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The recent results of [J. Dubail, J.-M. St\'ephan, J. Viti, P. Calabrese,

Scipost Phys. 2, 002 (2017)], which aim at providing access to large scale

correlation functions of inhomogeneous critical one-dimensional quantum systems

-- e.g. a gas of hard core bosons in a trapping potential -- are extended to a

dynamical situation: a breathing gas in a time-dependent harmonic trap. Hard

core bosons in a time-dependent harmonic potential are well known to be exactly

For any resource theory it is essential to identify tasks for which resource

objects offer advantage over free objects. We show that this identification can

always be accomplished for resource theories of quantum measurements in which

free objects form a convex subset of measurements on a given Hilbert space. To

this aim we prove that every resource measurement offers advantage for some

quantum state discrimination task. Moreover, we give an operational

We present arguments proving that the results obtained by Hassanabadi and

coworkers in the study of the D-dimensional Schr\"odinger equation with

molecular Hua potential through the supersymmetry method in quantum mechanics

are incorrect. We identified the inconsistencies in their reasoning on the

allowed values of the parameter q and we constructed the correct energy

spectrum.

VO$_{2}$ is a model material system which exhibits a metal to insulator

transition at 67$^\circ$C. This holds potential for future ultrafast switching

in memory devices, but typically requires a purely electronic process to avoid

the slow lattice response. The role of lattice vibrations is thus important,

but it is not well understood and it has been a long-standing source of

controversy. We use a combination of ultrafast spectroscopy and ab initio

quantum calculations to unveil the mechanism responsible for the transition. We

We study a complex action theory (CAT) whose path runs over not only past but

also future. We show that if we regard a matrix element defined in terms of the

future state at time $T_B$ and the past state at time $T_A$ as an expectation

value in the CAT, then we are allowed to have the Heisenberg equation, the

Ehrenfest's theorem and the conserved probability current density. In addition

we show that the expectation value at the present time $t$ of a future-included

We address the question of whether transport coefficients obtained from a

unitary closed system setting, i.e., the standard equilibrium Green-Kubo

formula, are the same as the ones obtained from a weakly driven nonequilibrium

steady-state calculation. We first derive a nonequilibrium Kubo-like expression

for the steady-state diffusion constant expressed as a time-integral of either

a current or a conserved density nonequilibrium correlation function. This

Quantum computers provide an opportunity to sample from probability

distributions that include non-trivial interference effects between a large

number of amplitudes of binary trees. Using a simple process wherein all

possible state histories can be specified by a binary tree, we construct an

explicit quantum algorithm that runs in polynomial time to sample from the

process once. An interesting feature of these binary trees is that the they are

not unitary, but can still be sampled on a quantum computer.

In this paper we present a deterministic polynomial time algorithm for

testing if a symbolic matrix in non-commuting variables over $\mathbb{Q}$ is

invertible or not. The analogous question for commuting variables is the

celebrated polynomial identity testing (PIT) for symbolic determinants. In

contrast to the commutative case, which has an efficient probabilistic

algorithm, the best previous algorithm for the non-commutative setting required

exponential time (whether or not randomization is allowed). The algorithm

The geometric entanglement entropy of a quantum field in the vacuum state is

known to be divergent and, when regularized, to scale as the area of the

boundary of the region. Here we introduce an operational definition of the

entropy of the vacuum restricted to a region: we consider a subalgebra of

observables that has support in the region and a finite resolution. We then

define the entropy of a state restricted to this subalgebra. For Gaussian

states, such as the vacuum of a free scalar field, we discuss how this entropy

Quantum state transfer between microwave and optical frequencies is essential

for connecting superconducting quantum circuits to coherent optical systems and

extending microwave quantum networks over long distances. To build such a

hybrid `quantum Internet,' an important experiment in the quantum regime is to

entangle microwave and optical modes. Based on the model of a generic cavity

electro-optomechanical system, we present a heralded scheme to generate

entangled microwave--optical photon pairs, which can bypass the efficiency