Related papers: Generalized uncertainty relations
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…
In this paper, the quantization and generalized uncertainty relation for some quantum deformed algebras are investigated. For several deformed algebras, the commutation relation between the position and the momentum operator is shown to be…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
Characterization and certification of nonlocal correlations is one of the the central topics in quantum information theory. In this work, we develop the detection methods of entanglement and steering based on the universal uncertainty…
Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be…
Kinetic Uncertainty Relations (KURs) set fundamental limits on the precision of nonequilibrium transport by bounding the signal-to-noise ratio of currents in terms of the dynamical activity, a quantity that counts exchange events between a…
This survey tries to investigate the truths and deficiencies of prevalent philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The respective philosophy, known as being eclipsed by unfinished controversies, is…
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…
Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be…
Wigner-friend scenarios -- in which external agents describe a closed laboratory containing a friend making a measurement -- highlight the difficulties inherent to quantum theory when accounting for measurements. In non-relativistic…
We present a notion of generalized entanglement which goes beyond the conventional definition based on quantum subsystems. This is accomplished by directly defining entanglement as a property of quantum states relative to a distinguished…
Recently, Maccone and Pati [Phys. Rev. Lett. {\bf 113}, 260401 (2014)] derived few inequalities among variances of incompatible operators which they called stronger uncertainty relations, stronger than Heisenberg-Robertson or Schrodinger…
The uncertainty principle is the most important for the foundations of quantum mechanics but it still remains failed to reach a consensus of its interpretation, which gives rise to debates upon its physical nature. In this work, we address…
The Landau-Pollak uncertainty relation treats a pair of rank one projection valued measures and imposes a restriction on their probability distributions. It gives a nontrivial bound for summation of their maximum values. We give a…
We provide a generalization of the idea of unitary designs to cover finite averaging over much more general operations on quantum states. Namely, we construct finite averaging sets for averaging quantum states over arbitrary reductive Lie…
The uncertainty principle is one of the features of quantum theory. Fine-grained uncertainty relations (FGURs) are a contemporary interpretation of this principle. Each FGUR is derived from a scenario where multiple measurements of a…
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…
We introduce a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such…
It is generally believed that classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences in a more transparent manner is central to the deeper understanding of foundational aspects and…
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…