We theoretically propose and experimentally demonstrate a nonclassicality test of a single-mode field in phase space, which has an analogy with the nonlocality test proposed by Banaszek and Wódkiewicz [Phys. Rev. Lett. 82, 2009 (1999)]. Our approach to deriving the classical bound draws on the fact that the Wigner function of a coherent state is a product of two independent distributions as if the orthogonal quadratures (position and momentum) in phase space behave as local realistic variables. Our method detects every pure nonclassical Gaussian state, which can also be extended to mixed states. Furthermore, it sets a bound for all Gaussian states and their mixtures, thereby providing a criterion to detect a genuine quantum non-Gaussian state. Remarkably, our phase-space approach with invariance under Gaussian unitary operations leads to an optimized test for a given non-Gaussian state. We experimentally show how this enhanced method can manifest quantum non-Gaussianity of a state by simply choosing phase-space points appropriately, which is essentially equivalent to implementing a squeezing operation on a given state.

Dynamical decoupling operations have been shown to reduce errors in quantum information processing. Leakage from an encoded subspace to the rest of the system space is a particularly serious problem for which leakage elimination operators (LEOs) were introduced. Here we provide an analysis of nonideal pulses, rather than the well-understood idealization or bang-bang controls. Under realistic conditions, we show that these controls will provide the same protection from errors as idealized controls. Our work indicates that the effectiveness of LEOs depends on the integral of the pulse sequence in the time domain, which has been missing because of the idealization of pulse sequences. Our results are applied to a three-level system for the nitrogen-vacancy centers under an external magnetic field and are illustrated by the fidelity dynamics of LEO sequences, ranging from regular rectangular pulses, random pulses, and even disordered (noisy) pulses.

We show that critical exponents of the transition to columnar order in a mixture of $2\times 1$ dimers and $2\times 2$ hard squares on the square lattice depends on the composition of the mixture in exactly the manner predicted by the theory of Ashkin-Teller criticality, including in the hard-square limit. This result settles the question regarding the nature of the transition in the hard-square lattice gas. It also provides the first example of a polydisperse system whose critical properties depend on composition. Our ideas also lead to some interesting predictions for a class of frustrated quantum magnets that exhibit columnar ordering of the bond energies at low temperature.

A projective measurement of energy (PME) on a quantum system is a quantum measurement determined by the Hamiltonian of the system. PME protocols exist when the Hamiltonian is given in advance. Unknown Hamiltonians can be identified by quantum tomography, but the time cost to achieve a given accuracy increases exponentially with the size of the quantum system. In this Letter, we improve the time cost by adapting quantum phase estimation, an algorithm designed for computational problems, to measurements on physical systems. We present a PME protocol without quantum tomography for Hamiltonians whose dimension and energy scale are given but which are otherwise unknown. Our protocol implements a PME to arbitrary accuracy without any dimension dependence on its time cost. We also show that another computational quantum algorithm may be used for efficient estimation of the energy scale. These algorithms show that computational quantum algorithms, with suitable modifications, have applications beyond their original context.

We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities are members of the complete set of full-correlation Bell inequalities discovered by Werner-Wolf-Żukowski-Brukner. For scenarios involving a small number of parties, we further verify that these inequalities are facet defining for the convex set of Bell-local correlations. Moreover, we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlying system is genuinely many-body entangled. In other words, our Bell inequalities, when supplemented with the appropriate quantum bounds, naturally serve as device-independent witnesses for entanglement depth, allowing one to certify genuine $k$-partite entanglement in an arbitrary $n\ge k$-partite scenario without relying on any assumption about the measurements being performed, or the dimension of the underlying physical system. A brief comparison is made between our witnesses and those based on some other Bell inequalities, as well as quantum Fisher information. A family of witnesses for genuine $k$-partite nonlocality applicable to an arbitrary $n\ge k$-partite scenario based on our Bell inequalities is also presented.

Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are $n$-particle states which do not exhibit $n$-partite correlations at all but still are genuinely $n$-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without multipartite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.

In quantum key distribution (QKD), the bit error rate is used to estimate the information leakage and hence determines the amount of privacy amplification—making the final key private by shortening the key. In general, there exists a threshold of the error rate for each scheme, above which no secure key can be generated. This threshold puts a restriction on the environment noises. For example, a widely used QKD protocol, the Bennett-Brassard protocol, cannot tolerate error rates beyond 25%. A new protocol, round-robin differential phase-shifted (RRDPS) QKD, essentially removes this restriction and can in principle tolerate more environment disturbance. Here, we propose and experimentally demonstrate a passive RRDPS QKD scheme. In particular, our 500 MHz passive RRDPS QKD system is able to generate a secure key over 50 km with a bit error rate as high as 29%. This scheme should find its applications in noisy environment conditions.

How can one detect entanglement between multiple optical paths sharing a single photon? We address this question by proposing a scalable protocol, which only uses local measurements where single photon detection is combined with small displacement operations. The resulting entanglement witness does not require postselection, nor assumptions about the photon number in each path. Furthermore, it guarantees that entanglement lies in a subspace with at most one photon per optical path and reveals genuinely multipartite entanglement. We demonstrate its scalability and resistance to loss by performing various experiments with two and three optical paths. We anticipate applications of our results for quantum network certification.

The phenomenon of many-body localization has received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at nonzero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalization following out-of-equilibrium dynamics. In this work, we establish a novel link between dynamical properties—a vanishing group velocity and the absence of transport—with entanglement properties of individual eigenvectors. For systems with a generic spectrum, we prove that strong dynamical localization implies that all of its many-body eigenvectors have clustering correlations. The same is true for parts of the spectrum, thus allowing for the existence of a mobility edge above which transport is possible. In one dimension these results directly imply an entanglement area law; hence, the eigenvectors can be efficiently approximated by matrix-product states.

We use two-time correlation functions to study the complex dynamics of dissipative many-body quantum systems. In order to measure, understand, and categorize these correlations we extend the framework of the adiabatic elimination method. We show that, for the same parameters and times, two-time correlations can display two distinct behaviors depending on the observable considered: a fast exponential decay or a much slower dynamics. We exemplify these findings by studying strongly interacting bosons in a double well subjected to phase noise. While the single-particle correlations decay exponentially fast with time, the density-density correlations display slow aging dynamics. We also show that this slow relaxation regime is robust against particle losses. Additionally, we use the developed framework to show that the dynamic properties of dissipatively engineered states can be drastically different from their Hamiltonian counterparts.

Interfacing between various elements of a computer—from memory to processors to long range communication—will be as critical for quantum computers as it is for classical computers today. Paramagnetic rare-earth doped crystals, such as ${\mathrm{Nd}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5(\mathrm{YSO})$, are excellent candidates for such a quantum interface: they are known to exhibit long optical coherence lifetimes (for communication via optical photons), possess a nuclear spin (memory), and have in addition an electron spin that can offer hybrid coupling with superconducting qubits (processing). Here we study two of these three elements, demonstrating coherent storage and retrieval between electron and ${}^{145}\mathrm{Nd}$ nuclear spin states in ${\mathrm{Nd}}^{3+}:\mathrm{YSO}$. We find nuclear spin coherence times can reach 9 ms at $\sim 5\mathrm{K}$, about 2 orders of magnitude longer than the electron spin coherence, while quantum state and process tomography of the storage or retrieval operation between the electron and nuclear spin reveal an average state fidelity of 0.86. The times and fidelities are expected to further improve at lower temperatures and with more homogeneous radio-frequency excitation.

Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement has been thought to be resource intensive to create in the first place—typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multiphoton walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer—fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection—is capable of significantly beating the shot-noise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.

We improve the precision of the interferometric weak-value-based beam deflection measurement by introducing a power recycling mirror, creating a resonant cavity. This results in all the light exiting to the detector with a large deflection, thus eliminating the inefficiency of the rare postselection. The signal-to-noise ratio of the deflection is itself magnified by the weak value. We discuss ways to realize this proposal, using a transverse beam filter and different cavity designs.

Most methods of optimal control cannot obtain accurate time-optimal protocols. The quantum brachistochrone equation is an exception, and has the potential to provide accurate time-optimal protocols for a wide range of quantum control problems. So far, this potential has not been realized, however, due to the inadequacy of conventional numerical methods to solve it. Here we show that the quantum brachistochrone problem can be recast as that of finding geodesic paths in the space of unitary operators. We expect this brachistochrone-geodesic connection to have broad applications, as it opens up minimal-time control to the tools of geometry. As one such application, we use it to obtain a fast numerical method to solve the brachistochrone problem, and apply this method to two examples demonstrating its power.

Metastable $\beta$ ice holds small guest molecules in stable gas hydrates, so its solid-liquid equilibrium is of interest. However, aqueous crystal-liquid transitions are very difficult to simulate. A new molecular dynamics algorithm generates trajectories in a generalized $NPT$ ensemble and equilibrates states of coexisting phases with a selectable enthalpy. With replicas spanning the range between $\beta$ ice and liquid water, we find the statistical temperature from the enthalpy histograms and characterize the transition by the entropy, introducing a general computational procedure for first-order transitions.

We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multifold product states. The approximation is measured by distinguishability under measurements that are implementable by fully-one-way local operations and classical communication (LOCC). Our result strengthens Brandão and Harrow’s de Finetti theorem where a kind of partially-one-way LOCC measurements was used for measuring the approximation, with essentially the same error bound. As main applications, we show (i) a quasipolynomial-time algorithm which detects multipartite entanglement with an amount larger than an arbitrarily small constant (measured with a variant of the relative entropy of entanglement), and (ii) a proof that in quantum Merlin-Arthur proof systems, polynomially many provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations.

We explore the high-temperature dynamics of the disordered, one-dimensional $XXZ$ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., “metallic”) phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.

Correlations that violate a Bell inequality are said to be nonlocal; i.e., they do not admit a local and deterministic explanation. Great effort has been devoted to study how the amount of nonlocality (as measured by a Bell inequality violation) serves to quantify the amount of randomness present in observed correlations. In this work we reverse this research program and ask what do the randomness certification capabilities of a theory tell us about the nonlocality of that theory. We find that, contrary to initial intuition, maximal randomness certification cannot occur in maximally nonlocal theories. We go on and show that quantum theory, in contrast, permits certification of maximal randomness in all dichotomic scenarios. We hence pose the question of whether quantum theory is optimal for randomness; i.e., is it the most nonlocal theory that allows maximal randomness certification? We answer this question in the negative by identifying a larger-than-quantum set of correlations capable of this feat. Not only are these results relevant to understanding quantum mechanics’ fundamental features, but also put fundamental restrictions on device-independent protocols based on the no-signaling principle.