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The earth mover's distance is a measure of the distance between two
probabilistic measures. It plays a fundamental role in mathematics and computer
science. The Kantorovich-Rubinstein theorem provides a formula for the earth
mover's distance on the space of regular probability Borel measures on a
compact metric space. In this paper, we investigate the quantum earth mover's
distance. We show a no-go Kantorovich-Rubinstein theorem in the quantum
setting. More precisely, we show that the trace distance between two quantum

We map Spekkens' toy model to a quantum mechanics defined over the finite
field $\mathbb{F}_5$. This allows us to define arbitrary linear combinations of
the epistemic states in the model. For Spekkens' elementary system with only
$2^2=4$ ontic states, the mapping is exact and the two models agree completely.
However, for a pair of elementary systems there exist interesting differences
between the entangled states of the two models.

Anyons occur in two-dimensional electron systems as excitations with
fractional charge in the topologically ordered states of the Fractional Quantum
Hall Effect (FQHE). Their dynamics are of utmost importance for topological
quantum phases and possible decoherence free quantum information approaches,
but observing these dynamics experimentally is challenging. Here we report on a
dynamical property of anyons: the long predicted Josephson relation fJ=e*V/h
for charges e*=e/3 and e/5, where e is the charge of the electron and h is

Anisotropic quantum Rabi model is a generalization of quantum Rabi model,
which allows its rotating and counter-rotating terms to have two different
coupling constants. It provides us with a fundamental model to understand
various physical features concerning quantum optics, solid-state physics, and
mesoscopic physics. In this paper, we propose an experimental feasible scheme
to implement anisotropic quantum Rabi model in a circuit quantum
electrodynamics system via periodic frequency modulation. An effective

The realization of topological quantum phases of matter remains a key
challenge to condensed matter physics and quantum information science. In this
work, we demonstrate that progress in this direction can be made by combining
concepts of tensor network theory with Majorana device technology. Considering
the topological double semion string-net phase as an example, we exploit the
fact that the representation of topological phases by tensor networks can be
significantly simpler than their description by lattice Hamiltonians. The

We consider a qubit initalized in a superposition of its pointer states,
exposed to pure dephasing due to coupling to a quasi-static environment, and
subjected to a sequence of single-shot measurements projecting it on chosen
superpositions. We show how with a few of such measurements one can
significantly diminish one's ignorance about the environmental state, and how
this leads to increase of coherence of the qubit interacting with a properly
post-selected environmental state. We give theoretical results for the case of

We analytically calculate the optical emission spectrum of nanolasers and
nano-LEDs based on a model of many incoherently pumped two-level emitters in a
cavity. At low pump rates we find two peaks in the spectrum for large coupling
strengths and numbers of emitters. We interpret the double-peaked spectrum as a
signature of collective Rabi splitting, and discuss the difference between the
splitting of the spectrum and the existence of two eigenmodes. We show that an

The existence and stability of the linear hydrogenic chain H$_3$ and
H${}_2^-$ in a strong magnetic field is established. Variational calculations
for H$_3$ and H${}_2^-$ are carried out in magnetic fields in the range
$10^{11}\leq B \leq 10^{13}\,$G with 17-parametric (14-parametric for
H${}_2^-$), physically adequate trial function. Protons are assumed infinitely
massive, fixed along the magnetic line. States with total spin projection
$S_z=-3/2$ and magnetic quantum numbers $M=-2,-3,-4$ are studied. It is shown

We investigate monogamy relations related to the R\'{e}nyi-$\alpha$
entanglement and polygamy relations related to the R\'{e}nyi-$\alpha$
entanglement of assistance. We present new entanglement monogamy relations
satisfied by the $\mu$-th power of R\'{e}nyi-$\alpha$ entanglement with
$\alpha\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $\mu\geqslant2$, and polygamy
relations satisfied by the $\mu$-th power of R\'{e}nyi-$\alpha$ entanglement of
assistance with $\alpha\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $0\leq\mu\leq1$.

Quantum annealing is a computing paradigm that has the ambitious goal of
efficiently solving large-scale combinatorial optimization problems of
practical importance. However, many challenges have yet to be overcome before
this goal can be reached. This perspectives article first gives a brief
introduction to the concept of quantum annealing, and then highlights new
pathways that may clear the way towards feasible and large scale quantum
annealing. Moreover, since this field of research is to a strong degree driven