Related papers: The Uncertainty Relationship In Magnetic Resonance…
The comprehensive integration of machine learning healthcare models within clinical practice remains suboptimal, notwithstanding the proliferation of high-performing solutions reported in the literature. A predominant factor hindering…
Introducing accelerated reconstruction algorithms into clinical settings requires measures of uncertainty quantification that accurately assess the relevant uncertainty introduced by the reconstruction algorithm. Many currently deployed…
Uncertainty principle is one of the fundamental principles of quantum mechanics. In this work, we derive two uncertainty equalities, which hold for all pairs of incompatible observables. We also obtain an uncertainty relation in weak…
The spatial resolution of magnetic resonance imaging (MRI) is fundamentally limited by the width of Lorentzian point spread functions (PSF) associated with the exponential decay rate of transverse magnetization (1/T2*). Here we show a…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
In a recent interesting Letter [Phys. Rev. Lett. 108, 140401 (2012)] I. Bialynicki-Birula and his coauthor have derived the uncertainty relation for the photons in three dimensions. However, some of their arguments are problematical, and…
The magneto-rotational instability (MRI) - which is due to an interplay between a sheared background and the magnetic field - is commonly considered a key ingredient for developing and sustaining turbulence in the outer envelope of binary…
Under the scenario of generalized measurements, it can be questioned how much of quantum uncertainty can be attributed to measuring device, independent of the uncertainty in the measured system. On the course to answer the question, we…
Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this Letter, we explore this…
The effect of the quantum feedback on the tightness of the variance-based uncertainty, the possibility of using quantum feedback to prepare the state with a better tightness, and the relationship between the tightness of the uncertainty and…
There is a constraining relation between the reliability of a quantum measurement and the extent to which the measurement process is, in principle, reversible. The greater the information that is gained, the less reversible the measurement…
We study the Schr\"odinger-Robertson uncertainty relations in an algebraic framework. Moreover, we show that some specific commutation relations imply new equalities, which are regarded as equality versions of well-known inequalities such…
Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI) represent versatile tools with diverse applications spanning physics, chemistry, geology, and medical science. This comprehensive review explores the foundational…
We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form $(\Delta P)(\Delta Q)\geq C\hbar$, where the `uncertainties' quantify the difference between the marginals of the…
The Robertson's formulation of the uncertainty relation is the most widely accepted form of the Heisenberg uncertainty relation (HUR). It gets modified when we consider it for entangled particles. But this formulation does not consider the…
Coherence of a quantum state intrinsically depends on the choice of the reference basis. A natural question to ask is the following: if we use two or more incompatible reference bases, can~there be some trade-off relation between the…
Magnetic resonance (MR) imaging is commonly used in the clinical setting to non-invasively monitor the body. There exists a large variability in MR imaging due to differences in scanner hardware, software, and protocol design. Ideally, a…
Based on mixedness definition as M=1-tr(\r{ho}^2), we obtain a new variance-based uncertainty equality along with an inequality for Hermitian operators of a single-qubit system. The obtained uncertainty equality can be used as a measure of…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not…