Related papers: An upper bound on the time required to implement u…
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…
We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases…
In this paper we investigate the limits of control for mixed-state quantum systems. The constraint of unitary evolution for non-dissipative quantum systems imposes kinematical bounds on the optimization of arbitrary observables. We…
We address the question: Given an arbitrary initial state and a general physical interaction what is the minimum time for reaching a target entangled state? We show that the minimum time is inversely proportional to the quantum mechanical…
In this dissertation I analyze Hamiltonian control of $d$-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies of quantum control due to the extreme precision with which the…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number…
Motivated by studies of ultimate speed of computers, we examine the question of minimum time of orthogonalization in a simple anharmonic oscillator and find an upper bound on the rate of computations. Furthermore, we investigate the growth…
We consider a bipartite quantum object, composed of a quantum system and a quantum actuator which is periodically reset. We show that the reduced dynamics of the system approaches unitarity as the reset frequency of the actuator is…
Generating a unitary transformation in the shortest possible time is of practical importance to quantum information processing because it helps to reduce decoherence effects and improve robustness to additive control field noise. Many…
The goal of this article is to present the minimal time needed for the null controllability and finite-time stabilization of one-dimensional first-order $2 \times 2$ linear hyperbolic systems. The main technical point is to show that we…
We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent…
Given a quantum gate implementing a $d$-dimensional unitary operation $U_d$, without any specific description but $d$, and permitted to use $k$ times, we present a universal probabilistic heralded quantum circuit that implements the exact…
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here…
The unitary generation of coherence from an incoherent thermal state is investigated. We consider a completely controllable Hamiltonian allowing to generate all possible unitary transformations. Optimizing the unitary control to achieve…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation…