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We introduce and solve from first principles a continuous-time quantum walk with absorption generated by a Lindblad boundary sink of arbitrary strength. Tracing out the sink maps the problem onto a non-Hermitian tight-binding Hamiltonian…
Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied. First, we show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic…
Dissipation generally leads to the decoherence of a quantum state. In contrast, numerous recent proposals have illustrated that dissipation can also be tailored to stabilize many-body entangled quantum states. While the focus of these works…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
We develop a theory of finite-time scaling for dynamic quantum criticality by considering the competition among an external time scale, an intrinsic reaction time scale and an imaginary time scale arising respectively from an external…
Quantum entanglement offers powerful opportunities for enhancing measurement sensitivity beyond classical limits, with optical atomic clocks serving as a leading platform for such advances. This chapter introduces the principles of…
The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that…
Providing entanglement for the design of quantum technologies in the presence of noise constitutes today's main challenge in quantum information science. A framework is required that assesses the build-up of entanglement in realistic…
In the last years several theoretical papers discussed if time can be an emergent property deriving from quantum correlations. Here, to provide an insight into how this phenomenon can occur, we present an experiment that illustrates Page…
The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final…
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…
We construct a metrology experiment in which the metrologist can sometimes amend her input state by simulating a closed timelike curve, a worldline that travels backward in time. The existence of closed timelike curves is hypothetical.…
All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks…
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
Why can the world resist the law of entropy increase and produce self-organizing structure? Does the entropy of an isolated system always only increase and never decrease? Can be thermodymamic degradation and self-organizing evolution…
The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock.…
We consider the 2D alternate quantum walk on a cylinder. We concentrate on the study of the motion along the open dimension, in the spirit of looking at the closed coordinate as a small or "hidden" extra dimension. If one starts from…
We investigate the time-evolution of quantum entanglement between an electron, liberated by a strong few-cycle laser pulse, and its parent ion-core. Since the standard procedure is numerically prohibitive in this case, we propose a novel…
A quantum trajectory is the natural response of a quantum system subject to external perturbations due to continuous indirect measurement. We completely characterize the asymptotic behavior of continuously monitored quantum systems in…