Quantum hypergraph states Rossi, M; Huber, M; Bruß, D ...
New journal of physics,
11/2013, Volume:
15, Issue:
11
Journal Article
Peer reviewed
Open access
We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two ...vertices are considered. We derive a generalized stabilizer formalism to describe this class of states. We introduce the notion of k-uniformity and show that this gives rise to classes of states which are inequivalent under the action of the local Pauli group. Finally we disclose a one-to-one correspondence with states employed in quantum algorithms, such as Deutsch-Jozsa's and Grover's.
We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyze the multipartite entanglement properties in the Deutsch-Jozsa, Grover, and ...Simon algorithms. Our results show that for these algorithms most instances involve multipartite entanglement.
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Graph states have been used to construct quantum error correction codes for independent errors. Hypergraph states generalize graph states, and symmetric hypergraph states have been shown to allow for ...the correction of correlated errors. In this paper, it is shown that symmetric hypergraph states are not useful for the correction of independent errors, at least for up to 30 qubits. Furthermore, error correction for error models with protected qubits is explored. A class of known graph codes for this scenario is generalized to hypergraph codes.
We study the entanglement properties of quantum hypergraph states of n qubits, focusing on multipartite entanglement. We compute multipartite entanglement for hypergraph states with a single ...hyperedge of maximum cardinality, for hypergraph states endowed with all possible hyperedges of cardinality equal to n−1 and for those hypergraph states with all possible hyperedges of cardinality greater than or equal to n−1. We then find a lower bound to the multipartite entanglement of a generic quantum hypergraph state. We finally apply the multipartite entanglement results to the construction of entanglement witness operators, able to detect genuine multipartite entanglement in the neighbourhood of a given hypergraph state. We first build entanglement witnesses of the projective type, then propose a class of witnesses based on the stabilizer formalism, hence called stabilizer witnesses, able to reduce the experimental effort from an exponential to a linear growth in the number of local measurement settings with the number of qubits.
1 Department of Nutritional Sciences and Toxicology, University of California at Berkeley, Berkeley; and
2 Children's Hospital Oakland Research Institute, Oakland, California
Submitted 25 August 2009
...; accepted in final form 2 November 2009
Calorie restriction (CR) increases longevity and retards the development of many chronic diseases, but the underlying metabolic signals are poorly understood. Increased fatty acid (FA) oxidation and reduced FA synthesis have been hypothesized to be important metabolic adaptations to CR. However, at metabolic steady state, FA oxidation must match FA intake plus synthesis; moreover, FA intake is low, not high, during CR. Therefore, it is not clear how FA dynamics are altered during CR. Accordingly, we measured food intake patterns, whole body fuel selection, endogenous FA synthesis, and gene expression in mice on CR. Within 2 days of CR being started, a shift to a cyclic, diurnal pattern of whole body FA metabolism occurred, with an initial phase of elevated endogenous FA synthesis respiratory exchange ratio (RER) >1.10, lasting 4–6 h after food provision, followed by a prolonged phase of FA oxidation (RER = 0.70, lasting 18–20 h). CR mice oxidized four times as much fat per day as ad libitum (AL)-fed controls (367 ± 19 vs. 97 ± 14 mg/day, P < O.001) despite reduced energy intake from fat. This increase in FA oxidation was balanced by a threefold increase in adipose tissue FA synthesis compared with AL. Expression of FA synthase and acetyl-CoA carboxylase mRNA were increased in adipose and liver in a time-dependent manner. We conclude that CR induces a surprising metabolic pattern characterized by periods of elevated FA synthesis alternating with periods of FA oxidation disproportionate to dietary FA intake. This pattern may have implications for oxidative damage and disease risk.
fat synthesis; lipogenesis; palmitoleate; heavy water
Address for reprint requests and other correspondence: M. D. Bruss, Dept. of Nutritional Sciences and Toxicology, Univ. of California at Berkeley, Morgan Hall, Rm. 309, Berkeley, CA 94720-3104 (e-mail: mattbruss{at}berkeley.edu ).
We study optimal eavesdropping in quantum cryptography with three-dimensional systems, and show that this scheme is more secure against symmetric attacks than protocols using two-dimensional states. ...We generalize the according eavesdropping transformation to arbitrary dimensions, and discuss the connection with optimal quantum cloning.
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We consider a subclass of bipartite CHSH-type Bell inequalities. We investigate operations which leave their Tsirelson bound invariant, but change their classical bound. The optimal observables are ...unaffected except for a relative rotation of the two laboratories. We illustrate the utility of these operations by giving explicit examples. We prove that, for a fixed quantum state and fixed measurement setup except for a relative rotation of the two laboratories, there is a Bell inequality that is maximally violated for this rotation, and we optimize some Bell inequalities with respect to the maximal violation. Finally, we optimize the qutrit to qubit ratio of some dimension witnessing Bell inequalities. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to '50 years of Bell's theorem'.
We introduce a classification of mixed three-qubit states, in which we define the classes of separable, biseparable, W, and Greenberger-Horne-Zeilinger states. These classes are successively embedded ...into each other. We show that contrary to pure W-type states, the mixed W class is not of measure zero. We construct witness operators that detect the class of a mixed state. We discuss the conjecture that all entangled states with positive partial transpose (PPTES) belong to the W class. Finally, we present a new family of PPTES "edge" states with maximal ranks.
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Increased Phosphorylation of Akt Substrate of 160 kDa (AS160) in Rat Skeletal Muscle in Response to Insulin or Contractile
Activity
Matthew D. Bruss 1 ,
Edward B. Arias 2 ,
Gustav E. Lienhard 3 and
...Gregory D. Cartee 2
1 Department of Kinesiology, University of Wisconsin-Madison, Madison, Wisconsin
2 Division of Kinesiology, University of Michigan, Ann Arbor, Michigan
3 Department of Biochemistry, Dartmouth Medical School, Hanover, New Hampshire
Address correspondence and reprint requests to Gregory D. Cartee, PhD, University of Michigan Kinesiology, Rm. 3040E, 401
Washtenaw Ave., Ann Arbor, MI 48109-2214. E-mail: gcartee{at}umich.edu
Abstract
In 3T3-L1 adipocytes, insulin-stimulated GLUT4 translocation requires phosphorylation of the protein designated Akt substrate
of 160 kDa (AS160). Both insulin and contractions activate Akt in skeletal muscle. Therefore, we assessed the effects in skeletal
muscle of each stimulus on phosphorylation of proteins, including AS160, on the Akt phosphomotif. Isolated rat epitrochlearis
muscles were incubated with insulin (for time course and dose response), stimulated to contract, or incubated with 5-aminoimidazole-4-carboxamide-1-β- d -ribofuranoside (AICAR) and used to assess the following: serine-phosphorylation of Akt (P-Akt), immunoreactivity with an
antibody recognizing the Akt phosphomotif (α-phospho-Ser/Thr Akt substrate PAS), and PAS immunoreactivity of samples immunoprecipitated
with anti-AS160. P-Akt peaked at 5 min of insulin, and PAS immunoreactivity subsequently peaked for proteins of 250 kDa (10
min) and 160 kDa (15 min). P-Akt, PAS-160, and PAS-250 increased significantly with 0.6 nmol/l insulin. Contractile activity
led to increased P-Akt and PAS immunoreactivity of proteins of 160 and 250 kDa. The 160-kDa protein was confirmed to be AS160
based on elevated PAS immunoreactivity in AS160 immunoprecipitates. Wortmannin inhibited insulin (120 nmol/l) and contraction
effects on AS160 phosphorylation. Incubation with AICAR caused increased phosphorylation of AMP-activated protein kinase and
AS160 but not Akt. Our working hypothesis is that phosphorylation of these putative Akt substrates is important for some of
the insulin and contraction bioeffects.
AICAR, 5-aminoimidazole-4-carboxamide-1-β-d-ribofuranoside
AS160, Akt substrate of 160 kDa
KHB, Krebs-Henseleit buffer
PAS, phospho-(Ser/Thr) Akt substrate
PI, phosphatidylinositol
TBST, Tris-buffered saline plus Tween
Footnotes
The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore
be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Accepted October 4, 2004.
Received March 23, 2004.
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