# All

We study the Landau-Zener transitions generalized to multistate systems.

Based on the work by Sinitsyn et al. [Phys. Rev. Lett. 120, 190402 (2018)], we

introduce the auxiliary Hamiltonians that are interpreted as the

counterdiabatic terms. We find that the counterdiabatic Hamiltonians satisfy

the zero curvature condition. The general structures of the auxiliary

Hamiltonians are studied in detail and the time-evolution operator is evaluated

by using a deformation of the integration contour and asymptotic forms of the

For a simple set of observables we can express, in terms of transition

probabilities alone, the Heisenberg Uncertainty Relations, so that they are

proven to be not only necessary, but sufficient too, in order for the given

observables to admit a quantum model. Furthermore distinguished

characterizations of strictly complex and real quantum models, with some

ancillary results, are presented and discussed.

Permutational Quantum Computing (PQC) [\emph{Quantum~Info.~Comput.},

\textbf{10}, 470--497, (2010)] is a natural quantum computational model

conjectured to capture non-classical aspects of quantum computation. An

argument backing this conjecture was the observation that there was no

efficient classical algorithm for estimation of matrix elements of the $S_n$

irreducible representation matrices in the Young's orthogonal form, which

correspond to transition amplitudes of a broad class of PQC circuits. This

The rich dynamics and phase structure of driven systems includes the recently

described phenomenon of the "discrete time crystal" (DTC), a robust phase which

spontaneously breaks the discrete time translation symmetry of its driving

Hamiltonian. Experiments in trapped ions and diamond nitrogen vacancy centers

have recently shown evidence for this DTC order. Here, we show nuclear magnetic

resonance (NMR) data of DTC behavior in a third, strikingly different system: a

Quantum cryptography is information-theoretically secure owing to its solid

basis in quantum mechanics. However, generally, initial implementations with

practical imperfections might open loopholes, allowing an eavesdropper to

compromise the security of a quantum cryptographic system. This has been shown

to happen for quantum key distribution (QKD). Here we apply experience from

implementation security of QKD to other quantum cryptographic primitives:

quantum digital signatures, quantum secret sharing, source-independent quantum

The power-law random banded matrices and the ultrametric random matrices are

investigated numerically in the regime where eigenstates are extended but all

integer matrix moments remain finite in the limit of large matrix dimensions.

Though in this case standard analytical tools are inapplicable, we found that

in all considered cases eigenvector distributions are extremely well described

by the generalised hyperbolic distribution which differs considerably from the

Optical interfaces for quantum emitters are a prerequisite for implementing

quantum networks. Here, we couple single molecules to the guided modes of an

optical nanofiber. The molecules are embedded within a crystal that provides

photostability and, due to the inhomogeneous broadening, a means to spectrally

address single molecules. Single molecules are excited and detected solely via

the nanofiber interface without the requirement of additional optical access.

Quantum walks, in virtue of the coherent superposition and quantum

interference, possess exponential superiority over its classical counterpart in

applications of quantum searching and quantum simulation. The quantum enhanced

power is highly related to the state space of quantum walks, which can be

expanded by enlarging the photon number and/or the dimensions of the evolution

network, but the former is considerably challenging due to probabilistic

generation of single photons and multiplicative loss. Here we demonstrate a

A method is presented by which uncertainty relations in the absence of

quantum memory can be converted to those in the presence of quantum memory. It

is shown that the lower bounds obtained through the method are tighter than

those having been achieved so far. The method is also used to obtain the

uncertainty relations for multiple measurements in the presence of quantum

memory. For a given state, the lower bounds on the sum of the relative

entropies of unilateral coherence are provided using uncertainty relations in

Using Gardiner and Collet's input-output model and the concept of cascade

system, we determine the filtering equation for a quantum system driven by

chosen non-classical states of light. The quantum system and electromagnetic

field are described by making use of quantum stochastic unitary evolution. We

consider two examples of the non-classical states of the field: a combination

of vacuum and single photon states and a mixture of two coherent states. We

describe the stochastic evolution conditioned on the results of the photon