation clear, and proofs rewritten to be clearer. Picture added for clarit

Maximum Entanglement in Squeezed Boson and Fermion States

A class of squeezed boson and fermion states is studied with particular emphasis on the nature of entanglement. We first investigate the case of bosons, considering two-mode squeezed states. Then we construct the fermion version to show that such states are maximum entangled, for both bosons and fermions. To achieve these results, we demonstrate some relations involving squeezed boson states. The generalization to the case of fermions is made by using Grassmann variables.Comment: 4 page

PR-box correlations have no classical limit

One of Yakir Aharonov's endlessly captivating physics ideas is the conjecture that two axioms, namely relativistic causality ("no superluminal signalling") and nonlocality, so nearly contradict each other that a unique theory - quantum mechanics - reconciles them. But superquantum (or "PR-box") correlations imply that quantum mechanics is not the most nonlocal theory (in the sense of nonlocal correlations) consistent with relativistic causality. Let us consider supplementing these two axioms with a minimal third axiom: there exists a classical limit in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this classical limit, PR-box correlations violate relativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound without assuming quantum mechanics.Comment: for a video of this talk at the Aharonov-80 Conference in 2012 at Chapman University, see quantum.chapman.edu/talk-10, published in Quantum Theory: A Two-Time Success Story (Yakir Aharonov Festschrift), eds. D. C. Struppa and J. M. Tollaksen (New York: Springer), 2013, pp. 205-21

Testing Quantum Dynamics using Signaling

We consider a physical system in which the description of states and measurements follow the usual quantum mechanical rules. We also assume that the dynamics is linear, but may not be fully quantum (i.e unitary). We show that in such a physical system, certain complementary evolutions, namely cloning and deleting operations that give a better fidelity than quantum mechanically allowed ones, in one (inaccessible) region, lead to signaling to a far-apart (accessible) region. To show such signaling, one requires certain two-party quantum correlated states shared between the two regions. Subsequent measurements are performed only in the accessible part to detect such phenomenon.Comment: 4 pages, 2 figures, RevTeX4; v2: published versio

Lineage tree analysis of immunoglobulin variable-region gene mutations in autoimmune diseases: chronic activation, normal selection

Autoimmune diseases show high diversity in the affected organs, clinical manifestations and disease dynamics. Yet they all share common features, such as the ectopic germinal centers found in many affected tissues. Lineage trees depict the diversification, via somatic hypermutation (SHM), of immunoglobulin variable-region (IGV) genes. We previously developed an algorithm for quantifying the graphical properties of IGV gene lineage trees, allowing evaluation of the dynamical interplay between SHM and antigen-driven selection in different lymphoid tissues, species, and disease situations. Here, we apply this method to ectopic GC B cell clones from patients with Myasthenia Gravis, Rheumatoid Arthritis, and Sjögren’s Syndrome, using data scaling to minimize the effects of the large variability due to methodological differences between groups. Autoimmune trees were found to be significantly larger relative to normal controls. In contrast, comparison of the measurements for tree branching indicated that similar selection pressure operates on autoimmune and normal control clones

Bell inequalities for random fields

The assumptions required for the derivation of Bell inequalities are not usually satisfied for random fields in which there are any thermal or quantum fluctuations, in contrast to the general satisfaction of the assumptions for classical two point particle models. Classical random field models that explicitly include the effects of quantum fluctuations on measurement are possible for experiments that violate Bell inequalities.Comment: 18 pages; 1 figure; v4: Essentially the published version; extensive improvements. v3: Better description of the relationship between classical random fields and quantum fields; better description of random field models. More extensive references. v2: Abstract and introduction clarifie

A comparison of resting state functional magnetic resonance imaging to invasive electrocortical stimulation for sensorimotor mapping in pediatric patients

Localizing neurologic function within the brain remains a significant challenge in clinical neurosurgery. Invasive mapping with direct electrocortical stimulation currently is the clinical gold standard but is impractical in young or cognitively delayed patients who are unable to reliably perform tasks. Resting state functional magnetic resonance imaging non-invasively identifies resting state networks without the need for task performance, hence, is well suited to pediatric patients. We compared sensorimotor network localization by resting state fMRI to cortical stimulation sensory and motor mapping in 16 pediatric patients aged 3.1 to 18.6 years. All had medically refractory epilepsy that required invasive electrographic monitoring and stimulation mapping. The resting state fMRI data were analyzed using a previously trained machine learning classifier that has previously been evaluated in adults. We report comparable functional localization by resting state fMRI compared to stimulation mapping. These results provide strong evidence for the utility of resting state functional imaging in the localization of sensorimotor cortex across a wide range of pediatric patients

A critical analysis of Popper's experiment

An experiment which could decide against the Copenhagen interpretation of quantum mechanics has been proposed by K. Popper and, subsequently, it has been criticized by M.J. Collett and R. Loudon. Here we show that both the above mentioned arguments are not correct because they are based on a misuse of basic quantum rules.Comment: 12 pages, 3 figures, RevTex; to be published on PR