Contextuality is a fundamental nonclassical property of quantum theory, which has recently been proven to be a key resource for achieving quantum speed-ups in some leading models of quantum computation. However, which of the forms of contextuality, and how much thereof, are required to obtain a speed-up in an arbitrary model of quantum computation remains unclear. In this Letter, we show that the relation between contextuality and a computational advantage is more complicated than previously thought. We achieve this by proving that generalized contextuality is present even within the simplest subset of quantum operations, the so-called single-qubit stabilizer theory, which offers no computational advantage and was previously believed to be completely noncontextual. However, the contextuality of the single-qubit stabilizer theory can be confined to transformations. Therefore, our result also demonstrates that the commonly considered prepare-and-measure scenarios (which ignore transformations) do not fully capture the contextuality of quantum theory.

The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision $\epsilon$, QPE requires $O(1)$ repetitions of circuits with depth $O(1/\epsilon )$, whereas each expectation estimation subroutine within VQE requires $O(1/{\epsilon }^2)$ samples from circuits with depth $O(1)$. We propose a generalized VQE algorithm that interpolates between these two regimes via a free parameter $\alpha \in [0,1]$, which can exploit quantum coherence over a circuit depth of $O(1/{\epsilon }^{\alpha })$ to reduce the number of samples to $O(1/{\epsilon }^{2(1-\alpha )})$. Along the way, we give a new routine for expectation estimation under limited quantum resources that is of independent interest.

We investigate the localization of two incoherent point sources with arbitrary angular and axial separations in the paraxial approximation. By using quantum metrology techniques, we show that a simultaneous estimation of the two separations is achievable by a single quantum measurement, with a precision saturating the ultimate limit stemming from the quantum Cramér-Rao bound. Such a precision is not degraded in the subwavelength regime, thus overcoming the traditional limitations of classical direct imaging derived from Rayleigh’s criterion. Our results are qualitatively independent of the point spread function of the imaging system, and quantitatively illustrated in detail for the Gaussian instance. This analysis may have relevant applications in three-dimensional surface measurements.

We demonstrate that linear combinations of subregion entropies with canceling boundary terms, commonly used to calculate the topological entanglement entropy, may suffer from spurious nontopological contributions even in models with zero correlation length. These spurious contributions are due to a specific kind of long-range string order and persist throughout certain subsystem symmetry-protected phases. We introduce an entropic quantity that measures the presence of such order, and hence should serve as an order parameter for the aforementioned phases.

Many-body interference between indistinguishable particles can give rise to strong correlations rooted in quantum statistics. We study such Hanbury Brown–Twiss-type correlations for number states of ultracold massive fermions. Using deterministically prepared ${}^6\mathrm{Li}$ atoms in optical tweezers, we measure momentum correlations using a single-atom sensitive time-of-flight imaging scheme. The experiment combines on-demand state preparation of highly indistinguishable particles with high-fidelity detection, giving access to two- and three-body correlations in fields of fixed fermionic particle number. We find that pairs of atoms interfere with a contrast close to 80%. We show that second-order density correlations arise from contributions from all two-particle pairs and detect intrinsic third-order correlations.

The ground breaking extension of the key concept of phase structure to nonequilibrium regimes was only recently achieved in Floquet systems, characterized by a time-dependent quantum Hamiltonian with a periodic driving source. However, despite the theoretical advances, only very few systems are known to display experimental Floquet phases, not one of them employing a laser emission-based mechanism. Here we report the first experimental observation of a Floquet phase in a photonic system, a disordered fiber laser with spatial eigenmode localization. We apply a periodically oscillating cw pumping source that drives the random couplings of the Floquet Hamiltonian. A photonic Floquet spin-glass phase is demonstrated in the random-lasing regime by extensive measurements of the Parisi overlap parameter and asymmetry properties of its distribution. In contrast, in the fluorescent regime below threshold, the absence of mode localization prevents the stabilization of a Floquet phase. Our results are nicely described by theoretical arguments.

Crystals with symmetry-protected topological order, such as topological insulators, promise coherent spin and charge transport phenomena even in the presence of disorder at room temperature. We demonstrate how to image and read out the local conductance of helical surface modes in the prototypical topological insulators ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ and ${\mathrm{BiSbTe}}_3$. We apply the so-called Shockley-Ramo theorem to design an optoelectronic probe circuit for the gapless surface states, and we find a well-defined conductance quantization at $1e^2/h$ within the experimental error without any external magnetic field. The unprecedented response is a clear signature of local spin-polarized transport, and it can be switched on and off via an electrostatic field effect. The macroscopic, global readout scheme is based on an electrostatic coupling from the local excitation spot to the readout electrodes, and it does not require coherent transport between electrodes, in contrast to the conventional Landauer-Büttiker description. It provides a generalizable platform for studying further nontrivial gapless systems such as Weyl semimetals and quantum spin-Hall insulators.

Magnetic structures of organic Mott insulators $X[\mathrm{Pd}(\text{dmit}{)}_2{]}_2$ ($X={\mathrm{Me}}_4\mathrm{P}$, ${\mathrm{Me}}_4\mathrm{Sb}$), of which electronic states are located near a quantum spin liquid ($X={\mathrm{EtMe}}_3\mathrm{Sb}$), are demonstrated by ${}^{13}\mathrm{C}$ nuclear magnetic resonance. Antiferromagnetic spectra and nuclear relaxations show two distinct magnetic moments within each $\mathrm{Pd}(\text{dmit}{)}_2$ molecule, which cannot be described by single band dimer-Mott model and requires intramolecular electronic correlation. This unconventional fragmentation of $S=1/2$ electron spin with strong quantum fluctuation is presumably caused by nearly degenerated intramolecular multiple orbitals, and shares a notion of quantum liquids where electronic excitations are fractionalized and $S=1/2$ spin is no longer an elementary particle.

$\mathrm{Ba}({\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ is a structural homologue of the pnictide high temperature superconductor, $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$, in which the Fe atoms are replaced by Ni. Superconductivity is highly suppressed in this system, reaching a maximum $T_c=2.3\mathrm{K}$, compared to 24 K in its iron-based cousin, and the origin of this $T_c$ suppression is not known. Using x-ray scattering, we show that $\mathrm{Ba}({\mathrm{Ni}}_{1-x}{\mathrm{Co}}_x{)}_2{\mathrm{As}}_2$ exhibits a unidirectional charge density wave (CDW) at its triclinic phase transition. The CDW is incommensurate, exhibits a sizable lattice distortion, and is accompanied by the appearance of $\alpha$ Fermi surface pockets in photoemission [B. Zhou et al., Phys. Rev. B 83, 035110 (2011)], suggesting it forms by an unconventional mechanism. Co doping suppresses the CDW, paralleling the behavior of antiferromagnetism in iron-based superconductors. Our study demonstrates that pnictide superconductors can exhibit competing CDW order, which may be the origin of $T_c$ suppression in this system.

The Majorana zero mode in the semiconductor-superconductor nanowire is one of the promising candidates for topological quantum computing. Recently, in islands of nanowires, subgap-state energies have been experimentally observed to oscillate as a function of the magnetic field, showing a signature of overlapped Majorana bound states. However, the oscillation amplitude either dies away after an overshoot or decays, sharply opposite to the theoretically predicted enhanced oscillations for Majorana bound states. We reveal that a steplike distribution of spin-orbit coupling in realistic devices can induce the decaying Majorana oscillations, resulting from the coupling-induced energy repulsion between the quasiparticle spectra on the two sides of the step. This steplike spin-orbit coupling can also lead to decaying oscillations in the spectrum of the Andreev bound states. For Coulomb-blockade peaks mediated by the Majorana bound states, the peak spacings have been predicted to correlate with peak heights by a $\pi /2$ phase shift, which was ambiguous in recent experiments and may be explained by the steplike spin-orbit coupling. Our work will inspire more works to reexamine effects of the nonuniform spin-orbit coupling, which is generally present in experimental devices.

A tragedy of the commons (TOC) occurs when individuals acting in their own self-interest deplete commonly held resources, leading to a worse outcome than had they cooperated. Over time, the depletion of resources can change incentives for subsequent actions. Here, we investigate long-term feedback between game and environment across a continuum of incentives in an individual-based framework. We identify payoff-dependent transition rules that lead to oscillatory TOCs in stochastic simulations and the mean field limit. Further extending the stochastic model, we find that spatially explicit interactions can lead to emergent, localized dynamics, including the propagation of cooperative wave fronts and cluster formation of both social context and resources. These dynamics suggest new mechanisms underlying how TOCs arise and how they might be averted.

Broadband-tunable sources of circularly polarized light are crucial in fields such as laser science, biomedicine, and spectroscopy. Conventional sources rely on nonlinear wavelength conversion and polarization control using standard optical components and are limited by the availability of suitably transparent crystals and glasses. Although a gas-filled hollow-core photonic crystal fiber provides pressure-tunable dispersion, long well-controlled optical path lengths, and high Raman conversion efficiency, it is unable to preserve a circular polarization state, typically exhibiting weak linear birefringence. Here we report a revolutionary approach based on a helically twisted hollow-core photonic crystal fiber, which displays circular birefringence, thus robustly maintaining a circular polarization state against external perturbations. This makes it possible to generate pure circularly polarized Stokes and anti-Stokes signals by rotational Raman scattering in hydrogen. The polarization state of the frequency-shifted Raman bands can be continuously varied by tuning the gas pressure in the vicinity of the gain-suppression point. The results pave the way to a new generation of compact and efficient fiber-based sources of broadband light with a fully controllable polarization state.

Majorana zero modes in a superconductor are midgap states localized in the core of a vortex or bound to the end of a nanowire. They are anyons with non-Abelian braiding statistics, but when they are immobile one cannot demonstrate this by exchanging them in real space and indirect methods are needed. As a real-space alternative, we propose to use the chiral motion along the boundary of the superconductor to braid a mobile vortex in the edge channel with an immobile vortex in the bulk. The measurement scheme is fully electrical and deterministic: edge vortices ($\pi$-phase domain walls) are created on demand by a voltage pulse at a Josephson junction and the braiding with a Majorana zero mode in the bulk is detected by the charge produced upon their fusion at a second Josephson junction.

We investigate signatures of topological quantum phase transitions (TQPTs) between the $Z_2$ quantum spin liquids (QSLs). In two spatial dimensions, $Z_2$ QSLs and their TQPTs are only well defined at zero temperature ($T=0$), and it is imperative to clarify their observable signatures under nonzero temperatures. Here, we present the vestiges of TQPTs between $Z_2$ QSLs with Majorana fermions in terms of thermal Hall conductivity ${\kappa }_{xy}$ at nonzero temperatures. The ${\kappa }_{xy}/T$ shows characteristic temperature dependences around TQPTs. We argue that an exponential upturn near $T=0$ and the peak of ${\kappa }_{xy}/T$ around massive excitation energy are observable smoking-gun signals of the TQPTs. Quantum critical fan-shape temperature dependences are uncovered across TQPTs. We also perform the parton mean-field analysis on a modified Kitaev model with next-nearest neighbor interactions finding TQPTs between the phases with different Chern numbers and their vestiges self-consistently. We discuss the implication of our results to the recent experiments in $\alpha \text{−}{\mathrm{RuCl}}_3$.

We report on the experimental evidence for a nanosecond timescale spin memory based on nonradiative excitons with large in-plane wave vector. The effect manifests itself in magnetic-field-induced oscillations of the energy of the optically active (radiative) excitons. The oscillations detected by a spectrally resolved pump-probe technique applied to a GaAs/AlGaAs quantum well structure in a transverse magnetic field persist over a timescale, which is orders of magnitude longer than the characteristic decoherence time in the system. The effect is attributed to the spin-dependent electron-electron exchange interaction of the optically active and inactive excitons. The spin relaxation time of the electrons belonging to nonradiative excitons appears to be much longer than the hole spin relaxation time.

We report our theoretical results on the order parameters for the pyrochlore metal ${\mathrm{Cd}}_2{\mathrm{Re}}_2{\mathrm{O}}_7$, which undergoes enigmatic phase transitions with inversion symmetry breaking. By carefully examining active electronic degrees of freedom based on the lattice symmetry, we propose that two parity-breaking phases at ambient pressure are described by unconventional multipoles, electric toroidal quadrupoles (ETQs) with different components, $x^2-y^2$ and $3z^2-r^2$, in the pyrochlore tetrahedral unit. We elucidate that the ETQs are activated by bond or spin-current order on $\mathrm{Re}─\mathrm{Re}$ bonds. Our ETQ scenario provides a key to reconciling the experimental contradictions, by measuring ETQ specific phenomena, such as peculiar spin splittings in the electronic band structure, magnetocurrent effect, and nonreciprocal transport under a magnetic field.

We show that every entangled state provides an advantage in ancilla-assisted bi- and multichannel discrimination that singles out its degree of entanglement, quantified in terms of the Schmidt number. The Schmidt-number robustness provides a compelling quantification of such an advantage, and, remarkably, the well-known robustness of entanglement exactly provides the largest multiplicative advantage an entangled state can provide compared to the case where no ancilla is used in a channel discrimination task.