The study of quantum information entropy in confined quantum systems plays a pivotal role in quantum information science. In this work, we investigate the quantum information entropy of a particle in a quantum well under an external electric field by calculating the Rényi entropy (), Tsallis entropy () and the Onicescu information energy (). Our findings reveal that these entropic measures exhibit a strong dependence on the entropy order ( α ). Although both and demonstrate a decreasing trend with increasing α for any given quantum state, they differ significantly in their sensitivity to α variations, displaying distinct behaviors that provide unique insights into quantum uncertainty. For the Onicescu information energy (), a sharp transition around α = 1 appears. This characteristic could be significant for designing and analyzing quantum systems, particularly in enhancing their information processing capabilities. By further examining how these entropic measures vary with quantum well width and electric field strength, we gain a deeper understanding of the system's controllability. This empowers researchers to select optimal metrics for specific applications and improve the accuracy of quantum analyses. This study underscores the importance of entropy‐based analysis in quantum mechanics for advancing quantum control, information theory, and technology development.
We consider the effects of weak measurements on the quantum critical ground state of the one-dimensional (a) tricritical and (b) critical quantum Ising model, by measuring in (a) the local energy and in (b) the local spin operator in a lattice formulation. By employing a controlled renormalization group (RG) analysis we find that each problem exhibits highly complex novel scaling behavior, arising from the intrinsically indeterministic ('random') nature of quantum mechanical measurements, which is governed by a measurement-dominated RG fixed point that we study within an
ε expansion. In the tricritical Ising case (a) we find (i): multifractal scaling behavior of energy and spin correlations in the measured groundstate, corresponding to an infinite hierarchy of independent critical exponents and, equivalently, to a continuum of universal scaling exponents for each of these correlations; (ii): the presence of logarithmic factors multiplying powerlaws in correlation functions, a hallmark of 'logarithmic conformal field theories' (CFT); (iii): universal 'effective central charges'
cn(eff) for the prefactors of the logarithm of subsystem size of the
nth Rényi entropies, which are independent of each other for different
n, in contrast to the unmeasured critical ground state, and (iv): a universal ("Affleck-Ludwig") 'effective boundary entropy'
Seff which we show, quite generally, to be related to the system-size independent part of the Shannon entropy of the measurement record, computed explicitly here to 1-loop order. - A subset of these results have so-far also been obtained within the
ε expansion for the measurement-dominated critical point in the critical Ising case (b).
Squeezed reservoirs provide a powerful means of engineering nonclassical noise and controlling irreversible dynamics in open quantum systems. Here we develop a comprehensive analysis of two coupled harmonic oscillators driven by independent squeezed baths, focusing on the emergence of coherence-driven entropy flow and the structure of exceptional points (EPs) in the corresponding Lindblad dynamics. Working entirely within the Gaussian formalism, we derive closed-form evolution equations for the covariance matrix and show that squeezing induces entropy generation only at *second order* in the anomalous correlations, a nonlinear mechanism absent in thermal environments. This entropy flow is accompanied by a rich non-Hermitian structure: by scanning the squeezing parameters we uncover a characteristic "exceptional-point fan" in the (M1, M2) plane, which separates a narrow PT-unbroken region of oscillatory dynamics from broad PT-broken sectors in which one normal mode becomes purely overdamped. This geometric organization of EPs reveals that PT symmetry survives only when the two reservoirs squeeze opposite quadratures, and is generically broken for in-phase squeezing. Our analysis establishes squeezed reservoirs as a natural setting where information-bearing noise drives irreversible behavior through coherent pathways, and lays the groundwork for experimentally accessible probes of entropy flow and critical mode behavior in more complex open systems.