Related papers: Tight bounds on recurrence time in closed quantum …
We study the time it takes for all states of a finite quantum system to return simultaneously to their original configuration. In particular, we define the recurrence time for a quantum system to be the time at which all time-evolved states…
Generic quantum systems --as much as their classical counterparts-- pass arbitrarily close to their initial state after sufficiently long time. Here we provide an essentially exact computation of such recurrence times for generic…
We consider an initially bound quantum particle subject to an external time-dependent field. When the external field is large, the particle shows a tendency to repeatedly return to its initial state, irrespective of whether the frequency of…
We consider a closed macroscopic quantum system in a pure state $\psi_t$ evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces $\mathcal{H}_\nu$ (macro spaces) of Hilbert space, each…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…
The Poincar\'e recurrence theorem shows that conservative systems in a bounded region of phase space eventually return arbitrarily close to their initial state after a finite amount of time. An analogous behavior occurs in certain quantum…
Randomly repeated measurements during the evolution of a closed quantum system create a sequence of probabilities for the first detection of a certain quantum state. The related discrete monitored evolution for the return of the quantum…
We show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial state, i.e., making a round trip along the great circle over S^2, must have a lower bound in quantum mechanics, if…
The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of…
In this paper by using geometric techniques, we provide upper bounds for the Poincar\'e recurrence time of a quantum mixed state with discrete spectrum of energies. In the case of discrete but finite spectrum we obtain two type of upper…
We show that the dynamics of generic quantum systems concentrate around their equilibrium value when measuring at arbitrary times. This means that the probability of finding them away from equilibrium is exponentially suppressed, with a…
Recurrence time quantifies the duration required for a physical system to return to its initial state, playing a pivotal role in understanding the predictability of complex systems. In quantum systems with subspace measurements, recurrence…
Evolution time of a qubit under a Hamiltonian operation is one of the key issues in quantum control, quantum information processing and quantum computing. It has a lower bound in Hermitian system, which is limited by the coupling between…
The recurrence time is the time a process first returns to its initial state. Using quantum walks on a graph, the recurrence time is defined through stroboscopic monitoring of the arrival of the particle to a node of the system. When the…
How long does it take a quantum particle to return to its origin? As shown previously under repeated projective measurements aimed to detect the return, the closed cycle yields a geometrical phase which shows that the average first detected…
The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state $\psi_I$ may need so as to evolve into a state orthogonal to itself. Recently [V. Giovannetti, S. Lloyd,…
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…
The reverse quantum speed limit (RQSL) gives an upper limit to the time for evolution between initial and final quantum states. We show that, in conjunction with the existence of a minimum time scale, the RQSL implies a lower limit to the…
I report a tight upper bound of the maximum speed of evolution from one quantum state $\rho$ to another $\rho'$ with fidelity $F(\rho,\rho')$ less than or equal to an arbitrary but fixed value under the action of a time-independent…