Finding a good compromise between the exploitation of known resources and the exploration of unknown, but potentially more profitable choices, is a general problem, which arises in many different scientific disciplines. We propose a stylized model for these exploration-exploitation situations, including population or economic growth, portfolio optimization, evolutionary dynamics, or the problem of optimal pinning of vortices or dislocations in disordered materials. We find the exact growth rate of this model for treelike geometries and prove the existence of an optimal migration rate in this case. Numerical simulations in the one-dimensional case confirm the generic existence of an optimum.

We introduce information-theoretic definitions for noise and disturbance in quantum measurements and prove a state-independent noise-disturbance tradeoff relation that these quantities have to satisfy in any conceivable setup. Contrary to previous approaches, the information-theoretic quantities we define are invariant under the relabelling of outcomes and allow for the possibility of using quantum or classical operations to “correct” for the disturbance. We also show how our bound implies strong tradeoff relations for mean square deviations.

We show by using statistically rigorous arguments that the technique of weak value amplification does not perform better than standard statistical techniques for the tasks of single parameter estimation and signal detection. Specifically, we prove that postselection, a necessary ingredient for weak value amplification, decreases estimation accuracy and, moreover, arranging for anomalously large weak values is a suboptimal strategy. In doing so, we explicitly provide the optimal estimator, which in turn allows us to identify the optimal experimental arrangement to be the one in which all outcomes have equal weak values (all as small as possible) and the initial state of the meter is the maximal eigenvalue of the square of the system observable. Finally, we give precise quantitative conditions for when weak measurement (measurements without postselection or anomalously large weak values) can mitigate the effect of uncharacterized technical noise in estimation.

Quantum digital signatures (QDSs) allow the sending of messages from one sender to multiple recipients, with the guarantee that messages cannot be forged or tampered with. Additionally, messages cannot be repudiated—if one recipient accepts a message, she is guaranteed that others will accept the same message as well. While messaging with these types of security guarantees are routinely performed in the modern digital world, current technologies only offer security under computational assumptions. QDSs, on the other hand, offer security guaranteed by quantum mechanics. All thus far proposed variants of QDSs require long-term, high quality quantum memory, making them unfeasible in the foreseeable future. Here, we present a QDS scheme where no quantum memory is required, which also needs just linear optics. This makes QDSs feasible with current technology.

A proposal to use trapped ions to implement spin-one $XXZ$ antiferromagnetic chains as an experimental tool to explore the Haldane phase is presented. We explain how to reach the Haldane phase adiabatically, demonstrate the robustness of the ground states to noise in the magnetic field and Rabi frequencies, and propose a way to detect them using their characteristics: an excitation gap and exponentially decaying correlations, a nonvanishing nonlocal string order, and a double degenerate entanglement spectrum. Scaling up to higher dimensions and more frustrated lattices, we obtain richer phase diagrams, and we can reach spin liquid phase, which can be detected by its entanglement entropy which obeys the boundary law.

We report on experiments demonstrating the reversible mapping of heralded single photons to long-lived collective optical atomic excitations stored in a ${\mathrm{Pr}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$ crystal. A cavity-enhanced spontaneous down-conversion source is employed to produce widely nondegenerate narrow-band ($\approx 2\mathrm{MHz}$) photon pairs. The idler photons, whose frequency is compatible with telecommunication optical fibers, are used to herald the creation of the signal photons, compatible with the ${\mathrm{Pr}}^{3+}$ transition. The signal photons are stored and retrieved using the atomic frequency comb protocol. We demonstrate storage times up to $4.5\mu \text{s}$ while preserving nonclassical correlations between the heralding and the retrieved photon. This is more than 20 times longer than in previous realizations in solid state devices, and implemented in a system ideally suited for the extension to spin-wave storage.

The problem of identifying measurement scenarios capable of revealing state-independent contextuality in a given Hilbert space dimension is considered. We begin by showing that for any given dimension $d$ and any measurement scenario consisting of projective measurements, (i) the measure of contextuality of a quantum state is entirely determined by its spectrum, so that pure and maximally mixed states represent the two extremes of contextual behavior, and that (ii) state-independent contextuality is equivalent to the contextuality of the maximally mixed state up to a global unitary transformation. We then derive a necessary and sufficient condition for a measurement scenario represented by an orthogonality graph to reveal state-independent contextuality. This condition is given in terms of the fractional chromatic number of the graph ${\chi }_f(G)$ and is shown to identify all state-independent contextual measurement scenarios including those that go beyond the original Kochen-Specker paradigm.

We precisely test scale invariance and examine local thermal equilibrium in the hydrodynamic expansion of a Fermi gas of atoms as a function of interaction strength. After release from an anisotropic optical trap, we observe that a resonantly interacting gas obeys scale-invariant hydrodynamics, where the mean square cloud size $⟨{\mathbf{r}}^2⟩=⟨x^2+y^2+z^2⟩$ expands ballistically (like a noninteracting gas) and the energy-averaged bulk viscosity is consistent with zero, $0.00(0.04)\mathrm{\hslash }n$, with $n$ the density. In contrast, the aspect ratios of the cloud exhibit anisotropic “elliptic” flow with an energy-dependent shear viscosity. Tuning away from resonance, we observe conformal symmetry breaking, where $⟨{\mathbf{r}}^2⟩$ deviates from ballistic flow.

In this Letter, we propose a hybrid scheme to implement a photonic controlled-$z$ (CZ) gate using photon storage in highly excited Rydberg states, which controls the effective photon-photon interaction using resonant microwave fields. Our scheme decouples the light propagation from the interaction and exploits the spatial properties of the dipole blockade phenomenon to realize a CZ gate with minimal loss and mode distortion. By excluding the coupling efficiency, fidelities exceeding 95% are achievable and are found to be mainly limited by motional dephasing and the finite lifetime of the Rydberg levels.

Consider anomalous energy spread in solid phases, i.e., ${⟨\mathrm{\Delta }{x}^2(t)⟩}_E\equiv \int {(x-{⟨x⟩}_E)}^2{\rho }_E(x,t)dx\propto t^{\beta }$, as induced by a small initial excess energy perturbation distribution ${\rho }_E(x,t=0)$ away from equilibrium. The second derivative of this variance of the nonequilibrium excess energy distribution is shown to rigorously obey the intriguing relation $d^2{⟨\mathrm{\Delta }{x}^2(t)⟩}_E/d{t}^2=2{\mathcal{C}}_{JJ}(t)/(k_B{T}^{2}c)$, where ${\mathcal{C}}_{JJ}(t)$ equals the thermal equilibrium total heat flux autocorrelation function and $c$ is the specific volumetric heat capacity. Its integral assumes a time-local Helfand-like relation. Given that the averaged nonequilibrium heat flux is governed by an anomalous heat conductivity, the energy diffusion scaling determines a corresponding anomalous thermal conductivity scaling behavior.

We consider a one-dimensional $XX$ spin chain in a nonequilibrium setting with a Lindblad-type boundary driving. By calculating large-deviation rate function in the thermodynamic limit, a generalization of free energy to a nonequilibrium setting, we obtain a complete distribution of current, including closed expressions for lower-order cumulants. We also identify two phase-transition-like behaviors in either the thermodynamic limit, at which the current probability distribution becomes discontinuous, or at maximal driving, when the range of possible current values changes discontinuously. In the thermodynamic limit the current has a finite upper and lower bound. We also explicitly confirm nonequilibrium fluctuation relation and show that the current distribution is the same under mapping of the coupling strength $\mathrm{\Gamma }\to 1/\mathrm{\Gamma }$.

Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a subgraph. We show that the maximum value of the correlations for classical, quantum, and more general theories is the independence number, the Lovász number, and the fractional packing number of this subgraph, respectively. We also show that, for any graph, there is always a correlation experiment such that the set of quantum probabilities is exactly the Grötschel-Lovász-Schrijver theta body. This identifies these combinatorial notions as fundamental physical objects and provides a method for singling out experiments with quantum correlations on demand.

The Gross-Pitaevskii equation—which describes interacting bosons in the mean-field approximation—possesses solitonic solutions in dimension one. For repulsively interacting particles, the stationary soliton is dark, i.e., is represented by a local density minimum. Many-body effects may lead to filling of the dark soliton. Using quasiexact many-body simulations, we show that, in single realizations, the soliton appears totally dark although the single particle density tends to be uniform.

We study the thermodynamics of Bose-Einstein condensation in a weakly interacting quasihomogeneous atomic gas, prepared in an optical-box trap. We characterize the critical point for condensation and observe saturation of the thermal component in a partially condensed cloud, in agreement with Einstein’s textbook picture of a purely statistical phase transition. Finally, we observe the quantum Joule-Thomson effect, namely isoenthalpic cooling of an (essentially) ideal gas. In our experiments this cooling occurs spontaneously, due to energy-independent collisions with the background gas in the vacuum chamber. We extract a Joule-Thomson coefficient ${\mu }_{\mathrm{JT}}>10^9\mathrm{K}/\mathrm{bar}$, about 10 orders of magnitude larger than observed in classical gases.

We compute the universal conductivity of the ($2+1$)-dimensional $XY$ universality class, which is realized for a superfluid-to-Mott insulator quantum phase transition at constant density. Based on large-scale Monte Carlo simulations of the classical ($2+1$)-dimensional $J$-current model and the two-dimensional Bose-Hubbard model, we can precisely determine the conductivity on the quantum critical plateau, $\sigma (\infty )=0.359(4){\sigma }_Q$ with ${\sigma }_Q$ the conductivity quantum. The universal conductivity curve is the standard example with the lowest number of components where the bottoms-up AdS/CFT correspondence from string theory can be tested and made to use [R. C. Myers, S. Sachdev, and A. Singh, Phys. Rev. D 83, 066017 (2011)]. For the first time, the shape of the $\sigma (i{\omega }_n)-\sigma (\infty )$ function in the Matsubara representation is accurate enough for a conclusive comparison and establishes the particlelike nature of charge transport. We find that the holographic gauge-gravity duality theory for transport properties can be made compatible with the data if temperature of the horizon of the black brane is different from the temperature of the conformal field theory. The requirements for measuring the universal conductivity in a cold gas experiment are also determined by our calculation.

We develop a general theory for a quantum-walk search on a star graph. A star graph has $N$ edges each of which is attached to a central vertex. A graph $G$ is attached to one of these edges, and we would like to find out to which edge it is attached. This is done by means of a quantum walk, a quantum version of a random walk. This walk contains $O(\sqrt{N})$ steps, which represents a speedup over a classical search, which would require $O(N)$ steps. The overall graph, star plus $G$, is divided into two parts, and we find that for a quantum speedup to occur, the eigenvalues associated with these two parts in the $N\to \infty$ limit must be the same. Our theory tells us how the initial state of the walk should be chosen, and how many steps the walk must make in order to find $G$.

We show that, in conserved-mass transport processes, the steady-state distribution of mass in a subsystem is uniquely determined from the functional dependence of variance of the subsystem mass on its mean, provided that the joint mass distribution of subsystems is factorized in the thermodynamic limit. The factorization condition is not too restrictive as it would hold in systems with short-ranged spatial correlations. To demonstrate the result, we revisit a broad class of mass transport models and its generic variants, and show that the variance of the subsystem mass in these models is proportional to the square of its mean. This particular functional form of the variance constrains the subsystem mass distribution to be a gamma distribution irrespective of the dynamical rules.

We discuss the current carrying nonequilibrium steady state of an open fermionic Hubbard chain that is strongly driven by Markovian incoherent processes localized at the chain ends. An explicit form of an exact many-body density operator for any value of the coupling parameter is presented. The structure of a matrix product form of the solution is encoded in terms of a novel diagrammatic technique that should allow for generalization to other integrable nonequilibrium models.

We reveal universal dynamical scaling behavior across adiabatic quantum phase transitions in networks ranging from traditional spatial systems (Ising model) to fully connected ones (Dicke and Lipkin-Meshkov-Glick models). Our findings, which lie beyond traditional critical exponent analysis and adiabatic perturbation approximations, are applicable even where excitations have not yet stabilized and, hence, provide a time-resolved understanding of quantum phase transitions encompassing a wide range of adiabatic regimes. We show explicitly that even though two systems may traditionally belong to the same universality class, they can have very different adiabatic evolutions. This implies that more stringent conditions need to be imposed than at present, both for quantum simulations where one system is used to simulate the other and for adiabatic quantum computing schemes.

We consider a quantum Otto cycle for a time-dependent harmonic oscillator coupled to a squeezed thermal reservoir. We show that the efficiency at maximum power increases with the degree of squeezing, surpassing the standard Carnot limit and approaching unity exponentially for large squeezing parameters. We further propose an experimental scheme to implement such a model system by using a single trapped ion in a linear Paul trap with special geometry. Our analytical investigations are supported by Monte Carlo simulations that demonstrate the feasibility of our proposal. For realistic trap parameters, an increase of the efficiency at maximum power of up to a factor of 4 is reached, largely exceeding the Carnot bound.