Related papers: On the connection between Complementarity and Unce…
The uncertainty principle is fundamentally rooted in the algebraic asymmetry between observables. We introduce a new class of uncertainty relations grounded in the resource theory of asymmetry, where incompatibility is quantified by an…
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…
The precision and response of trajectory observables offer valuable insights into the behavior of nonequilibrium systems. For classical systems, trade-offs between these characteristics and thermodynamic costs, such as entropy production…
The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a…
Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily…
Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…
For the power-law quantum wave packet in configuration space, the variance of the position observable may be divergent. Accordingly, the information-entropic formulation of the uncertainty principle becomes more appropriate than the…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
We show that for fermion states, measurements of any two finite outcome particle quantum numbers (e.g.\ spin) are not constrained by a minimum total uncertainty. We begin by defining uncertainties in terms of the outputs of a measurement…
Uncertainty relations are a distinctive characteristic of quantum theory that impose intrinsic limitations on the precision with which physical properties can be simultaneously determined. The modern work on uncertainty relations employs…
In this work we use the extremization method of various information-theoretic measures (Fisher information, Shannon entropy, Tsallis entropy) for $d$-dimensional quantum systems, which complementary describe the spreading of the quantum…
Uncertainty relations give upper bounds on the accuracy by which the outcomes of two incompatible measurements can be predicted. While established uncertainty relations apply to cases where the predictions are based on purely classical data…
We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
We employ quantum relative entropy to establish the relation between the measurement uncertainty and its disturbance on a state in the presence (and absence) of quantum memory. For two incompatible observables, we present the…
The quantum uncertainty principle stands as a cornerstone and a distinctive feature of quantum mechanics, setting it apart from classical mechanics. We introduce a tripartite quantum-memory-assisted entropic uncertainty relation, and extend…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual…
For a particle travelling through an interferometer, the trade-off between the available which-way information and the interference visibility provides a lucid manifestation of the quantum mechanical wave-particle duality. Here we analyze…
It is well known that the Mach-Zender interferometer exhibits a trade-off between the a priori which-path knowledge and the visibility of its interference pattern. This trade-off is expressed by the inequality $\mathcal{P}^2 + \mathcal{V}^2…
As the fundamental tool in quantum information science, the uncertainty principle is essential for manifesting nonclassical properties of quantum systems. Plenty of efforts on the uncertainty principle with two observables have been…