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We investigate dynamical properties of a quantum generalization of classical reversible Boolean networks. The state of each node is encoded as a single qubit, and classical Boolean logic operations are supplemented by controlled bit-flip and Hadamard operations. We consider synchronous updating schemes in which each qubit is updated at each step based on stored values of the qubits from the previous step. We investigate the periodic or quasiperiodic behavior of quantum networks, and we analyze the propagation of single site perturbations through the quantum networks with input degree one. A nonclassical mechanism for perturbation propagation leads to substantially different evolution of the Hamming distance between the original and perturbed states.

Topology identification comprises reconstructing the Hamiltonian, and thus the corresponding interaction terms, by properly processing measurements of its density operator within a fixed time interval. It finds application in several quantum technology contexts, ranging from quantum communication to quantum computing or sensing. In this paper we provide analytical conditions for the solvability of the topology identification problem for autonomous quantum dynamical networks (i.e., as in our case, not explicitly depending on time via the use of an external drive). The solvability condition is then converted in an algorithm for quantum network reconstruction that is easily implementable on standard computer facilities. The obtained algorithm is tested for Hamiltonian reconstruction on numerical examples based on the quantum walks formalism.

The approach to equilibrium of quantum mechanical systems is a topic as old as quantum mechanics itself, but has recently seen a surge of interest due to applications in quantum technologies, including, but not limited to, quantum computation and sensing. The mechanisms by which a quantum system approaches its long-time, limiting stationary state are fascinating and, sometimes, quite different from their classical counterparts. In this respect, quantum networks represent mesoscopic quantum systems of interest. In such a case, the graph encodes the elementary quantum systems (say qubits) at its vertices, while the links define the interactions between them. We study here the relaxation to equilibrium for a fully connected quantum network with controlled-not (cnot) gates representing the interaction between the constituting qubits. We give a number of results for the equilibration in these systems, including analytic estimates. The results are checked using numerical methods for systems with up to 15–16 qubits. It is emphasized in which way the size of the network controls the convergency.

We theoretically introduce and experimentally demonstrate the realization of a nonclassicality test that allows for arbitrarily low detection efficiency without invoking an extra assumption of independence of the devices. Our test and its implementation is set in a prepare-and-measure scenario with an upper limit on the classical communication capacity of the channel through which the systems are communicated. The essence for our test is the use of two preparation and two measurement devices, which are randomly paired in each round. Our work opens the possibility for experimental realizations of nonclassicality tests with off-the-shelf technology.

We propose a protocol for quantum networking based on deterministic quantum state transfer between distant memory nodes using photon-number superposition states (PNSS). In the suggested scheme, the quantum nodes are single atoms confined in high-finesse optical cavities linked by photonic channels. The quantum information written in a superposition of atomic Zeeman states of sending system is faithfully mapped through cavity-assisted Raman scattering onto PNSS of linearly polarized cavity photons. The photons travel to the receiving cavity, where they are coherently absorbed with unit probability creating the same superposition state of the second atom, thus ensuring high-fidelity transfer between distant nodes. We develop this approach at first for photonic qubit and show that this superposition state is no less reliably protected against the propagation losses compared to the single-photon polarization states, whereas the limitation associated with the delivery of more than one photon does not affect the process fidelity. Then, by preserving the advantages of qubits, we extend the developed technique to the case of state transfer by photonic qutrit, which evidently possesses more information capacity. This reliable and efficient scheme promises also a successful distribution of entanglement over long distances in quantum networks.

We report the design of a diamond-based honeycomblike phononic network in which a mechanical resonator couples to three distinct phononic crystal waveguides. This two-dimensional (2D) phononic network extends an earlier study on one-dimensional (1D) phononic networks with closed mechanical subsystems. With a special design for the phononic band structures of the waveguides, any two neighboring resonators in the 2D network and the waveguide between them can form a closed mechanical subsystem, which enables nearest neighbor coupling and at the same time circumvents the scaling problems inherent in typical large mechanical systems. The nearest neighbor mechanical coupling allows the theoretical implementation of Molmer-Sorensen quantum gates between spins in adjacent mechanical resonators through phonon-assisted spin transitions. Honeycomblike phononic networks of spin qubits with nearest neighbor coupling can serve as an experimental platform for quantum computing and especially topological quantum error corrections.

A method combining perturbation theory with a simplifying ansatz is used to describe the exciton-phonon dynamics in complex networks. This method, called ${\mathrm{PT}}^{*}$, is compared to exact calculations based on the numerical diagonalization of the exciton-phonon Hamiltonian for eight small-sized networks. It is shown that the accuracy of ${\mathrm{PT}}^{*}$ depends on the nature of the network, and three different situations were identified. For most graphs, ${\mathrm{PT}}^{*}$ yields a very accurate description of the dynamics. By contrast, for the Wheel graph and the Apollonian network, ${\mathrm{PT}}^{*}$ reproduces the dynamics only when the exciton occupies a specific initial state. Finally, for the complete graph, ${\mathrm{PT}}^{*}$ breaks down. These different behaviors originate in the interplay between the degenerate nature of the excitonic energy spectrum and the strength of the exciton-phonon interaction so that a criterion is established to determine whether or not ${\mathrm{PT}}^{*}$ is relevant. When it succeeds, our study shows the undeniable advantage of ${\mathrm{PT}}^{*}$ in that it allows us to perform very fast simulations when compared to exact calculations that are restricted to small-sized networks.

We consider a general class of models, where a reinforcement learning (RL) agent learns from cyclic interactions with an external environment via classical signals. Perceptual inputs are encoded as quantum states, which are subsequently transformed by a quantum channel representing the agent's memory, while the outcomes of measurements performed at the channel's output determine the agent's actions. The learning takes place via stepwise modifications of the channel properties. They are described by an update rule that is inspired by the projective simulation (PS) model and equipped with a glow mechanism that allows for a backpropagation of policy changes, analogous to the eligibility traces in RL and edge glow in PS. In this way, the model combines features of PS with the ability for generalization, offered by its physical embodiment as a quantum system. We apply the agent to various setups of an invasion game and a grid world, which serve as elementary model tasks allowing a direct comparison with a basic classical PS agent.

The Lieb-Robinson bound sets a theoretical upper limit on the speed at which information can propagate in nonrelativistic quantum spin networks. In its original version, it results in an exponentially exploding function of the evolution time, which is partially mitigated by an exponentially decreasing term that instead depends upon the distance covered by the signal (the ratio between the two exponents effectively defining an upper bound on the propagation speed). In the present paper, by properly accounting for the free parameters of the model, we show how to turn this construction into a stronger inequality where the upper limit only scales polynomially with respect to the evolution time. Our analysis applies to any chosen topology of the network, as long as the range of the associated interaction is explicitly finite. For the special case of linear spin networks we present also an alternative derivation based on a perturbative expansion approach which improves the previous inequality. In the same context we also establish a lower bound to the speed of the information spread which yields a nontrivial result at least in the limit of small propagation times.

A quantum internet connects remote quantum processors that need to interact and exchange quantum signals over a long distance through photonic channels. However, these quantum nodes operate at the wavelength ranges unsuitable for long-distance transmission. Therefore, quantum wavelength conversion to telecom bands is crucial for long-distance quantum networks based on optical fiber. Here, we propose wavelength conversion devices for single-photon polarization qubits using continuous-variable quantum teleportation that can efficiently convert qubits between near-infrared (780–795 nm suitable for interacting with atomic quantum nodes) and telecom wavelength (1300–1500 nm suitable for long-distance transmission). The teleportation uses entangled photon fields (i.e., nondegenerate two-mode squeezed state) that can be generated by four-wave mixing in a rubidium atomic gas using a diamond configuration of atomic transitions. The entangled fields can be emitted in two orthogonal polarizations with locked relative phase, making them especially suitable for interfacing with single-photon polarization qubits. Our work may pave the way for the realization of long-distance quantum networks.

Measurement-device-independent quantum key distribution (MDI QKD) is a crucial step for the quantum Internet, as it removes all detector side channels and enables secure QKD with untrusted nodes. However, MDI QKD faces a significant challenge from polarization alignment, since drift of the state of polarization affects the efficiency of key generation, especially when the quantum states are sent from remote locations. Conventional methods for polarization alignment either require additional resources, such as classical lasers or reference pulses, or interrupt the QKD process, which reduces the efficiency of the system. In this paper, an efficient polarization-alignment method in MDI QKD is proposed that leverages intrinsic events from MDI to directly calculate how to compensate for polarization drift. The proposed method does not require additional resources such as reference pulses, thereby eliminating bandwidth limitations, and it is fast, as it can directly calculate how to correct polarization with a small criterion fluctuation. We also introduce the polarization dimension in addition to the encoding dimension and establish a response-rate model for MDI QKD with additional polarization dimensions. Overall, the proposed method is a resource-efficient solution for polarization drift correction in MDI QKD, which can enhance the practicality and scalability of QKD networks.

The task of a telecloning protocol is to send an arbitrary qubit possessed by a sender to multiple receivers. Instead of performing Bell measurement at the sender's node, if one applies unsharp measurement, we show that the shared state can further be recycled for a certain number of telecloning protocol. Specifically, in case of a single sender and two receivers, the maximum attempting number, which is defined as the maximum number of rounds used by the channel to obtain quantum advantage in the fidelity, turns out to be 3 both for optimal and nonoptimal shared states for telecloning while the maximal number reduces to 2 in case of three receivers. Although the original telecloning with quantum advantage is possible for arbitrary numbers of receivers, we report that the recycling of resources is not possible in telecloning involving a single sender and more than three receivers, thereby demonstrating a no-go theorem. We also connect the maximal achievable fidelities in each round with the bipartite entanglement content of the reduced state between the sender and one of the receivers as well as with the monogamy score of entanglement.

Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.

Quantum networks allow in principle for completely novel forms of quantum correlations. In particular, quantum nonlocality can be demonstrated here without the need of having various input settings, but only by considering the joint statistics of fixed local measurement outputs. However, previous examples of this intriguing phenomenon all appear to stem directly from the usual form of quantum nonlocality, namely via the violation of a standard Bell inequality. Here we present novel examples of “quantum nonlocality without inputs,” which we believe represent a new form of quantum nonlocality, genuine to networks. Our simplest examples, for the triangle network, involve both entangled states and joint entangled measurements. A generalization to any odd-cycle network is also presented.

Thorough control of the optical mode of a single photon is essential for quantum information applications. We present a comprehensive experimental and theoretical study of a light-matter interface based on cavity quantum electrodynamics. We identify key parameters like the phases of the involved light fields and demonstrate absolute, flexible, and accurate control of the time-dependent complex-valued wave function of a single photon over several orders of magnitude. This capability will be an important tool for the development of distributed quantum systems with multiple components that interact via photons.

Multipartite entangled states are great resources for quantum networks. In this work, we study the distribution, or routing, of entangled states over fixed, but arbitrary, physical networks. Our simplified model represents each use of a quantum channel as the sharing of a Bell pair; local operations and classical communications are considered to be free. We introduce two protocols to distribute, respectively, Greenberger-Horne-Zeilinger (GHZ) states and arbitrary graph states over arbitrary quantum networks. The GHZ states' distribution protocol takes a single step and is optimal in terms of the number of Bell pairs used; the graph states' distribution protocol uses, at most, twice as many Bell pairs and steps as the optimal routing protocol for the worst-case scenario.

Quantum networks require functional nodes consisting of stationary registers with the capability of high-fidelity quantum processing and storage, which efficiently interface with photons propagating in an optical fiber. We report a significant step towards realization of such nodes using a diamond nanocavity with an embedded silicon-vacancy (SiV) color center and a proximal nuclear spin. Specifically, we show that efficient SiV-cavity coupling (with cooperativity $C>30$) provides a nearly deterministic interface between photons and the electron spin memory, featuring coherence times exceeding 1 ms. Employing coherent microwave control, we demonstrate heralded single photon storage in the long-lived spin memory as well as a universal control over a cavity-coupled two-qubit register consisting of a SiV and a proximal ${}^{13}\mathrm{C}$ nuclear spin with nearly second-long coherence time, laying the groundwork for implementing quantum repeaters.

Characterizing tradeoffs between simultaneous violations of multiple Bell inequalities in a large network has important physical consequences but is computationally demanding. We propose a graph-theoretic approach to efficiently produce Bell monogamy relations in arbitrary arrangements of qubits. All the relations obtained for bipartite Bell inequalities are tight and leverage only a single Bell monogamy relation. This feature is unique to bipartite Bell inequalities, as we show that there is no finite set of such elementary monogamy relations for multipartite inequalities. Nevertheless, many tight monogamy relations for multipartite inequalities can be obtained with our method as shown in explicit examples.

Decoherence in quantum searches, and in the Grover search, in particular, has already been extensively studied, leading very quickly to the loss of the quadratic speedup over the classical case, when searching for some target (marked) element within a set of size $N$. The noise models used were, however, almost always global. In this paper, we study Grover search under the influence of localized partially dephasing noise of rate $p$. We find that, in the case when the size $k$ of the affected subspace is much smaller than $N$ and the target is unaffected by the noise, namely when $kp\ll \sqrt{N}$, the quadratic speedup is retained. Once these restrictions are not met, the quadratic speedup is lost. If the target is affected by the noise, the noise rate needs to scale as $1/\sqrt{N}$ to keep the speedup. We also observe an intermediate region, where if $k\sim N^{\mu }$ and the target is unaffected, the speedup seems to obey $N^{\mu }$, which for $\mu >0.5$ is worse than the quantum, but better than the classical case. We also put obtained results for quantum searches into perspective of quantum walks and searches on graphs.

Measurement-device-independent quantum key distribution (MDI-QKD) can eliminate all detector side channels and it is practical with current technology. Previous implementations of MDI-QKD all used two symmetric channels with similar losses. However, the secret key rate is severely limited when different channels have different losses. Here we report the results of the first high-rate MDI-QKD experiment over asymmetric channels. By using the recent 7-intensity optimization approach, we $\text{demonstrate}>10\times \text{higher}$ key rate than the previous best-known protocols for MDI-QKD in the situation of large channel asymmetry, and extend the secure transmission distance by more than 20–50 km in standard telecom fiber. The results have moved MDI-QKD towards widespread applications in practical network settings, where the channel losses are asymmetric and user nodes could be dynamically added or deleted.