scholarly journals Suppressing measurement uncertainty in an inhomogeneous spin star system

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Saeed Haddadi ◽  
Mehrdad Ghominejad ◽  
Ahmad Akhound ◽  
Mohammad Reza Pourkarimi

AbstractThe uncertainty principle is known as a foundational element of quantum theory, providing a striking lower bound to quantify our prediction for the measured result of two incompatible observables. In this work, we study the thermal evolution of the entropic uncertainty bound in the presence of quantum memory for an inhomogeneous four-qubit spin-star system that is in the thermal regime. Intriguingly, our results show that the entropic uncertainty bound can be controlled and suppressed by adjusting the inhomogeneity parameter of the system.

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
R. A. Abdelghany ◽  
A.-B. A. Mohamed ◽  
M. Tammam ◽  
Watson Kuo ◽  
H. Eleuch

AbstractWe formulate the tripartite entropic uncertainty relation and predict its lower bound in a three-qubit Heisenberg XXZ spin chain when measuring an arbitrary pair of incompatible observables on one qubit while the other two are served as quantum memories. Our study reveals that the entanglement between the nearest neighbors plays an important role in reducing the uncertainty in measurement outcomes. In addition we have shown that the Dolatkhah’s lower bound (Phys Rev A 102(5):052227, 2020) is tighter than that of Ming (Phys Rev A 102(01):012206, 2020) and their dynamics under phase decoherence depends on the choice of the observable pair. In the absence of phase decoherence, Ming’s lower bound is time-invariant regardless the chosen observable pair, while Dolatkhah’s lower bound is perfectly identical with the tripartite uncertainty with a specific choice of pair.


Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1640
Author(s):  
Krzysztof Urbanowski

Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables A and B and such vectors that the lower bound for the product of standard deviations ΔA and ΔB calculated for these vectors is zero: ΔA·ΔB≥0. Here we discuss examples of such cases and some other inconsistencies which can be found performing a rigorous analysis of the uncertainty relations in some special cases. As an illustration of such cases matrices (2×2) and (3×3) and the position–momentum uncertainty relation for a quantum particle in the box are considered. The status of the uncertainty relation in PT–symmetric quantum theory and the problems associated with it are also studied.


2021 ◽  
Author(s):  
Tanja Schroeder ◽  
Michael Krautblatter

<div> <p><span>In the context of climate change, permafrost degradation is a key variable in understanding rock slope failures in high mountain areas. Permafrost degradation imposes a variety of environmental, economic and humanitarian impacts on infrastructure and people in high mountain areas. Therefore, new high-quality monitoring and modelling strategies are needed.</span></p> </div><div> <p><span>We developed a new, numerical, thermo-geophysical rock permafrost model (TGRPM) to assess spatial-temporal variations of the ground thermal regime in steep permafrost rock walls on the basis of 13-years of Electrical Resistivity Tomography (ERT) monitoring of permafrost at the Zugspitze. TGRPM is a simple to understand and workable numerical 2D MATLAB-model, which is adaptable to different topographic and sub-surface conditions, and further relies on a minimum of input-data to assess the surface energy balance and the ground thermal regime. It simulates the thermal response for permafrost rock walls, including their complex topography, to climate forcing over multiple years. It aims to assess seasonal and long-term permafrost development in steep alpine rock walls, as well as serving as a straightforward calculation routine, which is solely based on physical processes and does not require any fitting of certain parameters. </span></p> </div><div> <p><span>At first, the model was tested against direct temperature measurements from the LfU-borehole at the Zugspitze summit to prove its accuracy. Then, it is run against a 13-year ERT data-set from the Zugspitze Kammstollen to validate the ERT measurements.</span></p> </div><div> <p><span>Here, we show the first thermo-geophysical model referencing thermal evolution in a permafrost rock wall with temperature-calibrated ERT. The TGRPM successfully computes the thermal evolution within the Zugspitze mountain ridge from a 2D coupled energy balance and heat conduction scheme in complex topography. It furthermore validates the temperature-resistivity relationship by Krautblatter et al. (2010) for natural rock walls reaching a correlation of 85 to 95 % between measured, ERT-derived and modelled temperatures.</span></p> </div><div><span>Krautblatter, M., Verleysdonk, S., Flores-Orozco, A. & Kemna, A. (2010): Temperature-calibrated imaging of seasonal changes in permafrost rock walls by quantitative electrical resistivity </span><span>tomography </span>(Zugspitze, German/Austrian Alps). <em>J. Geophys. Res. </em>115: F02003.</div>


2019 ◽  
Vol 34 (22) ◽  
pp. 1950175 ◽  
Author(s):  
Saeed Haddadi ◽  
Mohammad Reza Pourkarimi ◽  
Ahmad Akhound ◽  
Mehrdad Ghominejad

In this paper, we study the thermal evolution of three types of quantum correlations under the homogeneous and inhomogeneous spin star Hamiltonian. It is shown that quantum discord (QD) is more stable than the other measures in the thermal regime, but concurrence is more efficient when the Hamiltonian parameters are employed. However, all quantum correlations can reach their maximum, if the inhomogeneous parameter raises. Quantum correlations can be enhanced by a weak external magnetic field and strong coupling parameter. But they vanish in the case of a strong magnetic field, weak coupling parameter, and high temperatures.


2020 ◽  
Vol 110 (12) ◽  
pp. 3197-3242
Author(s):  
Nicolò Drago ◽  
Sonia Mazzucchi ◽  
Valter Moretti

AbstractThe existence of a real linear space structure on the set of observables of a quantum system—i.e., the requirement that the linear combination of two generally non-commuting observables A, B is an observable as well—is a fundamental postulate of the quantum theory yet before introducing any structure of algebra. However, it is by no means clear how to choose the measuring instrument of a general observable of the form $$aA+bB$$ a A + b B ($$a,b\in {{\mathbb {R}}}$$ a , b ∈ R ) if such measuring instruments are given for the addends observables A and B when they are incompatible observables. A mathematical version of this dilemma is how to construct the spectral measure of $$f(aA+bB)$$ f ( a A + b B ) out of the spectral measures of A and B. We present such a construction with a formula which is valid for general unbounded self-adjoint operators A and B, whose spectral measures may not commute, and a wide class of functions $$f: {{\mathbb {R}}}\rightarrow {{\mathbb {C}}}$$ f : R → C . In the bounded case, we prove that the Jordan product of A and B (and suitably symmetrized polynomials of A and B) can be constructed with the same procedure out of the spectral measures of A and B. The formula turns out to have an interesting operational interpretation and, in particular cases, a nice interplay with the theory of Feynman path integration and the Feynman–Kac formula.


2010 ◽  
Vol 19 (14) ◽  
pp. 2319-2323
Author(s):  
SHAHAR HOD

The dimensionless fine-structure constant α ≡ e2/ℏc ≃ 1/137.036 has fascinated many scientists since its introduction by Sommerfeld almost a century ago. Dirac and Feynman have conjectured that this important physical constant may be composed of fundamental mathematical quantities like π. In this essay we argue that, the interplay between gravity, quantum theory, and thermodynamics may shed much light on the origins of this mysterious constant. In particular, we show that a unified quantum theory of gravity may set a lower bound on the value of the fine-structure constant, α > ln 3/48π ≃ 1/137. 3.


2018 ◽  
Vol 16 (02) ◽  
pp. 1850013 ◽  
Author(s):  
M. Revzen

Boolean logic is used to prove the CHSH inequalities. The proof elucidates the connection between Einstein elements of reality and quantum non-locality. The violation of the CHSH inequality by quantum theory is discussed and the two-stage view of quantum measurement relevance to incompatible observables is outlined.


2018 ◽  
Vol 96 (7) ◽  
pp. 700-704 ◽  
Author(s):  
Göktuğ Karpat

Uncertainty relations are a characteristic trait of quantum mechanics. Even though the traditional uncertainty relations are expressed in terms of the standard deviation of two observables, there exists another class of such relations based on entropic measures. Here we investigate the memory-assisted entropic uncertainty relation in an open quantum system scenario. We study the dynamics of the entropic uncertainty and its lower bound, related to two incompatible observables, when the system is affected by noise, which can be described by a correlated Pauli channel. In particular, we demonstrate how the entropic uncertainty for these two incompatible observables can be reduced as the correlations in the quantum channel grow stronger.


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