We present a new algorithm for calculating the Renyi entanglement entropy of interacting fermions using the continuous-time quantum Monte Carlo method. The algorithm only samples the interaction correction of the entanglement entropy, which by design ensures the efficient calculation of weakly interacting systems. Combined with Monte Carlo reweighting, the algorithm also performs well for systems with strong interactions. We demonstrate the potential of this method by studying the quantum entanglement signatures of the charge-density-wave transition of interacting fermions on a square lattice.

We investigate the distribution of bipartite and multipartite entanglement in multiqubit states. In particular, we define a set of monogamy inequalities sharpening the conventional Coffman-Kundu-Wootters constraints, and we provide analytical proofs of their validity for relevant classes of states. We present extensive numerical evidence validating the conjectured strong monogamy inequalities for arbitrary pure states of four qubits.

We pose a randomized boson-sampling problem. Strong evidence exists that such a problem becomes intractable on a classical computer as a function of the number of bosons. We describe a quantum optical processor that can solve this problem efficiently based on a Gaussian input state, a linear optical network, and nonadaptive photon counting measurements. All the elements required to build such a processor currently exist. The demonstration of such a device would provide empirical evidence that quantum computers can, indeed, outperform classical computers and could lead to applications.

We prove exactly that the squared entanglement of formation, which quantifies the bipartite entanglement, obeys a general monogamy inequality in an arbitrary multiqubit mixed state. Based on this kind of exotic monogamy relation, we are able to construct two sets of useful entanglement indicators: the first one can detect all genuine multiqubit entangled states even in the case of the two-qubit concurrence and $n$-tangles being zero, while the second one can be calculated via quantum discord and applied to multipartite entanglement dynamics. Moreover, we give a computable and nontrivial lower bound for multiqubit entanglement of formation.

Normal diffusion in corrugated potentials with spatially uncorrelated Gaussian energy disorder famously explains the origin of non-Arrhenius $\exp [-{\sigma }^2/(k_B{T}^2)]$ temperature dependence in disordered systems. Here we show that unbiased diffusion remains asymptotically normal also in the presence of spatial correlations decaying to zero. However, because of a temporal lack of self-averaging, transient subdiffusion emerges on the mesoscale, and it can readily reach macroscale even for moderately strong disorder fluctuations of $\sigma \sim 4-5k_{B}T$. Because of its nonergodic origin, such subdiffusion exhibits a large scatter in single-trajectory averages. However, at odds with intuition, it occurs essentially faster than one expects from the normal diffusion in the absence of correlations. We apply these results to diffusion of regulatory proteins on DNA molecules and predict that such diffusion should be anomalous, but much faster than earlier expected on a typical length of genes for a realistic energy disorder of several room $k_{B}T$, or merely $0.05–0.075\mathrm{eV}$.

Three-dimensional self-gravitating systems do not evolve to thermodynamic equilibrium but become trapped in nonequilibrium quasistationary states. In this Letter, we present a theory which allows us to a priori predict the particle distribution in a final quasistationary state to which a self-gravitating system will evolve from an initial condition which is isotropic in particle velocities and satisfies a virial constraint $2K=-U$, where $K$ is the total kinetic energy, and $U$ is the potential energy of the system.

Landauer’s principle states that it costs at least $k_{B}T\ln 2$ of work to reset one bit in the presence of a heat bath at temperature $T$. The bound of $k_{B}T\ln 2$ is achieved in the unphysical infinite-time limit. Here we ask what is possible if one is restricted to finite-time protocols. We prove analytically that it is possible to reset a bit with a work cost close to $k_{B}T\ln 2$ in a finite time. We construct an explicit protocol that achieves this, which involves thermalizing and changing the system’s Hamiltonian so as to avoid quantum coherences. Using concepts and techniques pertaining to single-shot statistical mechanics, we furthermore prove that the heat dissipated is exponentially close to the minimal amount possible not just on average, but guaranteed with high confidence in every run. Moreover, we exploit the protocol to design a quantum heat engine that works near the Carnot efficiency in finite time.

We study a problem of interconvertibility of two supraquantum resources: one is the so-called Popescu-Rohrlich (PR) box, which violates Clauser-Horne-Shimony-Holt inequality up to the maximal algebraic bound, and the second is the so-called random access code (RAC). The latter is a functionality that enables Bob (receiver) to choose one of two bits of Alice. It is known that a PR box supplemented with one bit of communication can be used to simulate a RAC. We ask the converse question: to what extent can a RAC can simulate a PR box? To this end, we introduce a “racbox”: a box such that when it is supplemented with one bit of communication it offers a RAC. As said, a PR box can simulate a racbox. The question we raise is whether any racbox can simulate a PR box. We show that a nonsignaling racbox, indeed, can simulate a PR box; hence, these two resources are equivalent. We also provide an example of a signaling racbox that cannot simulate a PR box. We give a resource inequality between racboxes and PR boxes and show that it is saturated.

We derive a general framework that lifts any set of bipartite to multipartite entanglement witnesses and we show how positive maps can naturally be incorporated into this framework. We show that some previous approaches for multipartite entanglement detection are intimately connected to the witnesses derived from partial transposition and that such criteria can easily be outperformed in higher dimensions by nondecomposable maps. As an exemplary case we present a witness that is capable of detecting genuine multipartite entanglement in bound entangled states.

General wisdom tells us that if two quantum states are “macroscopically distinguishable” then their superposition should be hard to observe. We make this intuition precise and general by quantifying the difficulty to observe the quantum nature of a superposition of two states that can be distinguished without microscopic accuracy. First, we quantify the distinguishability of any given pair of quantum states with measurement devices lacking microscopic accuracy, i.e., measurements suffering from limited resolution or limited sensitivity. Next, we quantify the required stability that has to be fulfilled by any measurement setup able to distinguish their superposition from a mere mixture. Finally, by establishing a relationship between the stability requirement and the “distinguishability with inaccurate measurements” of the two superposed states, we demonstrate that, indeed, the more distinguishable the states are, the more demanding the stability requirements.

Kochen-Specker (KS) sets are key tools for proving some fundamental results in quantum theory and also have potential applications in quantum information processing. However, so far, their intrinsic complexity has prevented experimentalists from using them for any application. The KS set requiring the smallest number of contexts has been recently found. Relying on this simple KS set, here we report an input state-independent experimental technique to certify whether a set of measurements is actually accessing a preestablished quantum six-dimensional space encoded in the transverse momentum of single photons.

We investigate theoretically the effects of a dynamically increasing medium index on optical-wave propagation in a rubidium condensate. A long pulsed pump laser coupling a $D2$ line transition produces a rapidly growing internally generated field. This results in a significant optical self-focusing effect and creates a dynamically growing medium index anomaly that propagates ultraslowly with the internally generated field. When a fast probe pulse injected after a delay catches up with the dynamically increasing index anomaly, it is forced to slow down and is prohibited from crossing the anomaly, thereby realizing an ultraslow optical-matter wave analog of a dynamic white-hole event horizon.

The direct measurement of a complex wave function has been recently realized by using weak values. In this Letter, we introduce a method that exploits sparsity for the compressive measurement of the transverse spatial wave function of photons. The procedure involves weak measurements of random projection operators in the spatial domain followed by postselection in the momentum basis. Using this method, we experimentally measure a 192-dimensional state with a fidelity of 90% using only 25 percent of the total required measurements. Furthermore, we demonstrate the measurement of a 19 200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique.

The ability of widely used sampling methods, such as molecular dynamics or Monte Carlo simulations, to explore complex free energy landscapes is severely hampered by the presence of kinetic bottlenecks. A large number of solutions have been proposed to alleviate this problem. Many are based on the introduction of a bias potential which is a function of a small number of collective variables. However constructing such a bias is not simple. Here we introduce a functional of the bias potential and an associated variational principle. The bias that minimizes the functional relates in a simple way to the free energy surface. This variational principle can be turned into a practical, efficient, and flexible sampling method. A number of numerical examples are presented which include the determination of a three-dimensional free energy surface. We argue that, beside being numerically advantageous, our variational approach provides a convenient and novel standpoint for looking at the sampling problem.

Certifying the entanglement of quantum states with Bell inequalities allows one to guarantee the security of quantum information protocols independently of imperfections in the measuring devices. Here, we present a similar procedure for witnessing entangled measurements, which play a central role in many quantum information tasks. Our procedure is termed semi-device-independent, as it uses uncharacterized quantum preparations of fixed Hilbert space dimension. Using a photonic setup, we experimentally certify an entangled measurement using only measurement statistics. We also apply our techniques to certify unentangled but nevertheless inherently quantum measurements.

Topological orders are exotic phases of matter existing in strongly correlated quantum systems, which are beyond the usual symmetry description and cannot be distinguished by local order parameters. Here we report an experimental quantum simulation of the Wen-plaquette spin model with different topological orders in a nuclear magnetic resonance system, and observe the adiabatic transition between two $Z_2$ topological orders through a spin-polarized phase by measuring the nonlocal closed-string (Wilson loop) operator. Moreover, we also measure the entanglement properties of the topological orders. This work confirms the adiabatic method for preparing topologically ordered states and provides an experimental tool for further studies of complex quantum systems.

We introduce the concept of a bosonic spin liquid condensate (SLC), where spinful bosons in a lattice form a zero-temperature spin disordered charge condensate that preserves the spin rotation symmetry, but breaks the U(1) symmetry due to a spinless order parameter with charge one. It has an energy gap to all the spin excitations. We show that such SLC states can be realized in a system of spin $S\ge 2$ bosons. In particular, we analyze the SLC phase diagram in the spin 2 case using a mean-field variational wave function method. We show there is a direct analogy between the SLC and the resonating-valence-bond state.

Steane’s 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal fault-tolerant gate set but possesses fault-tolerant $T$ and control-control-$Z$ gates. Combined with the Clifford group, either of these two gates generates a universal set. Here, we combine these two features by demonstrating how to fault-tolerantly convert between these two codes, providing a new method to realize universal fault-tolerant quantum computation. One interpretation of our result is that both codes correspond to the same subsystem code in different gauges. Our scheme extends to the entire family of quantum Reed-Muller codes.