Source: https://ieeexplore.ieee.org/document/9964024

My Highlights

Understand that this interplay is bidirectional rather than unidirectional, with the Quantum Internet exhibiting the potential of supporting and even enhancing classical Internet functionalities;

In this context, classicalInternet has been implicitly considered so far as an underlying communication infrastructure, aimed at providing services to the Quantum Internet.

A pivotal example of this dependence is provided by the quantum teleportation process [6], which represents one of the key communication protocols enabled by the Quantum Internet infrastructure. Specifically, quantum teleportation constitutes an astonishing strategy for transmitting a qubit without the physical transfer of the particle storing the qubit. But it requires two different communication resources. One is quantum: a pair of (maximally) entangled qubits shared between source and destination. And the other is classical: a pair of bits transmitted from the source to the destination. Indeed, classical signaling is not limited to teleportation, but it rather constitutes a requirement widespread within the different quantum network tasks and functionalities [5, 7], ranging from entanglement generation through distillation to swapping as discussed in the next section

Accordingly and by oversimplifying, the Quantum Internet can be modeled as some sort of complex system laying on top of the classical Internet protocol stack — as shown in Fig. 1a — and interacting with the former at the application layer.

it seems reasonable from the classical Internet perspective — and in agreement with the separation of concern approach, the key principle behind OSI and TCP/ IP design — to consider quantum teleportation as some sort of complex application down-calling classical end-to-end communication services provided by the classical Internet stack.

In fact, most of the quantum protocols require, as a prerequisite, the distribution of entangled quantum states shared between source and destination [2].

es shared between source and destination [2]. However, entanglement generation and distribution depend on a tight synchronization as well as on proper classical signaling exchanged between the entangled nodes [7]

However, entanglement generation and distribution depend on a tight synchronization as well as on proper classical signaling exchanged between the entangled nodes [7].

However, differently from quantum teleportation, QKD provides — rather than requests — a service to classical Internet, by generating keys for encrypting a classical message, as we analyze in more details later.

classical signaling is mandatory for entanglement swapping [9]
On the other hand, a diff erent modeling arises by considering another popular quantum communication protocol — namely, quantum superdense coding [1] — that enables the transmission of two bits by “coding” them into a qubit, under the assumption of sender and receiver pre-sharing an entangled resource. By accounting for the specificity of superdense coding, it sounds more reasonable to envision it — from the classical Internet perspective — as a sort of complex functionality of the physical layer of the classical Internet protocol stack, as shown in Fig. 1b

According to this model, packets received from the data link layer can be either encoded and then transmitted classically through the classical physical layer, or directed to some sort of quantum super-physical layer to be encoded according to the superdense protocol.

in the classical Internet, the achievable data rates are upper-bounded by the physical channel capacities, with no information transmitted reliably whenever the channel exhibits zero capacity.

if the information is transmitted through a concatenation of two different channels with different capacities, the data rate is upper-bounded by the minimum of the considered capacities.

if the information is transmitted through parallel channels, the data rate is upper-bounded by the sum of the individual capacities, according to the additivity property of the capacities.

apacities. Surprisingly, the paradigm shift from classical to quantum — imposed by Moore’s law and stimulated by Landauer: “Information is physical” — comes with a whole new dazzling phenomena that overcome the aforementioned information bottlenecks. Specifically, information can be encoded in quantum carriers that propagate through quantum communication channels. Interestingly, quantum channel capacities are not necessarily limited by the additivity: when quantum channels are used together for transmitting classical information, the overall capacity can be higher than the sum of the individual capacities characterizing the channels

on links follow the rules of quantum mechanics. Recently, it has been shown that also the placement of quantum channels can be quantized in order to beat some transmission limitations, which constitute major fundamental obstacles to the classical physical layer [10]

Recently, it has been shown that also the placement of quantum channels can be quantized in order to beat some transmission limitations, which constitute major fundamental obstacles to the classical physical layer [10].

Such limitations can be overcome by exploiting the quantum switch, a device that places quantum channels in a genuinely quantum superposition of causal orders [11].

Such limitations can be overcome by exploiting the quantum switch, a device that places quantum channels in a genuinely quantum superposition of causal orders [11]. In particular, feeding the quantum switch with two channels characterized by zero-capacities activates a non-vanishing capacity, by beating the classical bottleneck inequality [10]

Surprisingly, the paradigm shift from classical to quantum — imposed by Moore’s law and stimulated by Landauer: “Information is physical” — comes with a whole new dazzling phenomena that overcome the aforementioned information bottlenecks. Specifically, information can be encoded in quantum carriers that propagate through quantum communication channels. Interestingly, quantum channel capacities are not necessarily limited by the additivity: when quantum channels are used together for transmitting classical information, the overall capacity can be higher than the sum of the individual capacities characterizing the channels. This is known as the superadditivity phenomenon

enriching the classical physical layer with some sort of quantumness allows the classical Internet to overcome existing data rate bounds and bottlenecks.

access control protocol [12], can be easily adapted — by down-scaling its complexity — for the contention resolution of a classical communication channel.

let us consider a set of n nodes, each sharing a qubit being entangled in an n-qubit W state, that must coordinate each other to access a classical communication channel. Each of the involved nodes simply performs a local measurement of its W-state qubit. Accordingly [12], only one node of the set observes the outcome 1, whereas the remaining nodes observe the outcome 0. Crucially, each node can observe the outcome 1 with the same probability.

equent coordination among the involved nodes. Indeed, the measurement outcome 1 corresponds to the node allowed to use the communication resource, namely, only the elected leader can transmit on the shared channel.

by observing the outcome 0, the remaining nodes become aware of the unavailability of the channel and are not allowed to transmit.

entangled qubits, with a single operation, that is, a local measurement, the resource contention is solved.

entanglement natively provides a distributed, collision-free strategy for the access to a shared classical communication resource.

among the set of nodes, only the elected leader is aware of having won the resource access.

among the entangled states there exists a specific class of multipartite entangled states, referred to as W states, exhibiting the ability of fairly and randomly electing a leader among a set of nodes.

the aforementioned unique ability of W states — coupled with the maximally-connected feature [7] of GHZ states — has been exploited for jointly solving the access and the subsequent distillation of an EPR pair from a multiparty entangled state shared among the network nodes. This protocol, referred to as entanglement.

rely on the ability of duplicating the data packets and sending each redundant copy through different paths: this is an imposed limitation of no-cloning theorem of quantum information [6].

Instead, the quantum path is manifested by a quantum superposition between multiple paths that allows transmission of a single classical packet simultaneously through them. In other words, when quantum trajectories are allowed, the same packet is delivered via diff erent sets of intermediate nodes and point-to-point links that exhibit diff erent qualities of service.

multipath quantum network service exploits the bit quantum transmission service in order to obtain information on quantum trajectories over point-to-point links.

Quantum singlepath routing. Due to the no-cloning theorem, quantum information cannot be copied and sent through all the possible paths. Hence, a single path (orange) must be selected; c) Quantum coherent multipath routing. A quantum superposition (orange tube) among multiple paths allows the transmission of a single packet simultaneously through them.

each classicalInternet node onlyholds a partial knowledge of the network. Hence, the input data required to process the multipath quantum network service should be gathered and distributed so to converge at a given node.

Then, the node must exploit computational resources for processing such a (network) topological knowledge. However, this processing can be performed by exploiting again the Quantum Internet infrastructure through the distributed quantum computing paradigm.

a classical network architecture harnessing quantum eff ects allows one to route classical information encoded in quantum carriers through multiple quantum trajectories simultaneously, while preserving the quantum coherence of the quantum packet.

quantum computing can support network layer functionalities by exploiting quantum algorithms for classical routing problems [13].

While this quantum multipath routing shares similarities with the known classical multipath routing technique, namely, fault tolerance and increased network bandwidth, it still possesses certain genuinely quantum characteristics.

Similarly to the channel quantum access protocol, the multipath quantum network service interacts with the classical network layer. From the Quantum Internet perspective, this service relies on coherent control functionalities that, in turn, depend on entanglement generation and distribution.

currently we are in the noisy intermediate-scale quantum devices (NISQ) era. As a consequence, fault-tolerant quantum processors are yet to be available.

reliable and deterministic entanglement generation — as well as its distribution to remote nodes — represent still an open problem.

Even more, entanglement generation requires tight synchronization and signaling, unlikely satisfied by the best-effort nature of current classical Internet [7].