Related papers: Complexity in two-point measurement schemes
Suppose that particles are randomly distributed in $\bR^d$, and they are subject to identical stochastic motion independently of each other. The Smoluchowski process describes fluctuations of the number of particles in an observation region…
The rate of complexification of a quantum state is conjectured to be bounded from above by the average energy of the state. A different conjecture relates the complexity of a holographic CFT state to the on-shell gravitational action of a…
The spreading of entanglement in out-of-equilibrium quantum systems is currently at the centre of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we…
We discuss an expansion of the detection probabilities of biphoton states in terms of increasing orders of the joint spectral amplitude. The expansion enables efficient time- or frequency-resolved numerical simulations involving quantum…
We find that localised perturbations in a chaotic classical many-body system-- the classical Heisenberg We find that the effects of a localised perturbation in a chaotic classical many-body system--the classical Heisenberg chain at infinite…
Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $\gamma $ were introduced recently which measure the non-homogeneity of…
Continuing the previous initiatives arXiv: 2207.05347 and arXiv: 2212.06180, we pursue the exploration of operator growth and Krylov complexity in dissipative open quantum systems. In this paper, we resort to the bi-Lanczos algorithm…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time -- commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena,…
In a quantum change point problem, a source emitting particles in a fixed quantum state (default) switches to a different state at some stage, and the objective is to identify when the change happened by measuring a sequence of particles…
We explore further the suggestion to describe a pre- and post-selected system by a two-state, which is determined by two conditions. Starting with a formal definition of a two-state Hilbert space and basic operations, we systematically…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
Using the level--spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically…
Everything you ever wanted to know about what has come to be known as ``chaotic mixing:'' This paper describes the evolution of localised ensembles of initial conditions in 2- and 3-D time-independent potentials which admit both regular and…
Within a special multi-coin quantum walk scheme we analyze the effect of the entanglement of the initial coin state. For states with a special entanglement structure it is shown that this entanglement can be meausured with the mean value of…
Quantum entanglement is affected by unitary evolution, which spreads the entanglement through the whole system, and also by measurements, which usually tends to disentangle subsystems from the rest. Their competition has been known to…
In this work, we investigate the Krylov complexity in quantum optical systems subject to time--dependent classical external fields. We focus on various interacting quantum optical models, including a collection of two--level atoms, photonic…
We examine the physical manifestations of exceptional points and passage times in a two-level system which is subjected to quantum measurements and which admits a non-Hermitian description. Using an effective Hamiltonian acting in the…
Complex networks can model the structure and dynamics of different types of systems. It has been shown that they are characterized by a set of measures. In this work, we evaluate the variability of complex networks measures face to…
Generally, the local interactions in a many-body quantum spin system on a lattice do not commute with each other. Consequently, the Hamiltonian of a local region will generally not commute with that of the entire system, and so the two…