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In this paper, we construct the metric tensor and volume for the manifold of purifications associated with an arbitrary reduced density operator $\rho_S$. We also define a quantum coarse-graining (CG) to study the volume where macrostates are the manifolds of purifications, which we call surfaces of ignorance (SOI), and microstates are the purifications of $\rho_S$. In this context, the volume functions as a multiplicity of the macrostates that quantifies the amount of information missing from $\rho_S$. Using examples where the SOI are generated using representations of $SU(2)$, $SO(3)$, and $SO(N)$, we show two features of the CG. (1) A system beginning in an atypical macrostate of smaller volume evolves to macrostates of greater volume until it reaches the equilibrium macrostate in a process in which the system and environment become strictly more entangled, and (2) the equilibrium macrostate takes up the vast majority of the coarse-grainied space especially as the dimension of the total system becomes large. Here, the equilibrium macrostate corresponds to maximum entanglement between system and environment. To demonstrate feature (1) for the examples considered, we show that the volume behaves like the von Neumann entropy in that it is zero for pure states, maximal for maximally mixed states, and is a concave function w.r.t the purity of $\rho_S$. These two features are essential to typicality arguments regarding thermalization and Boltzmann's original CG., Comment: 12 pages, 10 figures. arXiv admin note: text overlap with arXiv:2111.07836

It is recognized that Grover arrived at his original quantum search algorithm inspired by his comprehension of the interference of classical waves originating from an array of antennas. It is also known that quantum-mechanical characterization of electromagnetic radiation is isomorphic to the treatment of the orientation of a spin-1/2 particle. In this paper, motivated by Grover's original intuition and starting from this mathematical equivalence, we present a quantitative link between the geometry of time-independent optimal-speed Hamiltonian evolutions on the Bloch sphere and the geometry of intensity-preserving propagation of light with maximal degree of coherence on the Poincar\'e sphere. Finally, identifying interference as the fundamental physical ingredient underlying both physical phenomena, we propose that our work can provide in retrospect a quantitative geometric background underlying Grover's powerful intuition., Comment: 22 pages, 1 figure, 3 tables

In the paper by Weedbrook et. al,1 a post-selected model of Lloyd's original formulation of quantum illumination (QI)2 was used to show that quantum discord explains the underlying advantage of QI over conventional illumination. The same model was used by Ray et. al3 to show that the normalized Hilbert-Schmidt inner product (HSIP) is a valid distinguishability measure when analyzing quantum illumination. This post-selected model assumes that the detector always detects a photon whether it be from the signal or noise from the environment; thus, the vacuum is excluded from this model. In this paper, we include the vacuum back into these analyses. In the case of,1 we show that the conclusion is unaffected by the inclusion of the vacuum. We then analyze the effects of including the vacuum when distinguishing between a noisy signal and noise. In this analysis, we found that the normalized HSIP is not monotonic with respect to the parameter that controls the brightness of the noise. Because of this, the normalized Hilbert-Schmidt inner product cannot be used as a distinguishability as was seen in the post-selected model. To reconcile this problem, we used the proposed alternative fidelity measure defined in,4 and found that it is monotonic in the vacuum added model for all the examples considered.

We use geometric concepts originally proposed by Anandan and Aharonov to show that the Farhi-Gutmann time optimal analog quantum search evolution between two orthogonal quantum states is characterized by unit efficiency dynamical trajectories traced on a projective Hilbert space. In particular, we prove that these optimal dynamical trajectories are the shortest geodesic paths joining the initial and the final states of the quantum evolution. In addition, we verify they describe minimum uncertainty evolutions specified by an uncertainty inequality that is tighter than the ordinary time-energy uncertainty relation. We also study the effects of deviations from the time optimality condition from our proposed Riemannian geometric perspective. Furthermore, after pointing out some physically intuitive aspects offered by our geometric approach to quantum searching, we mention some practically relevant physical insights that could emerge from the application of our geometric analysis to more realistic time-dependent quantum search evolutions. Finally, we briefly discuss possible extensions of our work to the geometric analysis of the efficiency of thermal trajectories of relevance in quantum computing tasks., 14 pages, 1 figure, 1 table

We show how to quantify tri-partite entanglement using entropies derived from experimental correlations. We use a multi-partite generalization of the entanglement of formation that is greater than zero if and only if the state is genuinely multi-partite entangled. We develop an entropic witness for tripartite entanglement, and show that the degree of violation of this witness places a lower limit on the tripartite entanglement of formation. We test our results in the three-qubit regime using the GHZ-Werner state and the W-Werner state, and in the high-dimensional pure-state regime using the triple-Gaussian wavefunction describing the spatial and energy-time entanglement in photon triplets generated in third-order spontaneous parametric down-conversion. In addition, we discuss the challenges in quantifying the entanglement for progressively larger numbers of parties, and give both entropic and target-state-based witnesses of multi-partite entanglement that circumvent this issue., 14 pages, 6 figures (removed inequality (formerly appendix B4) due to typo)

Quantum Illumination (QI)1 is a proposed remote targeting protocol using entangled states in which the experimenter sends a signal towards an expected target in a noisy environment that has a probability of reflecting off the surface or, in the case of no surface, being lost. Upon return, the noisy signal is jointly measured with the idler, which has been held in local memory, to determine if the surface has been detected. The idler effectively increases the brightness of the noisy signal to help distinguish it from the surrounding noise. Even though the returned mixed state is in the un-entangled regime, it has been shown that QI outperforms a conventional protocol that only sends separable states as the signal. We analyzed QI as a quantum channel discrimination protocol and circumvented computational issues that rely on diagonalization of the quantum states by using the normalized Hilbert-Schmidt (NH-S) inner product as a measure of state distinguishability.2 Because the NH-S inner product is simple to compute, for a choice of entangled pure state and bipartition, we were able to rank the performance of QI entirely in terms of the dimension of the composite Hilbert space and the purity of the idler subsystem. We also showed that the greatest advantage gained by quantum illumination over conventional illumination occurs when one uses a Bell state, and for a fixed dimension d, the optimal performance of QI is achieved when the purity of the idler subsystem is minimal. In this talk, we review the results of,2 and present our progress on extending this analysis to a broader class of quantum information protocols beyond QI.

Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another. Computing the error probability directly requires complete knowledge and diagonalization of the density matrices describing these states. Both of these fundamental requirements become impractically difficult to obtain as the dimension of the states grow large. In this article, we analyze quantum illumination as a quantum channel discrimination protocol and circumvent these issues by using the normalized Hilbert-Schmidt inner product as a measure of distinguishability. Using this measure, we show that the greatest advantage gained by quantum illumination over conventional illumination occurs when one uses a Bell state., Comment: 6 pages, 1 figure

There exist constant radial surfaces, $\mathcal{S}$, that may not be globally embeddable in $\mathbb{R}^3$ for Kerr spacetimes with $a>\sqrt{3}M/2$. To compute the Brown and York (B-Y) quasi-local energy (QLE), one must isometrically embed $\mathcal{S}$ into $\mathbb{R}^3$. On the other hand, the Wang and Yau (W-Y) QLE embeds $\mathcal{S}$ into Minkowski space. In this paper, we examine the W-Y QLE for surfaces that may or may not be globally embeddable in $\mathbb{R}^3$. We show that their energy functional, $E[\tau]$, has a critical point at $\tau=0$ for all constant radial surfaces in $t=constant$ hypersurfaces using Boyer-Lindquist coordinates. For $\tau=0$, the W-Y QLE reduces to the B-Y QLE. To examine the W-Y QLE in these cases, we write the functional explicitly in terms of $\tau$ under the assumption that $\tau$ is only a function of $\theta$. We then use a Fourier expansion of $\tau\left(\theta\right)$ to explore the values of $E[\tau\left(\theta\right)]$ in the space of coefficients. From our analysis, we discovered an open region of complex values for $E[\tau\left(\theta\right)]$. We also study the physical properties of the smallest real value of $E[\tau\left(\theta\right)]$, which lies on the boundary separating real and complex energies., Comment: 25 pages, 10 figures

Hamilton’s Ricci flow (RF) equations were recently expressed in terms of the edge lengths of a d-dimensional piecewise linear (PL) simplicial geometry, for d ≥ 2. The structure of the simplicial Ricci flow (SRF) equations are dimensionally agnostic. These SRF equations were tested numerically and analytically in 3D for simple models and reproduced qualitatively the solution of continuum RF equations including a Type-1 neckpinch singularity. Here we examine a continuum limit of the SRF equations for 3D neck pinch geometries with an arbitrary radial profile. We show that the SRF equations converge to the corresponding continuum RF equations as reported by Angenent and Knopf.

The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as a fractional rate of change of the normal vector.

There are many applications in use today, that are driven by a command line interface, rather than a graphical interface. Most of these applications are robust, popular and proven in general usage. The convenience and ease of use that a graphical interface provides might make these applications available to a wider range of users. Previous approaches for integrating a graphical interface into command driven software have focused on using a pipe variation to negotiate communication between two processes. The advantage of using a pipe is that communication can be established without knowledge of the source code for the command driven application; the disadvantages are that, the linkage can be slow and for some large applications, the system may stall. In this work, we describe a technique that exploits ostreams and subtyping to integrate a graphical interface into a command driven application. The technique we propose does not create a new process to construct the communication linkage nor does it require a sentinel to terminate the linkage. We use this technique to integrate a graphical interface into legacy code and a grader program that maintains a list of student grades. The grader program is coded in C++, exploits the Command and Envelope-Letter patterns, and uses the standard library containers, algorithms, and iterators to implement much of its functionality.

We examine a Type-1 neck pinch singularity in simplicial Ricci flow (SRF) for an axisymmetric piecewise flat 3-dimensional geometry with 3-sphere topology. SRF was recently introduced as an unstructured mesh formulation of Hamilton's Ricci flow (RF). It describes the RF of a piecewise-flat simplicial geometry. In this paper, we apply the SRF equations to a representative double-lobed axisymmetric piecewise flat geometry with mirror symmetry at the neck similar to the geometry studied by Angenent and Knopf (A-K). We choose a specific radial profile and compare the SRF equations with the corresponding finite-difference solution of the continuum A-K RF equations. The piecewise-flat 3-geometries considered here are built of isosceles-triangle-based frustum blocks. The axial symmetry of this model allows us to use frustum blocks instead of tetrahedra. The 2-sphere cross-sectional geometries in our model are regular icosahedra. We demonstrate that, under a suitably-pinched initial geometry, the SRF equations for this relatively low-resolution discrete geometry yield the canonical Type-1 neck pinch singularity found in the corresponding continuum solution. We adaptively remesh during the evolution to keep the circumcentric dual lattice well-centered. Without such remeshing, we cannot evolve the discrete geometry to neck pinch. We conclude with a discussion of future generalizations and tests of this SRF model., Comment: 15 pages, 7 figures, submitted to Geometry, Imaging and Computation, minor revisions

Background: The beta-amyloid (Aβ) peptide comprises the amyloid plaques that characterise Alzheimer's disease (AD), and is thought to significantly contribute towards disease pathogenesis. Oxidative stress is elevated in the AD brain, and there is substantial evidence that the interaction between Aβ and redox-active copper is a major contributing factor towards oxidative stress in AD. Results: The major findings of this study are that redox-active Cu(II)–Aβ causes pronounced axonal pathology in long-term neuronal cultures, including axonal fragmentation and the formation of hyperphosphorylated tau-immunoreactive axonal swellings. Notably, MAP-2 expressing dendritic processes remain largely un-affected by Cu(II)–Aβ treatment. These dystrophic axonal manifestations resemble some of the characteristic neuritic pathology of the AD brain. We show that Cu(II)–Aβ directly causes formation of intra-axonal swellings via the generation of free radicals and subsequent efflux of K + out of neurons. Conclusion: In summary, we report that redox-active Cu(II)–Aβ can induce substantial neurodegenerative changes in mature neurons, and may have an important role to play in the slowly progressing pathogenesis of AD.

BackgroundOne of the key pathological features of AD is the formation of insoluble amyloid plaques. The major constituent of these extracellular plaques is the beta-amyloid peptide (Aβ), although Aβ is also found to accumulate intraneuronally in AD. Due to the slowly progressive nature of the disease, it is likely that neurons are exposed to sublethal concentrations of both intracellular and extracellular Aβ for extended periods of time.ResultsIn this study, we report that daily exposure to a sublethal concentration of Aβ(1-40) (1 µM) for six days induces substantial apoptosis of cortical neurons cultured from Tg2576 mice (which express substantial but sublethal levels of intracellular Aβ). Notably, untreated Tg2576 neurons of similar age did not display any signs of apoptosis, indicating that the level of intracellular Aβ present in these neurons was not the cause of toxicity. Furthermore, wildtype neurons did not become apoptotic under the same chronic Aβ(1-40) treatment. We found that this apoptosis was linked to Tg2576 neurons being unable to maintain K(+) homeostasis following Aβ treatment. Furthermore, blocking K(+) efflux protected Tg2576 neurons from Aβ-induced neurotoxicity. Interestingly, chronic exposure to 1 µM Aβ(1-40) caused the generation of axonal swellings in Tg2576 neurons that contained dense concentrations of hyperphosphorylated tau. These were not observed in wildtype neurons under the same treatment conditions.ConclusionsOur data suggest that when neurons are chronically exposed to sublethal levels of both intra- and extra-cellular Aβ, this causes a K(+)-dependent neurodegeneration that has pathological characteristics similar to AD.

Nuclear factor kappaB (NFκB) is a key transcriptional regulator of inflammatory genes. We investigated the modulatory effects of olfactory ensheathing cells (OECs), microglia and meningeal fibroblasts on translocation of NFκB to astrocyte nuclei. The percentage of activated astrocytes in co-cultures with OECs was significantly less than for co-cultures with microglia (p

Whether a well is being re-entered, after having been abandoned for some time or it simply needs to be repaired to be functional, many operators choose to cement a new smaller outside diameter (OD) casing string inside the old one. Wells previously abandoned have been re-evaluated and found to respond to fracture stimulation using newer methods; however, to accomplish this, the casing string must have integrity. Casing integrity is also of significance to operators in view of state regulations. The challenges of this type of operation are many. One of these is to avoid excessive surge pressures while running the new casing and means that on many occasions running rates of the casing may have to be approximately 1 foot per second. Excessive surge pressure can fracture a formation of interest, making it difficult to obtain the desired production rates. Another challenge is to match casing size for stimulation with achieving successful cement isolation of an annular space. Smaller diameter casing will result in increased friction pressure and therefore treatment rate restrictions. Stimulation may require multistage completions to be effective. The increased cost of stimulation must be balanced with the need to achieve cement isolation. Presented are the analyses of various scenarios examining fracture gradient, old casing burst pressures, fracture stimulation rates and pressures and equivalent circulating densities of potential cement slurries. Case histories are used to illustrate these scenarios and present situations in which the cost of the cement pumped versus what should have been required is compared. Also presented, are the operational and cost differences regarding stimulation as a function of casing internal diameter. In one case over three times the quantity cement, which should have been necessary to achieve circulation back to surface, was pumped without circulating.

The RUNX1 gene, which is essential for normal hematopoiesis, is frequently rearranged by the t(8;21) chromosomal translocation in acute myeloid leukemia. The resulting RUNX1-ETO fusion protein contributes to leukemic progression by directing aberrant association of transcriptional cofactors and epigenetic modifiers to RUNX1 target genes. For example, the GM-CSF gene is activated by RUNX1, but is repressed by RUNX1-ETO. Here we show that RUNX1 normally cooperates with the histone acetyltransferase, CBP, to regulate GM-CSF expression at two levels. Firstly, it directs the establishment of a competent chromatin environment at the GM-CSF promoter prior to gene activation. It then participates in the transcriptional activation of the promoter in response to immune stimuli. In contrast, RUNX1-ETO, which cannot associate with CBP, is unable to transactivate the GM-CSF promoter and is associated with the generation of a repressive chromatin environment at the promoter.

Following central nervous system injury, astrocytes rapidly respond by undergoing a stereotypical pattern of molecular and morphological alterations termed "reactive" astrogliosis. We have reported previously that metallothioneins (MTs) are rapidly expressed by reactive astrocytes and that their secretion and subsequent interaction with injured neurons leads to improved neuroregeneration. We now demonstrate that exogenous MT induces a reactive morphology and elevated GFAP expression in cultured astrocytes. Furthermore, these astrogliotic hallmarks were mediated via JAK/STAT and RhoA signalling pathways. However, rather than being inhibitory, MT induced a form of astrogliosis that was permissive to neurite outgrowth and which was associated with decreased chondroitin sulphate proteoglycan (CSPG) expression. The results suggest that MT has an important role in mediating permissive astrocytic responses to traumatic brain injury.

BACKGROUND: A major pathological hallmark of AD is the deposition of insoluble extracellular beta-amyloid (Abeta) plaques. There are compelling data suggesting that Abeta aggregation is catalysed by reaction with the metals zinc and copper. METHODOLOGY/PRINCIPAL FINDINGS: We now report that the major human-expressed metallothionein (MT) subtype, MT-2A, is capable of preventing the in vitro copper-mediated aggregation of Abeta1-40 and Abeta1-42. This action of MT-2A appears to involve a metal-swap between Zn7MT-2A and Cu(II)-Abeta, since neither Cu10MT-2A or carboxymethylated MT-2A blocked Cu(II)-Abeta aggregation. Furthermore, Zn7MT-2A blocked Cu(II)-Abeta induced changes in ionic homeostasis and subsequent neurotoxicity of cultured cortical neurons. CONCLUSIONS/SIGNIFICANCE: These results indicate that MTs of the type represented by MT-2A are capable of protecting against Abeta aggregation and toxicity. Given the recent interest in metal-chelation therapies for AD that remove metal from Abeta leaving a metal-free Abeta that can readily bind metals again, we believe that MT-2A might represent a different therapeutic approach as the metal exchange between MT and Abeta leaves the Abeta in a Zn-bound, relatively inert form.