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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