We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested in the quantized average displacement of the walker, which is probed by monitoring the photon loss. We confirm the topological properties of the system by observing localized edge states at the boundary of regions with different topological invariants. We further demonstrate the robustness of both the topological properties and the measurement scheme of the topological invariants against disorder.

We study the statistics of the kinetic (or, equivalently, potential) energy for $N$ noninteracting fermions in a $1d$ harmonic trap of frequency $\omega$ at finite temperature $T$. Remarkably, we find an exact solution for the full distribution of the kinetic energy, at any temperature $T$ and for any $N$, using a nontrivial mapping to an integrable Calogero-Moser-Sutherland model. As a function of temperature $T$ and for large $N$, we identify (i) a quantum regime, for $T\sim \hslash \omega$, where quantum fluctuations dominate and (ii) a thermal regime, for $T\sim N\hslash \omega$, governed by thermal fluctuations. We show how the mean and the variance as well as the large deviation function associated with the distribution of the kinetic energy cross over from the quantum to the thermal regime as $T$ increases.

In this Letter, we study the effect of topological zero modes on entanglement Hamiltonians and the entropy of free chiral fermions in $(1+1)\mathrm{D}$. We show how Riemann-Hilbert solutions combined with finite rank perturbation theory allow us to obtain exact expressions for entanglement Hamiltonians. In the absence of the zero mode, the resulting entanglement Hamiltonians consist of local and bilocal terms. In the periodic sector, the presence of a zero mode leads to an additional nonlocal contribution to the entanglement Hamiltonian. We derive an exact expression for this term and for the resulting change in the entanglement entropy.

Some physical objects are hardly accessible to direct experimentation. It is then desirable to infer their properties based solely on the interactions they have with systems over which we have control. In this spirit, here we introduce schemes for assessing the nonclassicality of the inaccessible objects as characterized by quantum discord. We consider two probes individually interacting with the inaccessible object but not with each other. The schemes are based on monitoring entanglement dynamics between the probes. Our method is robust and experimentally friendly, as it allows the probes and the object to be open systems and makes no assumptions about the initial state, dimensionality of involved Hilbert spaces, and details of the probe-object Hamiltonian. We apply our scheme to a membrane-in-the-middle optomechanical system, to detect system-environment correlations in open system dynamics as well as nonclassicality of the environment, and we foresee potential benefits for the inference of the nonclassical nature of gravity.

We derive and implement a general method to characterize the nonclassicality in compound discrete- and continuous-variable systems. For this purpose, we introduce the operational notion of conditional hybrid nonclassicality which relates to the ability to produce a nonclassical continuous-variable state by projecting onto a general superposition of discrete-variable subsystem. We discuss the importance of this form of quantumness in connection with interfaces for quantum communication. To verify the conditional hybrid nonclassicality, a matrix version of a nonclassicality quasiprobability is derived and its sampling approach is formulated. We experimentally generate an entangled, hybrid Schrödinger cat state, using a coherent photon-addition process acting on two temporal modes, and we directly sample its nonclassicality quasiprobability matrix. The introduced conditional quantum effects are certified with high statistical significance.

Given a certain amount of entanglement available as a resource, what is the most efficient way to accomplish a quantum task? We address this question in the relevant case of continuous variable quantum teleportation protocols implemented using two-mode Gaussian states with a limited degree of entanglement and energy. We first characterize the class of single-mode phase-insensitive Gaussian channels that can be simulated via a Braunstein-Kimble protocol with nonunit gain and minimum shared entanglement, showing that infinite energy is not necessary apart from the special case of the quantum limited attenuator. We also find that apart from the identity, all phase-insensitive Gaussian channels can be simulated through a two-mode squeezed state with finite energy, albeit with a larger entanglement. We then consider the problem of teleporting single-mode coherent states with Gaussian-distributed displacement in phase space. Performing a geometrical optimization over phase-insensitive Gaussian channels, we determine the maximum average teleportation fidelity achievable with any finite entanglement and for any realistically finite variance of the input distribution.

We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically processed in a nested loop by an electrically programmable gate sequence. This architecture can process any input state and an arbitrary number of modes with almost minimum resources, and offers a universal gate set for both qubits and continuous variables. Furthermore, quantum computing can be performed fault tolerantly by a known scheme for encoding a qubit in an infinite-dimensional Hilbert space of a single light mode.

A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime dimensional qudits and two-dimensional systems with real wave functions. The phenomenon of state-independent contextuality poses a priori an obstruction to characterizing the case of regular qubits, the fundamental building block of quantum computation. Here, we establish contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits. We illustrate our result with a concrete scheme related to measurement-based quantum computation.

Compression of a message up to the information it carries is key to many tasks involved in classical and quantum information theory. Schumacher [B. Schumacher, Phys. Rev. A 51, 2738 (1995)] provided one of the first quantum compression schemes and several more general schemes have been developed ever since [M. Horodecki, J. Oppenheim, and A. Winter, Commun. Math. Phys. 269, 107 (2007); I. Devetak and J. Yard, Phys. Rev. Lett. 100, 230501 (2008); A. Abeyesinghe, I. Devetak, P. Hayden, and A. Winter, Proc. R. Soc. A 465, 2537 (2009)]. However, the one-shot characterization of these quantum tasks is still under development, and often lacks a direct connection with analogous classical tasks. Here we show a new technique for the compression of quantum messages with the aid of entanglement. We devise a new tool that we call the convex split lemma, which is a coherent quantum analogue of the widely used rejection sampling procedure in classical communication protocols. As a consequence, we exhibit new explicit protocols with tight communication cost for quantum state merging, quantum state splitting, and quantum state redistribution (up to a certain optimization in the latter case). We also present a port-based teleportation scheme which uses a fewer number of ports in the presence of information about input.

Determination of the quantum nature of correlations between two spatially separated systems plays a crucial role in quantum information science. Of particular interest is the questions of if and how these correlations enable quantum information protocols to be more powerful. Here, we report on a distributed quantum computation protocol in which the input and output quantum states are considered to be classically correlated in quantum informatics. Nevertheless, we show that the correlations between the outcomes of the measurements on the output state cannot be efficiently simulated using classical algorithms. Crucially, at the same time, local measurement outcomes can be efficiently simulated on classical computers. We show that the only known classicality criterion violated by the input and output states in our protocol is the one used in quantum optics, namely, phase-space nonclassicality. As a result, we argue that the global phase-space nonclassicality inherent within the output state of our protocol represents true quantum correlations.

Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal type-II error probability in a quantum hypothesis test of two Gaussian states given a fixed constraint on the type-I error probability. This formula is a direct function of the mean vectors and covariance matrices of the quantum Gaussian states in question. We give an application to quantum illumination, which is the task of determining whether there is a low-reflectivity object embedded in a target region with a bright thermal-noise bath. For the asymmetric-error setting, we find that a quantum illumination transmitter can achieve an error probability exponent stronger than a coherent-state transmitter of the same mean photon number, and furthermore, that it requires far fewer trials to do so. This occurs when the background thermal noise is either low or bright, which means that a quantum advantage is even easier to witness than in the symmetric-error setting because it occurs for a larger range of parameters. Going forward from here, we expect our formula to have applications in settings well beyond those considered in this paper, especially to quantum communication tasks involving quantum Gaussian channels.

We derive a monogamy inequality for any local quantum resource and entanglement. It results from the fact that there is always a convex measure for a quantum resource, as shown here, and from the relation between entanglement and local entropy. One of its consequences is an entanglement monogamy different from that usually discussed. If the local resource is nonuniformity or coherence, it is satisfied by familiar resource and entanglement measures. The ensuing upper bound for the local coherence, determined by the entanglement, is independent of the basis used to define the coherence.

We consider heat transport via systems with broken time-reversal symmetry. We apply magnetic fields to the one-dimensional charged particle systems with transverse motions. The standard momentum conservation is not satisfied. To focus on this effect clearly, we introduce a solvable model. We exactly demonstrate that the anomalous transport with a new exponent can appear. We numerically show the violation of the standard relation between the power-law decay in the equilibrium correlation and the diverging exponent of the thermal conductivity in the open system.

We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.

We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical simulation of large system sizes and systematic extrapolation to the infinite system size limit. For systems smaller than the correlation length, the average entanglement follows a subthermal volume law, whose coefficient is a universal scaling function. The full distribution of entanglement follows a universal scaling form, and exhibits a bimodal structure that produces universal subleading power-law corrections to the leading volume law. For systems larger than the correlation length, the short interval entanglement exhibits a discontinuous jump at the transition from fully thermal volume law on the thermal side, to pure area law on the MBL side.

We study correlations in fermionic lattice systems with long-range interactions in thermal equilibrium. We prove a bound on the correlation decay between anticommuting operators and generalize a long-range Lieb-Robinson-type bound. Our results show that in these systems of spatial dimension $D$ with, not necessarily translation invariant, two-site interactions decaying algebraically with the distance with an exponent $\alpha \ge 2D$, correlations between such operators decay at least algebraically to 0 with an exponent arbitrarily close to $\alpha$ at any nonzero temperature. Our bound is asymptotically tight, which we demonstrate by a high temperature expansion and by numerically analyzing density-density correlations in the one-dimensional quadratic (free, exactly solvable) Kitaev chain with long-range pairing.

We define a simple model of conformal field theory in random space-time environments, which we refer to as stochastic conformal field theory. This model accounts for the effects of dilute random impurities in strongly interacting critical many-body systems. On one hand, surprisingly, although impurities are separated by macroscopic distances, we find that the infinite-time steady state is factorized on microscopic lengths, a signature of the emergence of localization. The stationary state also displays vanishing energy current and strong uncorrelated spatial fluctuations of local observables. On the other hand, at finite times, the transient shows a crossover from ballistic to diffusive energy propagation. In this regime and a Markovian limit, concentrating on current-generating initial states with a temperature imbalance, we show that the energy current and density satisfy simple dissipative hydrodynamic equations. We describe the space-time scales at which nonequilibrium currents exist. We show that a light-cone effect subsists in the presence of impurities although a momentum burst propagates transiently on a diffusive scale only.