Related papers: Quantum speed limits: from Heisenberg's uncertaint…
Recently, Jones and Kok [P. J. Jones and P. Kok, Phys. Rev. A 82, 022107 (2010)] presented alternative geometric derivations of the Mandelstam-Tamm [L. Mandelstam and I. Tamm, J. Phys. (USSR) 9, 249 (1945)] and Margolus-Levitin [N. Margolus…
We review various bounds concerning out-of-equilibrium dynamics in few-level and many-body quantum systems. We primarily focus on closed quantum systems but will also mention some related results for open quantum systems and classical…
This paper is a continuation of the paper [V.S.Mashkevich, gr-qc/9409010]. Indeterministic quantum gravity is a theory that unifies general relativity and quantum theory involving indeterministic conception, i.e., quantum jumps. By the same…
I consider in this book a formulation of Quantum Mechanics. Usually QM is formulated based on the notion of time and space, both of which are thought a priori given quantities or notions. However, when we try to define the notion of…
Optimal control theory is a promising candidate for a drastic improvement of the performance of quantum information tasks. We explore its ultimate limit in paradigmatic cases, and demonstrate that it coincides with the maximum speed limit…
While playing an important role in the foundations of quantum theory, Quantum Speed Limits (QSL) have no role in discussions about the search for quantum gravity. We fill this gap by analysing what QSL arises when superposing spherically…
The question of how fast a quantum state can evolve has attracted a considerable attention in connection with quantum measurement, metrology, and information processing. Since only orthogonal states can be unambiguously distinguished, a…
Quantum Mechanics (QM) is one of the pillars of modern physics: an impressive amount of experiments have confirmed this theory and many technological applications are based on it. Nevertheless, at one century since its development, various…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this…
We propose a mathematically rigorous unified framework for hybrid quantum mechanics that systematically combines algebraic deformation and spatial non-locality within a single operator formalism. By constructing a self-adjoint hybrid…
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…
The time-energy uncertainty relation is often invoked as a heuristic explanation for virtual particles in interacting quantum field theories. However, this interpretation breaks down upon closer scrutiny for several reasons. Although…
By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy…
Quantum Mechanics (QM) has faced deep controversies and debates since its origin when Werner Heisenberg proposed the first mathematical formalism capable to operationally account for what had been recently discovered as the new field of…
Quantum mechanics imposes fundamental constraints known as quantum speed limits (QSLs) on the information processing speed of all quantum systems. Every QSL known to date comes from the restriction imposed on the evolution time between two…
We propose a reformulation of quantum mechanics in which the distinction between definite and indefinite becomes the fundamental primitive. Inspired by suggestions of Heisenberg, Schrodinger and Dyson that the past can't be described in…
Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus…
Physical systems that power motion and create structure in a fixed amount of time dissipate energy and produce entropy. Whether living or synthetic, systems performing these dynamic functions must balance dissipation and speed. Here, we…