Related papers: Upper limit on the acceleration of a quantum evolu…
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…
Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines…
Quantum mechanics dictates bounds for the minimal evolution time between predetermined initial and final states. Several of these Quantum Speed Limit (QSL) bounds were derived for non-unitary dynamics using different approaches. Here, we…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
The speed limits on entanglement are defined as the maximal rate at which entanglement can be generated or degraded in a physical process. We derive the speed limits on entanglement, using the relative entropy of entanglement and…
The notion of quantum speed limit (QSL) refers to the fundamental fact that two quantum states become completely distinguishable upon dynamical evolution only after a finite amount time, called the QSL time. A different, but related concept…
Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and…
We prove fundamental rigorous bounds on the speed of quantum evolution for a quantum system coupled to a thermal bath. The bounds are formulated in terms of expectation values of few-body observables derived from the system-bath…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
In an isolated system, the time evolution of a given observable in the Heisenberg picture can be efficiently represented in Krylov space. In this representation, an initial operator becomes increasingly complex as time goes by, a feature…
In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space.…
We consider the quantum dynamical evolution of a fully-connected quantum system subjected to random projective measurements and study the first detection time of an extended subspace of the Hilbert space. Exact analytical expressions are…
We consider quantum metrology for unitary evolutions generated by parameter-dependent Hamiltonians. We focus on the unitary evolutions generated by the Ising Hamiltonian that describes the dynamics of a one-dimensional chain of spins with…
Quantum speed limit (QSL) is a fundamental concept in quantum mechanics and provides a lower bound on the evolution time. The attainability of QSL, greatly depending on the understanding of QSL, is a long-standing open problem especially…
The hilbert-space structure of quantum mechanics is related to the causal structure of space-time. The usual measurement hypotheses apparently preclude nonlinear or stochastic quantum evolution. By admitting a difference in the calculus of…
We probe the quantum speed limit (QSL) of an electron when it is trapped in a non-uniform magnetic field. We show that the QSL increases to a large value, but within the regime of causality, by choosing a proper variation in magnetic…
The minimal evolution time between two distinguishable states is of fundamental interest in quantum physics. Very recently Mirkin et al. argue that some most common quantum-speed-limit (QSL) bounds which depend on the actual evolution time…
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…
The upper bounds for the rate of fluctuation growth of an observable in both open and closed quantum systems have been studied actively recently. In our recent work we showed that the rate of fluctuation growth for an observable in a closed…
Precision measurements of gravitational acceleration, or gravimetry, enable the testing of physical theories and find numerous applications in geodesy and space exploration. By harnessing quantum effects, high-precision sensors can achieve…