Correlations in excited states of local Hamiltonians

Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix)

From Ground States to Local Hamiltonians

Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space, by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles.Comment: 11 pages, 2 figures, to be published in PR

No-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems

One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to implement, the preparation of the resource state becomes a crucial task. An appealing approach is simply to cool a strongly correlated quantum many-body system to its ground state. In addition to requiring the ground state of the system to be universal for one-way quantum computing, we also want the Hamiltonian to have non-degenerate ground state protected by a fixed energy gap, to involve only two-body interactions, and to be frustration-free so that measurements in the course of the computation leave the remaining particles in the ground space. Recently, significant efforts have been made to the search of resource states that appear naturally as ground states in spin lattice systems. The approach is proved to be successful in spin-5/2 and spin-3/2 systems. Yet, it remains an open question whether there could be such a natural resource state in a spin-1/2, i.e., qubit system. Here, we give a negative answer to this question by proving that it is impossible for a genuinely entangled qubit states to be a non-degenerate ground state of any two-body frustration-free Hamiltonian. What is more, we prove that every spin-1/2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states, a stronger result that is interesting independent of the context of one-way quantum computing.Comment: 5 pages, 1 figur

Ground-State Spaces of Frustration-Free Hamiltonians

We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of `reduced spaces' to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\Theta_k$ and discuss its relationship with ground states of $k$-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in $\Theta_2$ are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in $\Theta_k$ may not be the join of atoms, indicating a richer structure for $\Theta_k$ beyond the convex structure. Our study of $\Theta_k$ deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from a new angle of reduced spaces.Comment: 23 pages, no figur

The calcilytic agent NPS 2143 rectifies hypocalcemia in a mouse model with an activating calcium-sensing-receptor (CaSR) mutation:relevance to autosomal dominant hypocalcemia type 1 (ADH1)

Autosomal dominant hypocalcemia type 1 (ADH1) is caused by germline gain-of-function mutations of the calcium-sensing receptor (CaSR) and may lead to symptomatic hypocalcemia, inappropriately low serum parathyroid hormone (PTH) concentrations and hypercalciuria. Negative allosteric CaSR modulators, known as calcilytics, have been shown to normalise the gain-of-function associated with ADH-causing CaSR mutations in vitro and represent a potential targeted therapy for ADH1. However, the effectiveness of calcilytic drugs for the treatment of ADH1-associated hypocalcemia remains to be established. We have investigated NPS 2143, a calcilytic compound, for the treatment of ADH1 by in vitro and in vivo studies involving a mouse model, known as Nuf, which harbors a gain-of-function CaSR mutation, Leu723Gln. Wild-type (Leu723) and Nuf mutant (Gln723) CaSRs were expressed in HEK293 cells and the effect of NPS 2143 on their intracellular calcium responses determined by flow cytometry. NPS 2143 was also administered as a single intraperitoneal bolus to wild-type and Nuf mice and plasma concentrations of calcium and PTH, and urinary calcium excretion measured. In vitro administration of NPS 2143 decreased the intracellular calcium responses of HEK293 cells expressing the mutant Gln723 CaSR in a dose-dependent manner, thereby rectifying the gain-of-function associated with the Nuf mouse CaSR mutation. Intraperitoneal injection of NPS 2143 in Nuf mice led to significant increases in plasma calcium and PTH without elevating urinary calcium excretion. These studies of a mouse model with an activating CaSR mutation demonstrate NPS 2143 to normalize the gain-of-function causing ADH1, and improve the hypocalcemia associated with this disorder

Identification of genes expressed by immune cells of the colon that are regulated by colorectal cancer-associated variants.

A locus on human chromosome 11q23 tagged by marker rs3802842 was associated with colorectal cancer (CRC) in a genome-wide association study; this finding has been replicated in case-control studies worldwide. In order to identify biologic factors at this locus that are related to the etiopathology of CRC, we used microarray-based target selection methods, coupled to next-generation sequencing, to study 103 kb at the 11q23 locus. We genotyped 369 putative variants from 1,030 patients with CRC (cases) and 1,061 individuals without CRC (controls) from the Ontario Familial Colorectal Cancer Registry. Two previously uncharacterized genes, COLCA1 and COLCA2, were found to be co-regulated genes that are transcribed from opposite strands. Expression levels of COLCA1 and COLCA2 transcripts correlate with rs3802842 genotypes. In colon tissues, COLCA1 co-localizes with crystalloid granules of eosinophils and granular organelles of mast cells, neutrophils, macrophages, dendritic cells and differentiated myeloid-derived cell lines. COLCA2 is present in the cytoplasm of normal epithelial, immune and other cell lineages, as well as tumor cells. Tissue microarray analysis demonstrates the association of rs3802842 with lymphocyte density in the lamina propria (p = 0.014) and levels of COLCA1 in the lamina propria (p = 0.00016) and COLCA2 (tumor cells, p = 0.0041 and lamina propria, p = 6 × 10(-5)). In conclusion, genetic, expression and immunohistochemical data implicate COLCA1 and COLCA2 in the pathogenesis of colon cancer. Histologic analyses indicate the involvement of immune pathways

HiTrust: building cross-organizational trust relationship based on a hybrid negotiation tree

Small-world phenomena have been observed in existing peer-to-peer (P2P) networks which has proved useful in the design of P2P file-sharing systems. Most studies of constructing small world behaviours on P2P are based on the concept of clustering peer nodes into groups, communities, or clusters. However, managing additional multilayer topology increases maintenance overhead, especially in highly dynamic environments. In this paper, we present Social-like P2P systems (Social-P2Ps) for object discovery by self-managing P2P topology with human tactics in social networks. In Social-P2Ps, queries are routed intelligently even with limited cached knowledge and node connections. Unlike community-based P2P file-sharing systems, we do not intend to create and maintain peer groups or communities consciously. In contrast, each node connects to other peer nodes with the same interests spontaneously by the result of daily searches

Modelling Survival Events with Longitudinal Covariates Measured with Error

In survival analysis, time-dependent covariates are usually present as longitudinal data collected periodically and measured with error. The longitudinal data can be assumed to follow a linear mixed effect model and Cox regression models may be used for modelling of survival events. The hazard rate of survival times depends on the underlying time-dependent covariate measured with error, which may be described by random effects. Most existing methods proposed for such models assume a parametric distribution assumption on the random effects and specify a normally distributed error term for the linear mixed effect model. These assumptions may not be always valid in practice. In this article, we propose a new likelihood method for Cox regression models with error-contaminated time-dependent covariates. The proposed method does not require any parametric distribution assumption on random effects and random errors. Asymptotic properties for parameter estimators are provided. Simulation results show that under certain situations the proposed methods are more efficient than the existing methods. © 2013 Copyright Taylor and Francis Group, LLC

Can initial vaginal bleeding patterns in etonogestrel implant users predict subsequent bleeding in the first 2 years of use?

ObjectivesTo evaluate if a simple method for characterizing vaginal bleeding patterns in etonogestrel contraceptive implant users can predict subsequent patterns and bleeding-related discontinuation over the first 2 years of use.Study designWe reanalyzed phase 3 study bleeding data for non-breastfeeding participants from the United States, Europe, Russia and Chile during the first 2 years of implant use to characterize and correlate bleeding patterns. We used 90-day reference periods with period 1.1 starting at Day 29 and ending at Day 118. We dichotomized bleeding patterns as "favorable" (amenorrhea, infrequent bleeding and normal frequency bleeding without prolonged bleeding) or "unfavorable' (prolonged and/or frequent bleeding) and tracked user groups based on these bleeding patterns in reference period 1.1 through Year 1 and from Year 1 through Year 2, respectively.ResultsWe evaluated data from 537 and 428 women with up to 1 and 2 years use, respectively. Of the 325 (60.5%) women with favorable bleeding in reference period 1.1, 275 (84.6%) reported favorable bleeding also in reference period 2, 197 (60.6%) reported favorable bleeding throughout Year 1, and favorable bleeding in 75-85% of reference periods in Year 2. Among 212 (39.5%) women with unfavorable bleeding in reference period 1.1, 118 (55.7%) continued with unfavorable bleeding in reference period 2, while about 40%-50% reported favorable patterns in RP 2, 3 and/or 4. Initial favorable bleeding resulted in lower discontinuation rates than initial unfavorable bleeding in years 1 (3.7% vs 12.7%, p≪.0001) and 2 (2.5% vs 16.5%, p≪.0001).ConclusionImplant users with favorable bleeding in the first reference period are likely to continue with favorable bleeding over the next 2 years. Initial bleeding patterns predict overall continuation rates in years 1 and 2. Implications Statement When evaluating vaginal bleeding in any 90-day reference period over 2 years of etonogestrel implant use, approximately 80% of women with favorable and 40% with unfavorable bleeding patterns will have favorable bleeding in the next reference periods. These findings can facilitate counseling regarding bleeding for women using the etonogestrel implant