scholarly journals Extended Quantum Conditional Entropy and Quantum Uncertainty Inequalities

2013 ◽  
Vol 323 (2) ◽  
pp. 487-495 ◽  
Author(s):  
Rupert L. Frank ◽  
Elliott H. Lieb
2020 ◽  
Vol 10 (22) ◽  
pp. 8266
Author(s):  
C. Aris Chatzidimitriou-Dreismann

During the last few decades, considerable advances in quantum information theory have shown deep existing connections between quantum correlation effects (like entanglement and quantum discord) and thermodynamics. Here the concept of conditional entropy plays a considerable role. In contrast to the classical case, quantum conditional entropy can take negative values. This counter-intuitive feature, already well understood in the context of information theory, was recently shown theoretically to also have a physical meaning in quantum thermodynamics [del Rio et al. Nature 2011, 474, 61]. Extending this existing work, here we provide evidence of the significance of negative conditional entropy in a concrete experimental context: Incoherent Neutron Scattering (INS) from protons of H2 in nano-scale environments; e.g., in INS from H2 in C-nanotubes, the data of the H2 translational motion along the nanotube axis seems to show that the neutron apparently scatters from a fictitious particle with mass of 0.64 atomic mass units (a.m.u.)—instead of the value of 2 a.m.u. as conventionally expected. An independent second experiment confirms this finding. However, taking into account the possible negativity of conditional entropy, we explain that this effect has a natural interpretation in terms of quantum thermodynamics. Moreover, it is intrinsically related to the number of qubits capturing the interaction of the two quantum systems H2 and C-nanotube. The considered effect may have technological applications (e.g., in H-storage materials and fuel cells).


2007 ◽  
Vol 56 (7) ◽  
pp. 3937
Author(s):  
Zhou Bing-Ju ◽  
Liu Xiao-Juan ◽  
Fang Mao-Fa ◽  
Zhou Qing-Ping ◽  
Liu Ming-Wei

Author(s):  
Liliane Campos

By decentring our reading of Hamlet, Stoppard’s tragicomedy questions the legitimacy of centres and of stable frames of reference. So Liliane Campos examines how Stoppard plays with the physical and cosmological models he finds in Hamlet, particularly those of the wheel and the compass, and gives a new scientific depth to the fear that time is ‘out of joint’. In both his play and his own film adaptation, Stoppard’s rewriting gives a 20th-century twist to these metaphors, through references to relativity, indeterminacy, and the role of the observer. When they refer to the uncontrollable wheels of their fate, his characters no longer describe the destruction of order, but uncertainty about which order is at work, whether heliocentric or geocentric, random or tragic. When they express their loss of bearings, they do so through the thought experiments of modern physics, from Galilean relativity to quantum uncertainty, drawing our attention to shifting frames of reference. Much like Schrödinger’s cat, Stoppard’s Rosencrantz and Guildenstern are both dead and alive. As we observe their predicament, Campos argues, we are placed in the paradoxical position of the observer in 20th-century physics, and constantly reminded that our time-specific relation to the canon inevitably determines our interpretation.


Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 286
Author(s):  
Soheil Keshmiri

Recent decades have witnessed a substantial progress in the utilization of brain activity for the identification of stress digital markers. In particular, the success of entropic measures for this purpose is very appealing, considering (1) their suitability for capturing both linear and non-linear characteristics of brain activity recordings and (2) their direct association with the brain signal variability. These findings rely on external stimuli to induce the brain stress response. On the other hand, research suggests that the use of different types of experimentally induced psychological and physical stressors could potentially yield differential impacts on the brain response to stress and therefore should be dissociated from more general patterns. The present study takes a step toward addressing this issue by introducing conditional entropy (CE) as a potential electroencephalography (EEG)-based resting-state digital marker of stress. For this purpose, we use the resting-state multi-channel EEG recordings of 20 individuals whose responses to stress-related questionnaires show significantly higher and lower level of stress. Through the application of representational similarity analysis (RSA) and K-nearest-neighbor (KNN) classification, we verify the potential that the use of CE can offer to the solution concept of finding an effective digital marker for stress.


Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 378
Author(s):  
Taeyong Kwon ◽  
Seongsim Yoon ◽  
Sanghoo Yoon

Uncertainty in the rainfall network can lead to mistakes in dam operation. Sudden increases in dam water levels due to rainfall uncertainty are a high disaster risk. In order to prevent these losses, it is necessary to configure an appropriate rainfall network that can effectively reflect the characteristics of the watershed. In this study, conditional entropy was used to calculate the uncertainty of the watershed using rainfall and radar data observed from 2018 to 2019 in the Goesan Dam and Hwacheon Dam watersheds. The results identified radar data suitable for the characteristics of the watershed and proposed a site for an additional rainfall gauge. It is also necessary to select the location of the additional rainfall gauged by limiting the points where smooth movement and installation, for example crossing national borders, are difficult. The proposed site emphasized accessibility and usability by leveraging road information and selecting a radar grid near the road. As a practice result, the uncertainty of precipitation in the Goesan and Hwacheon Dam watersheds could be decreased by 70.0% and 67.9%, respectively, when four and three additional gauge sites were installed without any restriction. When these were installed near to the road, with five and four additional gauge sites, the uncertainty in the Goesan Dam and Hwacheon Dam watersheds were reduced by up to 71.1%. Therefore, due to the high degree of uncertainty, it is necessary to measure precipitation. The operation of the rainfall gauge can provide a smooth site and configure an appropriate monitoring network.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Peter Brown ◽  
Hamza Fawzi ◽  
Omar Fawzi

AbstractThe rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum states jointly held by the adversary and the parties that are consistent with the statistics that are seen by the parties. Here, we introduce a method to approximate such entropic quantities. Applied to the setting of device-independent randomness generation and quantum key distribution, we obtain improvements on protocol rates in various settings. In particular, we find new upper bounds on the minimal global detection efficiency required to perform device-independent quantum key distribution without additional preprocessing. Furthermore, we show that our construction can be readily combined with the entropy accumulation theorem in order to establish full finite-key security proofs for these protocols.


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