The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has
many equivalent (albeit formally different) realizations as a nonlocal
generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the
other hand, if the process is to be restricted to a bounded domain, there are
many inequivalent proposals for what a boundary-data respecting fractional
Laplacian should actually be. This ambiguity holds true not only for each
specific choice of the process behavior at the boundary (like e.g. absorbtion,

Full quantum capability devices can provide secure communications, but they
are challenging to make portable given the current technology. Besides,
classical portable devices are unable to construct communication channels
resistant to quantum computers. Hence, communication security on portable
devices cannot be guaranteed. Semi-Quantum Key Distribution (SQKD) and
Semi-Quantum Direct Communication (SQDC) attempt to break the quandary by
lowering the receiver's required quantum capability so that secure

We report on the first experimental reconstruction of an entanglement
quasiprobability. In contrast to related techniques, the negativities in our
distributions are a necessary and sufficient identifier of entanglement and
enable a full characterization of the quantum state. A reconstruction algorithm
is developed, a polarization Bell state is prepared, and its entanglement is
certified based on the reconstructed entanglement quasiprobabilities, with a
high significance and without correcting for imperfections.

Weak values have been shown to be helpful especially when considering them as
the outcomes of weak measurements. In this paper we show that in principle, the
real and imaginary parts of the weak value of any operator may be elucidated
from expectation values of suitably defined density, flux and hermitian
commutator operators. Expectation values are the outcomes of strong
(projective) measurements implying that weak values are general properties of
operators in association with pre- and post-selection and they need not be

The wave function in quantum mechanics presents an interesting challenge to
our understanding of the physical world. In this paper, I show that the wave
function can be understood as four intrinsic relations on physical space. My
account has three desirable features that the standard account lacks: (1) it
does not refer to any abstract mathematical objects, (2) it is free from the
usual arbitrary conventions, and (3) it explains why the wave function has its

A free-falling nanodiamond containing a nitrogen vacancy centre in a spin
superposition should experience a superposition of forces in an inhomogeneous
magnetic field. We propose a practical design that brings the internal
temperature of the diamond to under 10 K. This extends the expected spin
coherence time from 2 ms to 500 ms, so the spatial superposition distance could
be increased from 0.05 nm to over 1 $\mu$m, for a 1 $\mu$m diameter diamond and
a magnetic inhomogeneity of only 10$^4$ T/m. The low temperature allows

Recent advances in the field of strongly correlated electron systems allow to
access the entanglement properties of interacting fermionic models, by means of
Monte Carlo simulations. We briefly review the techniques used in this context
to determine the entanglement entropies and correlations of the entanglement
Hamiltonian. We further apply these methods to compute the spin two-point
function of entanglement Hamiltonian for a stripe embedded into a correlated

We show that the quantum description of measurement based on decoherence
fixes the bug in quantum theory discussed in [D. Frauchiger and R. Renner, {\em
Quantum theory cannot consistently describe the use of itself}, Nat. Comm. {\bf
9}, 3711 (2018)]. Assuming that the outcome of a measurement is determined by
environment-induced superselection rules, we prove that different agents acting
on a particular system always reach the same conclusions about its actual

We present the experimental generation of light with directly observable
close-to ideal thermal statistical properties. The thermal light state is
prepared using a spontaneous Raman emission in a warm atomic vapor. The photon
number statistics is evaluated by both the measurement of second-order
correlation function and by the detailed analysis of the corresponding photon
number distribution, which certifies the quality of the Bose-Einstein
statistics generated by natural physical mechanism. We further demonstrate the

The permutational invariance of identical two-level systems allows for an
exponential reduction in the computational resources required to study the
Lindblad dynamics of coupled spin-boson ensembles evolving under the effect of
both local and collective noise. Here we take advantage of this speedup to
study several important physical phenomena in the presence of local incoherent
processes, in which each degree of freedom couples to its own reservoir.
Assessing the robustness of collective effects against local dissipation is