This Tutorial will introduce the mathematical framework for describing
systems of identical particles, and explain the notion of indistinguishability.
We will then focus our attention on dynamical systems of free particles and
formally introduce the concept of many-particle interference. Its impact on
many-particle transition probabilities is computationally challenging to
evaluate, and it becomes rapidly intractable for systems with large numbers of
identical particles. Hence, this Tutorial will build up towards alternative,

The growing field of quantum computing is based on the concept of a q-bit
which is a delicate superposition of 0 and 1, requiring cryogenic temperatures
for its physical realization along with challenging coherent coupling
techniques for entangling them. By contrast, a probabilistic bit or a p-bit is
a robust classical entity that fluctuates between 0 and 1, and can be
implemented at room temperature using present-day technology. Here, we show
that a probabilistic coprocessor built out of room temperature p-bits can be

S-money [Proc. R. Soc. A 475, 20190170 (2019)] schemes define virtual tokens
designed for networks with relativistic or other trusted signalling
constraints. The tokens allow near-instant verification and guarantee
unforgeability without requiring quantum state storage. We present refined two
stage S-money schemes. The first stage, which may involve quantum information
exchange, generates private user token data. In the second stage, which need
only involve classical communications, users determine the valid presentation

Photosynthetic organisms use networks of chromophores to absorb sunlight and
deliver the energy to reaction centres, where charge separation triggers a
cascade of chemical steps to store the energy. We present a detailed model of
the light-harvesting complexes in purple bacteria, including explicit
interaction with sunlight; energy loss through radiative and non-radiative
processes; and dephasing and thermalizing effects of coupling to a vibrational
bath. An important feature of the model is that we capture the effect of slow

We establish the general framework of quantum fluctuation theorems by finding
the symmetry between the forward and backward transitions of any given quantum
channel. The Petz recovery map is adopted as the reverse quantum channel, and
the notion of entropy production in thermodynamics is extended to the quantum
regime. Our result shows that the fluctuation theorems, which are normally
considered for thermodynamic processes, can be a powerful tool to study the

We study bosons in a one-dimensional hard wall box potential. In the case of
contact interaction, the system is exactly solvable by Bethe ansatz, as first
shown by Gaudin in 1971. Although contained in the exact solution, the boundary
energy for this problem is only approximately calculated by Gaudin at the
leading order at weak repulsion. Here we derive an exact integral equation that
enables one to calculate the boundary energy in the thermodynamic limit at an

We propose a quantum classifier, which can classify data under the supervised
learning scheme using a quantum feature space. The input feature vectors are
encoded in a single qu$N$it (a $N$ level quantum system), as opposed to more
commonly used entangled multi-qubit systems. For training we use the much used
quantum variational algorithm -- a hybrid quantum-classical algorithm -- in
which the forward part of the computation is performed on a quantum hardware

We present a method to generate NOON states with three photons by injecting
photons in an array of three waveguides. Conditional measurements project the
wave function in a given (desired) state. In passing, we show how the array of
three waveguides, that effectively reproduces the interaction of three fields,
may be reduced to the interaction of two fields.

The technological refinement of experimental techniques has recently allowed
the generation of two-photon polarization entangled states at low Earth orbit,
which have been subsequently applied to quantum communications. This
achievement paves the way to study the interplay between General Relativity and
Quantum Mechanics in new setups. Here, we study the generation of two-photon
entangled states via large scale Franson and Hugged interferometric arrays in
the presence of a weak gravitational field. We show that for certain

Para positronium composed by an electron-antielectron pair is an unstable
system decaying into two high energetic gamma photons via self annihilation
process, due to the conservation of the charge conjugation parity in
electromagnetically interacting systems. Therefore, the spectrum covering all
fundamental properties of the para-positronium system includes an imaginary
part corresponding to the proper decay time besides the real parts
corresponding to the total annihilation energy and binding energy,