Related papers: The minimal time of dynamic evolution to an arbitr…
Grover's quantum search algorithm is analyzed for the case in which the initial state is an arbitrary pure quantum state $|\phi>$ of $n$ qubits. It is shown that the optimal time to perform the measurement is independent of $| \phi>$,…
We derive an upper bound for the time needed to implement a generic unitary transformation in a $d$ dimensional quantum system using $d$ control fields. We show that given the ability to control the diagonal elements of the Hamiltonian,…
Recent works on quantum resource theories of non-Gaussianity, which are based upon the type of tools available in contemporary experimental settings, put Gaussian states and their convex combinations on equal footing. Motivated by this, in…
In the Schr{\"o}dinger picture, the state of a quantum system evolves in time and the quantum speed limit describes how fast the state of a quantum system evolves from an initial state to a final state. However, in the Heisenberg picture…
The short-time and global behaviour are studied for autonomous linear evolution equations defined by generators of uniformly bounded holomorphic semigroups in a Hilbert space. A general criterion for log-convexity in time of the norm of the…
We study quantum brachistochrone problem for the spin-1 system in a magnetic field of a constant absolute value. Such system gives us a possibility to examine in detail the statement of papers [A. Carlini {\it et al.}, Phys. Rev. Lett. {\bf…
In this paper we are concerned with the learnability of energies from data obtained by observing time evolutions of their critical points starting at random initial equilibria. As a byproduct of our theoretical framework we introduce the…
In this work we study an inverse dynamical problem for a bipartite quantum system governed by the time local master equation: to find the class of generators which give rise to a certain time evolution with the constraint of fixed reduced…
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…
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and…
Sparse quantum state preparation is a common subroutine in quantum algorithms, where classical data with few nonzero entries must be loaded into a quantum state. In this work, we consider the Grover-Rudolph algorithm, which has recently…
In this paper, a branching random walk $(V(x))$ in the boundary case is studied, where the associated one dimensional random walk is in the domain of attraction of an $\alpha-$stable law with $1<\alpha<2$. Let $M_n$ be the minimal position…
We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from $\hat{H}_0$ to $\hat{H}_1$ in a…
We develop a variational formalism in order to study the structure of low energy spectra of frustrated quantum spin systems. It is first applied to trial wavefunctions of ladders with one spin-1/2 on each site. We determine energy minima of…
Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive analytical error bounds on expectation values of system…
We study the dynamics of a bounded gravitational collapsing configuration emitting gravitational waves, where the exterior spacetime is described by Robinson-Trautman geometries. The full nonlinear regime is examined by using the Galerkin…
We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal velocity bound, which states that the…
This article is concerned with a system of particles interacting with the quantized electromagnetic field (photons) in the non relativistic Quantum Electrodynamics (QED) framework and governed by the Pauli-Fierz Hamiltonian. We are…
Minimum-time quantum control protocols can be obtained from the quantum brachistochrone formalism [Carlini, Hosoya, Koike, and Okudaira, Phys. Rev. Lett. 96, 06053, (2006)]. We point out that the original treatment implicitly applied the…
Bounds of the minimum evolution time between two distinguishable states of a system can help to assess the maximal speed of quantum computers and communication channels. We study the quantum speed limit time of a composite quantum states in…