The stages of a quantum internet: As indispensable as the internet has become in our daily lives, it still has many shortcomings, not least of which is that communication can be intercepted and information stolen. If, however, the internet attained the capability of transmitting quantum information—qubits—many of these security concerns would be addressed. Wehner et al. review what it will take to achieve this so-called quantum internet and propose stages of development that each correspond to increasingly powerful applications. Although a full-blown quantum internet, with functional quantum computers as nodes connected through quantum communication channels, is still some ways away, the first long-range quantum networks are already being planned. Science , this issue p. eaam9288

A quantum internet is the holy grail of quantum information processing, enabling the deployment of a broad range of quantum technologies and protocols on a global scale. However, numerous challenges must be addressed before the quantum internet can become a reality. Perhaps the most crucial of these is the realization of a quantum repeater, an essential component in the long-distance transmission of quantum information. As the analog of a classical repeater, extender, or booster, the quantum repeater works to overcome loss and noise in the quantum channels constituting a quantum network. Here the conceptual frameworks and architectures for quantum repeaters, as well as the experimental progress toward their realization, are reviewed. Various near-term proposals to overcome the limits to the communication rates set by point-to-point quantum communication are also discussed. Finally, the manner in which quantum repeaters fit within the broader challenge of designing and implementing a quantum internet is overviewed.

Quantum channels enable the implementation of communication tasks inaccessible to their classical counterparts. The most famous example is the distribution of secret key. However, in the absence of quantum repeaters, the rate at which these tasks can be performed is dictated by the losses in the quantum channel. In practice, channel losses have limited the reach of quantum protocols to short distances. Quantum repeaters have the potential to significantly increase the rates and reach beyond the limits of direct transmission. However, no experimental implementation has overcome the direct transmission threshold. Here, we propose three quantum repeater schemes and assess their ability to generate secret key when implemented on a setup using nitrogen-vacancy (NV) centers in diamond with near-term experimental parameters. We find that one of these schemes—the so-called single-photon scheme, requiring no quantum storage—has the ability to surpass the capacity—the highest secret-key rate achievable with direct transmission—by a factor of 7 for a distance of approximately 9.2 km with near-term parameters, establishing it as a prime candidate for the first experimental realization of a quantum repeater.

We consider the problem of optimizing the achievable EPR-pair distribution rate between multiple source-destination pairs in a quantum Internet, where the repeaters may perform a probabilistic Bell-state measurement and we may impose a minimum end-to-end fidelity as a requirement. We construct an efficient linear programming (LP) formulation that computes the maximum total achievable entanglement distribution rate, satisfying the end-to-end fidelity constraint in polynomial time (in the number of nodes in the network). Our LP formulation gives the optimal rate for a class of entanglement generation protocols where the repeaters have very short-lived quantum memories. We also propose an efficient algorithm that takes the output of the LP solver as an input and runs in polynomial time (in the number of nodes) to produce the set of paths to be used to achieve the entanglement distribution rate. Moreover, we point out a practical entanglement generation protocol that can achieve those rates.

Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and is well understood for channels modelled by classical physics. However, when quantum effects are involved, we do not know how to compute channel capacities. This is because the formula for the quantum capacity involves maximizing the coherent information over an unbounded number of channel uses. In fact, entanglement across channel uses can even increase the coherent information from zero to non-zero. Here we study the number of channel uses necessary to detect positive coherent information. In all previous known examples, two channel uses already sufficed. It might be that only a finite number of channel uses is always sufficient. We show that this is not the case: for any number of uses, there are channels for which the coherent information is zero, but which nonetheless have capacity.