Related papers: Bounds to unitary evolution
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…
This is a short survey on existing upper and lower bounds on the probability of the union of a finite number of events using partial information given in terms of the individual or pairwise event probabilities (or their sums). New proofs…
Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related…
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
As quantum computers and simulators begin to produce results that cannot be verified classically, it becomes imperative to develop a variety of tools to detect and diagnose experimental errors on these devices. While state or process…
The quantum speed limit provides fundamental bound on how fast a quantum system can evolve between the initial and the final states. For the unitary evolution, the celebrated Mandelstam-Tamm (MT) bound has been widely studied for various…
We consider the well-known problem of the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time birth and death processes on $\mathbb{Z}$ with time varying and possible state-dependent…
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…
We extend the work in New J. Phys. 19, 103015 (2017) by deriving a lower bound for the minimum time necessary to implement a unitary transformation on a generic, closed quantum system with an arbitrary number of classical control fields.…
We give upper and lower bounds for the ground-state energy of the infinite-U Hubbard model. In two dimensions, using these bounds we are able to rule out the possibility of phase separation between the undoped-insulating state and an…
In spite of their evident logical character, particle statistics symmetries are not among the inherently quantum features exploited in quantum computation. A difficulty may be that, being a constant of motion of a unitary evolution, a…
This paper is concerned with the initial-boundary value problem for an evolutionary variational inequality complying with three intrinsic properties: complete irreversibility, unilateral equilibrium of an energy and an energy conservation…
In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another…
We derive general lower energy bounds for the ground state energy of any translationally invariant quantum lattice Hamiltonian. The bounds are given by the ground state energy of renormalized Hamiltonians on finite clusters.
By combining the Minkowski inequality and the quantum Chernoff bound, we derive easy-to-compute upper bounds for the error probability affecting the optimal discrimination of Gaussian states. In particular, these bounds are useful when the…
A novel method for deriving energy conditions in stable field theories is described. In a local classical theory with one spatial dimension, a local energy condition always exists. For a relativistic field theory, one obtains the dominant…
Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly…
Quantum process tomography provides a means of measuring the evolution operator for a system at a fixed measurement time $t$. The problem of using that tomographic snapshot to predict the evolution operator at other times is generally…
By extending the concept of energy-constrained diamond norms, we obtain continuity bounds on the dynamics of both closed and open quantum systems in infinite-dimensions, which are stronger than previously known bounds. We extensively…
In the framework of finite-dimensional Fock space models, for a predefined fixed mean number of particles $\bar{n}_{k}$, it is shown that there is a ``large'' multi-dimensional subspace $s_{\bar{n}_{k}}$ of initial pure states, in the space…