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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