scholarly journals Witnessing Wigner Negativity

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 471
Author(s):  
Ulysse Chabaud ◽  
Pierre-Emmanuel Emeriau ◽  
Frédéric Grosshans

Negativity of the Wigner function is arguably one of the most striking non-classical features of quantum states. Beyond its fundamental relevance, it is also a necessary resource for quantum speedup with continuous variables. As quantum technologies emerge, the need to identify and characterize the resources which provide an advantage over existing classical technologies becomes more pressing. Here we derive witnesses for Wigner negativity of single mode and multimode quantum states, based on fidelities with Fock states, which can be reliably measured using standard detection setups. They possess a threshold expectation value indicating whether the measured state has a negative Wigner function. Moreover, the amount of violation provides an operational quantification of Wigner negativity. We phrase the problem of finding the threshold values for our witnesses as an infinite-dimensional linear optimisation. By relaxing and restricting the corresponding linear programs, we derive two hierarchies of semidefinite programs, which provide numerical sequences of increasingly tighter upper and lower bounds for the threshold values. We further show that both sequences converge to the threshold value. Moreover, our witnesses form a complete family – each Wigner negative state is detected by at least one witness – thus providing a reliable method for experimentally witnessing Wigner negativity of quantum states from few measurements. From a foundational perspective, our findings provide insights on the set of positive Wigner functions which still lacks a proper characterisation.

Author(s):  
L. García-Álvarez ◽  
A. Ferraro ◽  
G. Ferrini

Abstract In this work, we study the Wigner phase-space representation of qubit states encoded in continuous variables (CV) by using the Gottesman–Kitaev–Preskill (GKP) mapping. We explore a possible connection between resources for universal quantum computation in discrete-variable (DV) systems, i.e. non-stabilizer states, and negativity of the Wigner function in CV architectures, which is a necessary requirement for quantum advantage. In particular, we show that the lowest Wigner logarithmic negativity corresponds to encoded stabilizer states, while the maximum negativity is associated with the most non-stabilizer states, H-type and T-type quantum states.


2015 ◽  
Vol 781 ◽  
pp. 379-383
Author(s):  
Warut Suampun

A numerical study of the widely used fixed-threshold criterion for expressing transient stability constraints in optimal power flow (TSCOPF) is conducted. Based on a stability-region framework, a more accurate expression of transient stability constraint in TSCOPF is presented. A method for computing system exact threshold values is proposed and employed for the study of threshold values under different conditions. It is shown via numerical results on the WSCC9 and IEEE145 systems that the exact threshold value for each system and contingency is in fact not a constant, and can vary greatly depending on several factors such as types of contingency, loading conditions, and network topology.


2011 ◽  
Vol 24 (23) ◽  
pp. 5968-5997 ◽  
Author(s):  
Michael G. McGauley ◽  
David S. Nolan

Abstract As the climate changes, the ability to predict changes in the frequency of tropical cyclogenesis is becoming of increasing interest. A unique approach is proposed that utilizes threshold values in potential intensity, wind shear, vorticity, and normalized saturation deficit. Prior statistical methods generally involve creating an index or equation based on averages of important meteorological parameters for a given region. The new method assumes that threshold values exist for each important parameter for which cyclogenesis is unlikely to develop. This technique is distinct from previous approaches that seek to determine how each of these parameters interdependently favors cyclogenesis. To determine three of the individual threshold values (shear, potential intensity, and vorticity), an idealized climate is first established that represents the most advantageous but realistic (MABR) environment. An initial numerical simulation of tropical cyclone genesis in the MABR environment confirms that it is highly favorable for cyclogenesis. Subsequent numerical simulations vary each parameter individually until no tropical cyclone develops, thereby determining the three threshold values. The new method of point downscaling, whereby background meteorological features are represented by a single vertical profile, is used in the simulations to greatly simplify the approach. The remaining threshold parameter (normalized saturation deficit) is determined by analyzing the climatological record and choosing a value that is statistically observed to prevent cyclogenesis. Once each threshold value is determined, the fraction of time each is exceeded in the location of interest is computed from the reanalysis dataset. The product of each fraction for each of the relevant parameters then gives a statistical probability as to the likelihood of cyclogenesis. For predicting regional and monthly variations in frequency of genesis, this approach is shown to generally meet or exceed the predictive skills of earlier statistical attempts with some failure only during several off-season months. This method also provides a more intuitive rationale of the results.


2018 ◽  
Vol 60 (3) ◽  
pp. 382-387 ◽  
Author(s):  
Qingqiang Zhu ◽  
Wenrong Zhu ◽  
Jing Ye ◽  
Jingtao Wu ◽  
Wenxin Chen ◽  
...  

Background Few studies have reported on the use of intravoxel incoherent motion (IVIM) for renal tumors. Purpose To investigate the value of IVIM for distinguishing renal tumors. Material and Methods Thirty-one patients with clear cell renal cell carcinomas (CCRCCs), 13 patients with renal angiomyolipomas with minimal fat (RAMFs), eight patients with chromophobe renal cell carcinomas (ChRCCs), and ten patients with papillary renal cell carcinomas (PRCCs) were examined. The tissue diffusivity (D), pseudodiffusivity (D*), and perfusion fraction (f) were calculated. Results The D and f values were highest for CCRCCs, lowest for PRCCs, and intermediate for ChRCCs and RAMFs ( P < 0.05). The D values of CCRCCs differed significantly from those of ChRCCs and PRCCs ( P < 0.05). The D* values were highest for RAMFs, lowest for ChRCCs, and intermediate for CCRCCs and PRCCs ( P < 0.05). Statistically significant differences were observed between the D* values of CCRCCs and RAMFs ( P < 0.05). The D* values of the CCRCCs differed significantly from the D* values of the ChRCCs ( P < 0.05). Using the D and f values of 1.10 and 0.41, respectively, as the threshold values for differentiating CCRCCs from RAMFs, ChRCCs, and PRCCs, the best results had sensitivities of 81.0% and 66.8% and specificities of 85.7% and 81.0%, respectively. Using the D* value of 0.038 as the threshold value for differentiating RAMFs from CCRCCs, ChRCCs, and PRCCs, the best result obtained had a sensitivity of 90.5% and specificity of 76.2%. Conclusion IVIM may provide information for differentiating renal tumor types.


2011 ◽  
Vol 31 (9) ◽  
pp. 0900107
Author(s):  
彭堃墀 Peng Kunchi ◽  
贾晓军 Jia Xiaojun ◽  
苏晓龙 Su Xiaolong ◽  
谢常德 Xie Changde

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
W. Wang ◽  
Y. Wu ◽  
Y. Ma ◽  
W. Cai ◽  
L. Hu ◽  
...  

Abstract Two-mode interferometers lay the foundations for quantum metrology. Instead of exploring quantum entanglement in the two-mode interferometers, a single bosonic mode also promises a measurement precision beyond the shot-noise limit (SNL) by taking advantage of the infinite-dimensional Hilbert space of Fock states. Here, we demonstrate a single-mode phase estimation that approaches the Heisenberg limit (HL) unconditionally. Due to the strong dispersive nonlinearity and long coherence time of a microwave cavity, quantum states of the form $$\left( {\left| 0 \right\rangle + \left| N \right\rangle } \right)/\sqrt 2$$ 0 + N ∕ 2 can be generated, manipulated and detected with high fidelities, leading to an experimental phase estimation precision scaling as ∼N−0.94. A 9.1 dB enhancement of the precision over the SNL at N = 12 is achieved, which is only 1.7 dB away from the HL. Our experimental architecture is hardware efficient and can be combined with quantum error correction techniques to fight against decoherence, and thus promises quantum-enhanced sensing in practical applications.


Buildings ◽  
2018 ◽  
Vol 8 (12) ◽  
pp. 171 ◽  
Author(s):  
Luigi Giovannini ◽  
Fabio Favoino ◽  
Valerio Lo Verso ◽  
Anna Pellegrino ◽  
Valentina Serra

A simplified approach to calculate the daylight glare comfort class (imperceptible, perceptible, disturbing, or intolerable glare) on annual basis and for a grid of points in a space is presented. This method relies on the calculation of the vertical illuminance (Ev) for each grid point only, which is compared to an Ev threshold value for each daylight glare comfort class. These Ev threshold values are determined through a comparison with the Daylight Glare Probability (DGP) values on an annual basis through a fault-detection technique, for a reduced number of points. Compared to an annual calculation of exact DGP values on a certain grid, this approach is able to evaluate the daylight glare comfort classes only, but it is less time consuming. The paper presents and critically discusses this simplified method by means of its application to different case-studies: south and west oriented office in Turin (Lat 45.1° N), in which the DGP is assessed for three points in the space, considering glazing with different transmission properties (specular or scattering) and visible transmittances, as well as three operable internal shading systems (one venetian blinds and two roller blinds, for solar or glare control). For the presented case studies, the average error in the classification of the space according to daylight glare comfort classes is below 5% when comparing this simplified approach to related DGP values.


2006 ◽  
Vol 3 (3) ◽  
pp. 357-369 ◽  
Author(s):  
K. K. Yates ◽  
R. B. Halley

Abstract. The severity of the impact of elevated atmospheric pCO2 to coral reef ecosystems depends, in part, on how seawater pCO2 affects the balance between calcification and dissolution of carbonate sediments. Presently, there are insufficient published data that relate concentrations of pCO2 and CO32− to in situ rates of reef calcification in natural settings to accurately predict the impact of elevated atmospheric pCO2 on calcification and dissolution processes. Rates of net calcification and dissolution, CO32− concentrations, and pCO2 were measured, in situ, on patch reefs, bare sand, and coral rubble on the Molokai reef flat in Hawaii. Rates of calcification ranged from 0.03 to 2.30 mmol CaCO3 m−2 h−1 and dissolution ranged from –0.05 to –3.3 mmol CaCO3 m−2 h−1. Calcification and dissolution varied diurnally with net calcification primarily occurring during the day and net dissolution occurring at night. These data were used to calculate threshold values for pCO2 and CO32− at which rates of calcification and dissolution are equivalent. Results indicate that calcification and dissolution are linearly correlated with both CO32− and pCO2. Threshold pCO2 and CO32− values for individual substrate types showed considerable variation. The average pCO2 threshold value for all substrate types was 654±195 μatm and ranged from 467 to 1003 μatm. The average CO32− threshold value was 152±24 μmol kg−1, ranging from 113 to 184 μmol kg−1. Ambient seawater measurements of pCO2 and CO32− indicate that CO32− and pCO2 threshold values for all substrate types were both exceeded, simultaneously, 13% of the time at present day atmospheric pCO2 concentrations. It is predicted that atmospheric pCO2 will exceed the average pCO2 threshold value for calcification and dissolution on the Molokai reef flat by the year 2100.


Author(s):  
Tapas Si ◽  
Arunava De ◽  
Anup Kumar Bhattacharjee

This paper presents a new method for the segmentation of Magnetic Resonance Imaging (MRI) of brain tumor. First, discrete wavelet transform (DWT)-based soft-thresholding technique is used for removing noise in the MRI. Second, intensity inhomogeneity (IIH) independent of noise is removed from the MRI image. Third, again DWT is used to sharpen the de-noised and IIH corrected image. In this method, the image is decomposed into first level using wavelet decomposition and approximate values are assigned to zero and reconstruct the image results in detailed image. The detailed image is added with the pre-processed image to produce sharpened image. Entropy maximization using Grammatical Swarm (GS) algorithm is used to obtain a set of threshold values and a threshold value is selected with the expert knowledge to separate the lesion part from the other non-diseased cells in the image.


Behaviour ◽  
1958 ◽  
Vol 13 (1-2) ◽  
pp. 1-87 ◽  
Author(s):  
J.J.A. Van Iersel ◽  
A.C. Angela Bol

AbstractIn the present paper are regarded as 'preening', besides the preening movements performed with the bill, also other movements directed to the care of the plumage, such as 'shaking', 'head-shaking' and 'head-rubbing'. Various preening movements are distinguished by the part of the plumage. These various movements are performed in a certain order in the preening bouts 'after bathing'. It is argued that this order indicates differences in threshold value. Head-shaking, breast- and shoulder-preening have low threshold values; shaking(?), preening of the inside of the wing, the tail and the pinions, and head-rubbing have high thresholds; back-, wingbow- and wing-preening have intermediate thresholds. Higher threshold-values go together with greater complexity of motor-pattern. Both threshold values and number of movements per minute, which are positively correlated, are regarded as indicative of the level of the preening drive. This drive fluctuates rapidly and extensively in the first few minutes of the bouts after bathing, more slowly and over a narrower range in later minutes. These are short fluctuations which are superimposed upon one long fluctuation, consisting in a rapid increase, followed by a more gradual decrease. Data concerning brooding Terns indicate inhibitory relations between various behaviour systems: intensive brooding inhibits preening and nest-building strongly, escape rather strongly, and aggression to a certain extent. Escape has an inhibitory influence on brooding and nest-building. It is shown that the occurrence of preening 'during brooding' in most cases is associated with a weak activity of the (otherwise) inhibiting system (brooding), and it therefore is thought to be caused by disinhibition and further by (probably permanently present) activating factors for the preening system. In these cases neither the appearance of the movements, nor the behavioural context provides any reason to regard them as displacement preening. Moreover the composition of this preening (the types of movement and their percentage of the total) is similar to that of preening 'after bathing'. However, other cases of preening are specifically connected with (ambivalent) aggressive or escape behaviour: head-shaking often immediately follows the relatively aggressive 'gackering'; one or a few preening movements often are performed immediately, or sometimes a few (2-3) minutes after escape behaviour. In these cases the preening has to be considered as displacement, because of the (sometimes) "frantic" appearance, and mainly because of the context. Moreover, its composition differs from that of preening 'after bathing', in that low threshold movements are especially frequent. Several data indicate the displacement character of the preening which occurs 2-3 minutes after disappearance of overt (escape) behaviour. It is especially stressed that a movement may still be a displacement, though it is not directly accompanied by overt escape behaviour, and even when no such behaviour occurs at al. The latter is born out by the case of the non-aggressive opponents of 'gackering' birds, which do not perform any escape/aggressive behaviour, but still show head-shaking. It is shown that the displacement preening results from conflicts, either between brooding and escape ('nest-reliefs', 'nest- and 'air-alarms'), or between aggression and escape ('gackering'). The occurrence of displacement is shown to depend on the relation between the conflicting drives: the strengths of these must not diverge too much from a certain ratio, which is called 'effective equality'. On the basis of the established inhibitory relations between the various behaviour systems a hypothesis on the displacement mechanism is offered ('disinhibition hypothesis'). The idea of "sparking over of motivational impulses" is rejected. It is argued that a conflict-which occurs when the conflicting drives are 'effectively equal'-consists in mutual inhibition of these two drives, resulting in removal (reduction) of their inhibitory activity on other systems. A conflict between brooding (aggression) and escape thus results in removal (reduction) of the inhibition by brooding (aggression) on preening. Provided some '+factors' for preening are present, preening will then occur.. From this point of view the terms "allochthonous" and "autochthonous" are superfluous. The frequency and intensity of displacement (the latter measured by the number of movements per case and their threshold values) are as a rule positively correlated with the strength of both conflicting drives. It is argued that this is due to a greater average degree of 'effective equality' of strong conflicting drives, since the degree of 'effective equality' is thought to determine the chance, the degree and the duration of disinhibition of the displacement system. When both drives are strong, but one strongly exceeds the other ('inequality'), the chance of displacement decreases considerably, but if it does occur it is intense. So, in these cases-and some other-frequency and intensity of displacement are not correlated. Rain is shown to have a preening-releasing effect in all situations considered. Head-shaking seems to be facilitated most strongly. The influence of rain is likely to be a direct activation of the preening system. The increase of the preening frequency in rain (of a constant strength) is not equal in the various situations : the 'degree of facilitation' is correlated with the frequency of preening during dry weather and further it depends on the type of situation (conflict or non-conflict situation; type of conflict). For this an explanation is given on the basis of the view on the displacement mechanism and the nature of the conflict presented in this paper.


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