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The boundaries of fractional quantum Hall states can host multiple, interacting one-dimensional edge modes, which test our understanding of strongly interacting systems. Here the authors observe the edge-mode equilibration transition that was predicted for the ν=2/3 fractional quantum Hall state.

Open quantum systems are subject to dephasing that ultimately destroys the information they hold. Here, the authors use a superconducting qubit to show that dephasing also has a geometric origin, which can either reduce or restore coherence depending on the path of the quantum system in its Hilbert space.

Quantum vacuum fluctuations can create pairs of virtual particles that annihilate each other. Here, the authors show that the conventional theory that these particles have no measurable effect on real particles does not apply to anyons, exotic quasiparticles that are intermediate between fermions and bosons.

Two challenging questions related to the quantum Hall effect (QHE) are how edge reconstruction works and where the current flows. A new model now gives the answer for two types of QHE states — two separate downstream chiral edge channels are involved.

Helical modes are induced in a high-mobility two-dimensional electron gas without strong spin–orbit coupling. This platform provides a versatile playground for investigating compounded quantum Hall edge states.

Measuring quantum entanglement remains a demanding task. The authors introduce two functions to quantify entanglement induced by fermionic or bosonic statistics, in transport experiments. Both functions, in theory and experiment, are remarkably resilient against the nonuniversal effects of interactions.

The accepted picture of transport in the fractional quantum Hall effect regime is that neutral modes are present only in hole-conjugate fractional states. Inoue et al.show the presence of upstream neutral modes and energy transport through the bulk in all tested non-hole-conjugate fractional states.

Fractional quantum statistics has recently been identified in quantum transport experiments, but the entanglement that may be associated with it remains elusive. Here the authors theoretically and experimentally investigate statistics-induced entanglement in an anyonic collider with Andreev-like tunnelling.

Quantum Hall ferromagnets can host magnons, collective spin-wave excitations, which have possible uses in spin-wave based information processing. Detecting these excitations electrically can be challenging. Here, Kumar, Srivastav, Roy, Park and coauthors demonstrate a noise-based approach to detecting magnons.

The relationship between the integer and fractional quantum Hall states are of fundamental importance in condensed matter physics. Here, the authors report a universality of phase transitions in both regimes in ultraclean trilayer graphene samples.

Quantum Hall liquids play host to a wide range of unusual physics. Here, the authors use an electronic Fabry-Pérot interferometer to observe modulations of a quantum Hall liquid’s area, which can offer a means to study the statistics of fractional charges.

The knowledge of quantum numbers of the edge modes is essential for understanding fractional Hall states containing counter-propagating downstream and upstream modes. Here the authors identify the edge quantum numbers by probing a crossover from non-equilibrated to equilibrated edge mode regime in thermal conductance.

Shot noise has traditionally been used to measure the charge of quasiparticles in a variety of mesoscopic systems. However, at sufficiently low temperatures, this usual notion tends to break down for fractional quantum Hall effect states.

Recently graphene has emerged as a new platform for the study of quantum Hall states. Here, by means of noise measurements, the authors report evidence for the existence of the upstream mode and its ballistic nature in the hole-conjugate fractional quantum Hall state in a bilayer graphene device.

To design and manipulate qubits, it is necessary to engineer multidimensional non-equilibrium steady states immune to decoherence in an open system. Here the authors devise a symmetry-based framework to create such non-equilibrium steady states showing characteristics of degenerate vacua of a unitary topological system.

The geometric phase is a deep and influential concept in modern physics and related sciences. This Review briefly discusses its origin, mathematical formulation and various forms, some of which are topological; then elaborates on contemporary optical and condensed-matter applications.