Related papers: Quantum speed limits: from Heisenberg's uncertaint…
In quantum control, quantum speed limits provide fundamental lower bounds on the time that is needed to implement certain unitary transformations. Using Lie algebraic methods, we link these speed limits to symmetries of the control…
The Heisenberg and Mandelstam-Tamm time-energy uncertainty relations are analyzed. The conlusion resulting from this analysis is that within the Quantum Mechanics of Schr\"{o}dinger and von Neumann, the status of these relations can not be…
Heisenberg's uncertainty principle provides a fundamental limitation on an observer's ability to simultaneously predict the outcome when one of two measurements is performed on a quantum system. However, if the observer has access to a…
We discuss quantum speed limits (QSLs) for finite-dimensional quantum systems undergoing general physical processes. These QSLs were obtained using two families of entropic measures, namely the square root of the Jensen-Shannon divergence,…
The time-energy uncertainty relation in nonrelativistic quantum mechanics has been intensely debated with regard to its formal derivation, validity, and physical meaning. Here, we analyze two formal relations proposed by Mandelstam and Tamm…
One version of the energy-time uncertainty principle states that the minimum time $T_{\perp}$ for a quantum system to evolve from a given state to any orthogonal state is $h/(4 \Delta E)$ where $\Delta E$ is the energy uncertainty. A…
We cast observable measure of quantum coherence or asymmetry as a resource to control the quantum speed limit (QSL) for unitary evolutions. For non-unitary evolutions, QSL depends on that of the state of the system and environment together.…
It is well known that the problem of divergence in the physical interpretation of quantum mechanics originating from the uncertainty principle has not yet been resolved. Attempting to clear the constraints and confusion of this situation…
The Heisenberg uncertainty principle is one of the most famous features of quantum mechanics. However, the non-determinism implied by the Heisenberg uncertainty principle --- together with other prominent aspects of quantum mechanics such…
We analyze state preparation within a restricted space of local control parameters between adiabatically connected states of control Hamiltonians. We formulate a conjecture that the time integral of energy fluctuations over the protocol…
The certainty principle (2005) allowed to conceptualize from the more fundamental grounds both the Heisenberg uncertainty principle (1927) and the Mandelshtam-Tamm relation (1945). In this review I give detailed explanation and discussion…
The bulk-boundary correspondence provides a guiding principle for tackling strongly correlated and coupled systems. In the present work, we apply the concept of the bulk-boundary correspondence to thermodynamic bounds described by classical…
Here we describe the quantum limit to measurement of the classical gravitational field. Specifically, we write down the optimal quantum Cramer-Rao lower bound, for any single parameter describing a metric for spacetime. The standard…
The ability to accurately control a quantum system is a fundamental requirement in many areas of modern science such as quantum information processing and the coherent manipulation of molecular systems. It is usually necessary to realize…
Quantum speed limits (QSLs) impose fundamental constraints on the evolution speed of quantum systems. Traditionally, the Mandelstam-Tamm (MT) and Margolus-Levitin (ML) bounds have been widely employed, relying on the standard deviation and…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
The "speed" of unitary quantum evolution was recently shown to be connected to entanglement in multipartite quantum systems. Here, we discuss a tighter version of the Mandelstam-Tamm uncertainty relation that depends on the Fisher…
As a foundation of modern physics, uncertainty relations describe an ultimate limit for the measurement uncertainty of incompatible observables. Traditionally, uncertain relations are formulated by mathematical bounds for a specific state.…
The notion of the quantum angle is introduced. The quantum angle turns out to be a metric on the set of physical states of a quantum system. Its kinematics and dynamics is studied. The certainty principle for quantum systems is formulated…
It is commonly recognized now that Dark Energy (Lambda-term) is of crucial importance both at the early (inflationary) stage of cosmological evolution and at the present time. However, little is known about its nature and origin till now.…