Effects of Quantum Communication in Large-Scale Networks at Minimum Latency Sekav ˇcnik Simon and N otzel Janis

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Effects of Quantum Communication in Large-Scale

Networks at Minimum Latency

Sekavˇ

cnik, Simon and N¨

otzel, Janis

Abstract—Quantum communication technology offers several

advanced strategies. However, their practical use is often times

not yet well understood. In this work we therefore analyze the

concept of a futuristic large-scale robotic factory, where each

robot has a computing unit associated to it. The computing unit

assists the robot with large computational tasks that have to be

performed in real-time. Each robot moves randomly in a vicinity

of its computing unit, and in addition both the robot and the

unit can change location. To minimize latency, the connection is

assumed as optical wireless. Due to the mobility, a permanent

optimal assignment of frequency bands is assumed to increase

communication latency and is therefore ruled out. Under such

assumptions, we compare the different capacity scaling of different

types of such architectures, where the one is built utilizing

quantum communication techniques, and the other based on

conventional design methods.

I. INTRODUCTION

ROBOTS in a factory need low latency communication

with their respective computing units, therefore commu-

nication over the air is preferred over the ﬁber communi-

cation. Coordination and synchronisation, although desirable

in a multi-access scenario, is time-consuming and therefore

adds to latency, induced from the communication between

parties that is necessary to achieve a coordinated strategy [1].

In a situation with multiple Robot-Compute Unit (RCU)s an

interference between the pairs will arise if the communication

is not synchronised.

This concept can be traced back several years to works such

as [2], where the inherent computational limitations of robotic

units, inherited from the robot size, shape, power supply,

motion mode, and working environment are discussed and the

topic of upgrading or even just adapting robotic computing

performance after the robot is built, is brought up. As a solution

to such problems, computational ofﬂoading is discussed. The

work [2] suggests a separation of the communication into an

Machine to Machine (M2M) layer where robots communicate

amongst themselves and an Machine to Cloud (M2C) layer

where they communicate with the cloud.

As the focus of the present work is to clarify a hypothetical

use of quantum technologies by showing a separation of

performance under a clean cut futuristic use case, we consider a

special case where no communication takes place on the M2M

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layer (only ofﬂoading of computational problems from robot

to computing unit), and where the communication on the M2C

layer is divided into two planes. The ﬁrst plane is realized

through a free space optical- or LiFi link, and is assumed to

induce the minimum possible latency, but suffers from noise.

The second plane is realized for example via optical ﬁber. It is

assumed to deliver low noise connectivity, but does not have to

obey any latency constraint. Based on such a design, we can

show the different properties of three types of communication

links in comparison. In all three cases, our main focus is on

the low-latency wireless M2C communication part only. In all

three cases, the physical properties of the links under study are

characterized by loss τ, transmit power n, baud-rate (number

of pulses per second) band (thermal) noise ν.

The ﬁrst link uses established communication techniques.

Given a speciﬁed amount of available spectrum, loss and power,

it and operates at the Shannon limit. We call such a system an

Optimal Single Shot Receiver (OSSR).

The second link uses a Optimal Joint Detection Receiver

(OJDR). This system is therefore assumed to operate at the

Holevo limit. Following [3], such a link can be expected to

outperform the ﬁrst link in situations where it utilizes a large

amount of spectral bandwidth.

The third link uses an Optimal Entanglement-Assisted Re-

ceiver (OEAR). It uses the second plane of the M2C link to

generate entanglement, which is then utilized as a way to boost

transmission capacity on the wireless M2C link.

To avoid any delays arising from coordination, we study

two extreme approaches to assigning spectral bandwidth to the

RCUs: In the ﬁrst one we use Orthogonal Frequency Division

Multiple Access (OFDM) to assign an individual slice of the

available spectrum to each participant. In the second one we

base our analysis on Code Division Multiple Access (CDMA),

so that every RCU can utilize the entire available spectrum. In

both cases, we do not discuss details of an implementation.

Studying these three systems in comparison in the envisioned

scenario is interesting for the following reasons: Quantum

Information Processing (QIP) has, for communication systems,

so far pointed out the existence of inﬁnite-fold gains [4] -

however, most of these arise in parameter regimes (b, n, τ, ν)

which are never realized in practice. However, it is obvious

from the literature [5] that e.g. baud-rates in the established

optical ﬁber links have increased steadily over time. Therefore,

our analysis aims to point out how QIP can start to play a role

arXiv:2210.13267v3 [quant-ph] 16 Jan 2023

in future networks given certain trends.

To explain the basics of the approach let us clarify the

differences between the three different links. In all cases where

the product τn/b is small enough (for example below one),

the OJDR will eventually display a logarithmic advantage over

the OSSR [3] that scales with τn/b. This clariﬁes how a

trend towards increasing baud-rates can establish QIP as the

technology of choice - if CDMA outperforms OFDM in our

selected use case.

Further, it has been shown [4] that in cases where ν1and

n/b 1, the OEAR outperforms even the OJDR by a factor

which again scales as −log(n/b). While current commercial

systems satisfy n/b 1, the condition ν1still fuels some

hope that a design based on CDMA and the OEAR could

eventually be the superior choice. For such a system, we show

some hypothetical advantage utilizing the concept of massive

Multiple-Input Multiple-Output (mMIMO).

II. SETUP

Each RCU is characterized by a loss parameter τ, its transmit

power of nphotons per second, the baud-rate b(or symbol rate)

and the amount of (thermal) noise νaffecting the link. The total

available spectrum in the factory is B, and since bdictates not

only the number of symbols per second but also the spectral

width of the signal it must hold b≤B. All parameters are

assumed to be equal for each RCU. The K2units are placed

on a K×Kgrid with vertical and horizontal distance between

neighbouring nodes equal to d. We consider two types of loss:

In the pure loss model the interference power scales as

r=τRCU

r2(1)

In the two-ray loss model [6], we consider shadowing and

scattering effects, which lead to an interference power of

r=τRCU

r4(2)

between RCUs separated by a distance of r. Interference is

only relevant when CDMA is used, it equals zero otherwise.

Fig. 1. The robot arm might carry a small communication unit, which to avoid

additional costs, resulting in low energy transmission. This situation necessarily

results in a communication link with a high noise and low transmission

energy. In the case where OEAR is used, we may assume an additional ﬁber

connection, which has a higher latency but provides enough capacity to ﬁll

entanglement buffers at the end of the RCU pair.

For numerical results we assume the equipment is operating

in the C-band around 1550nm where standard equipment is

cheaply available and set B= 1012s−1. The energy per photon

is then ≈1.3·10−19J. Correspondingly, a source radiating 1W

of power emits ≈7.8·1018 photons per second. We calculate

the transmittivity based on the De Friis model in equation (12)

as τRCU = 1.5·10−6and τ= 10−7, for which we chose the

gain of both antennas to equal 104(40dB) and set the distance

between RCU nodes 10mand the distance between RCUs to

20m. Transmission power equals 1mW , corresponding to n=

7.8·1015, leading to τn/b ≈10−31but n/b ≈1041.

If CDMA is used then each RCU experiences interference

power ν/b where νis equal to

I:= X

(x,y)∈N

r( where X∈ {L, S})(3)

where Nis the set of coordinates of all RCUs, except the one

where the noise is being measured. Thermal noise is accounted

for by adding νT H = 109/b noise photons for the entire

C-band, a number which is derived from [7, Eq. (1)]. This

corresponds to a situation where the factory is at a temperature

of 300Kwithout sunlight.

Each RCU can either use the OSSR, the OJDR or the OEAR.

Given parameters b, n, τ, ν, the corresponding capacities [8, 9,

10] are:

CJ(b, τ, n, ν) = g(n+ν

b)−g(ν

b)·b(4)

CS(b, τ, n, ν) = log 1 + τ·n

b+ν·b(5)

CE(b, τ, n, ν) = X

x=0,1g(τ·n+x·ν

b)−g(dx(τ, n

b,ν

b))b(6)

where g(x) = (x+ 1) log(x+ 1) −xlog xand

dx(τ, n, ν) = (d(τ, n, ν)−1+(−1)x((τ−1)n+ν))/2(7)

d(τ, n, ν) = p((1 + τ)n+ν+ 1)2−4τn(n+ 1).(8)

The issue of entanglement generation, distribution and storage

is omitted. In the model entanglement is always available to

the OEAR based link.

III. RESULTS

For both interference models we observe a roughly tenfold

increase in link capacity (see Figure 5) when the OJDR is

used instead of the OSSR and both use CDMA. For the

pure loss scenario (X=L) the interference power scales

as PL

I≈n·log K, which leads to a slight decrease of the

observed advantage towards a factor of 5when K= 104. For

the two-ray loss model, PS

Iconverges to a constant when K

grows and the advantage is constant at large K. For the pure

loss case our numerical results indicate that a hierarchy can be

established according to which CDMA has a superior scaling

over OFDM, when equal link technologies are compared (see

ﬁgure 2). As our analysis is matched to the power budgets

and baud-rates of current equipment, the requirement n/b 1

for the OEAR to show its superiority over the OJDR, is not

satisﬁed. We conclude the OEAR can provide advantage with a

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EffectsofQuantumCommunicationinLarge-ScaleNetworksatMinimumLatencySekavcnik,SimonandN¨otzel,JanisAbstractQuantumcommunicationtechnologyoffersseveraladvancedstrategies.However,theirpracticaluseisoftentimesnotyetwellunderstood.Inthisworkwethereforeanalyzetheconceptofafuturisticlarge-scaleroboticfact...

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Effects of Quantum Communication in Large-Scale Networks at Minimum Latency Sekav ˇcnik Simon and N otzel Janis

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