Related papers: Average of uncertainty-product for bounded observa…
Minimum-uncertainty squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples…
Uncertainty quantification (UQ) is essential for deploying machine learning models in safety-critical physical systems, yet classical Bayesian approaches incur substantial computational overhead. We establish a formal connection between…
The metric-adjusted skew information establishes a connection between the geometrical formulation of quantum statistics and the measures of quantum information. We study uncertainty relations in product and summation forms of…
We introduce a new method to estimate unknown pure $d$-dimensional quantum states using the probability distributions associated with only three measurement bases. Measurement results of $2d$ projectors are employed to generate a set of…
We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…
Precision control of a quantum system requires accurate determination of the effective system Hamiltonian. We develop a method for estimating the Hamiltonian parameters for some unknown two-state system and providing uncertainty bounds on…
The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…
We study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
In this work, we perform an in-depth study of recently introduced average-case quantum distances. The average-case distances approximate the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
We present a new uncertainty principle for risk-aware statistical estimation, effectively quantifying the inherent trade-off between mean squared error ($\mse$) and risk, the latter measured by the associated average predictive squared…
We uncover the quantum fluctuation-response inequality, which, in the most general setting, establishes a bound for the mean difference of an observable at two different quantum states, in terms of the quantum relative entropy. When the…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
Two types of errors can occur when discriminating pairs of quantum states. Asymmetric state discrimination involves minimizing the probability of one type of error, subject to a constraint on the other. We give explicit expressions bounding…
The challenge of understanding quantum measurement persists as a fundamental issue in modern physics. Particularly, the abrupt and energy-non-conserving collapse of the wave function appears to contradict classical thermodynamic laws. The…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group operators. It is shown that within any…
Various measures have been suggested recently for quantifying the coherence of a quantum state with respect to a given basis. We first use two of these, the l_1-norm and relative entropy measures, to investigate tradeoffs between the…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
We introduce two uncertainty relations based on the state-dependent norm of commutators, utilizing generalizations of the B\"ottcher-Wenzel inequality. The first relation is mathematically proven, while the second, tighter relation is…