# From data transmission to value creation: optical fiber's role in the digital revolution

When Charles K. Kao during the 1970’s went around the globe showing the feasibility of using optical fiber for telecom, he probably never imagined that he would be awarded the Nobel prize in physics, and that this media would be crucial for communication over the following decades.
But how can we create new value from a technology that is quite old?

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One way of creating new value is to use it for new types of communication, for example quantum communication. We launched the first quantum link in Sweden in 2018 together with Stokab and the Royal Institute of Technology (KTH), where we used single-photon qubits to transmit information between two endpoints. The link consists of around 20 km of single mode fiber linking the Nanophotonics lab at KTH and Ericsson headquarters in Kista.

One of our first milestones was to measure the polarization drift in the link. It is well known that polarization of light is not maintained over fiber (unless we use polarization maintaining fiber) because optical fiber suffers from birefringence and is affected by environmental factors. However, maintaining polarization is crucial for sending information using this degree of freedom. Physically, polarization describes the direction and amplitude of the electric field which evolves in time and propagates in a specific direction. In mathematical terms, polarization can be described by its basis (orientation of the polarization vector or Stokes vector): horizontal/vertical (H/V), diagonal/antidiagonal (D/A), right/left (R/L). In this matter, we can choose our qubits to be on a specific basis. Polarization is usually visualized by its Stokes vector on a Poincaré sphere. Figure 1 (a) shows the evolution of the normalized Stokes parameters along the fiber link during a 20-hour period as a function of time. The data was recorded between May 17th and May 18th, 2020. H-polarization is sent from the Nanophotonics lab to Ericsson lab and measured there with a polarimeter. Figure 1 (b) shows how the normalized Stokes parameters on the Poincaré sphere evolve over a period of 5 days in May 2020.

Figure 1. The evolution of the normalized Stokes parameters and the excursion of the polarization around the diagonal direction as a function of time. H polarization is sent from the Nanophotonics lab to Ericsson lab and measured there [1].

The second milestone was to stabilize the polarization of the link.  This was accomplished by applying a gradient descent algorithm to the feedback loop given to the polarization controller elements in our setup and by using two reference lasers (one for each basis) with a similar wavelength. This allows us to control the polarization of single photon qubits in two different bases without measuring them. Note that when we measure the polarization of the qubits, we destroy them and then the quantum information is also gone.

### Quantum link to send information using the lowest amount of energy possible

Using the polarization degree of freedom in single photons allows us to implement quantum protocols such as BB84 used in Quantum key distribution (QKD) applications, and it also allows us to implement error-correction protocols to polarized single photons to convey information from point A to point B. One of the first experiments after stabilizing the polarization was to use polarized single photons with a forward error correction protocol to send images between the two ends of the optical link. To do that, we used two orthogonal states of a single photon (|H⟩, |V ⟩) and the no photon state|0⟩ which are mutually orthogonal. With these three states and the help of graph theory we found six codewords that enabled us to detect and correct errors.

Table 1. Example of a code with 6 codewords.

This error-correction protocol was applied when sending an image using the quantum link. Both the original file, a 32x32 monochromatic image of the Ericsson’s logotype and the received images are shown in Figure 2.

Figure 2. The original image was sent using the code: |HHH>, |VVV>, |000>. The resulting image is reproduced for the time bin sizes (τ ) 0.017 s (a), 0.011 s (b), 0.007 s (c), 0.003 s (d), respectively. These small bin sizes could not be realised in our experiment due to the slow modulator. Therefore, they were simulated in post processing by sub sampling photon events from a larger time bin. The average photon counts (n) for these increasingly small time bins were 42, 26, 6.1 and 2.7, respectively. Red pixels indicate that an error was detected but no recovery could be performed at the receiver.

The images show the results for one specific encoding 0 -> HHH and 1 -> VVV and different time bin sizes. Considering that a red pixel is an error that can be detected but not corrected, we can see that the code is capable of correcting the loss of 2 photons and detecting an additional loss. The detected but non-corrected errors can be mitigated by retransmitting the signal, a common practice in classical communications.

Besides single photon protocols, there are other protocols that use entangled photons to send information from A to B. One method to determine if two photons are entangled or correlated is to measure what is called the g2(t)  function. The  function describes the correlation between two temporally separated intensity signals with time difference equal to t2-t1 from one light source.A value of 1 corresponds to uncorrelated photons meaning the detection events are completely unrelated, a value of 0 corresponds to maximum entangled photons.

In this experiment, we created two photons, called exciton (X) and bi-exciton (XX) using quantum dot (QD) light sources and we measured the g2(0) function of X and XX. The g2(0) represents the conditional probability of how likely is to detect a second photon at the same time one photon was already detected. The  value measured for the X at KTH was 0.049, the  value for the XX at KTH was 0.169, and the  value for X at Ericsson was 0.176 [2].  These results are far below the single emitter limit of 0.5 which allows for applying QKD protocols such as E91.

Details of what an exciton and biexciton is:

When an electron inside the valence band of a QD is excited into a higher energy state, a hole with opposite spin is created in the valence band. An electron in the conduction band can bind to such a hole through their mutual Coulomb interaction to form a quasiparticle called an Exciton (X). The lifetime of an exciton is in the nanosecond range, and it ends when the electron deexcites down into the valence band via photon emission (see Figure 3 [2]). The bi-exciton (XX), which is a quasi-particle consisting of two electron-hole pairs (see Figure 4 [2]),  experiences additional binding energy compared to two separate X. Unlike the exciton, the biexciton cannot transition directly into the ground state but rather has to do a cascaded biexciton exciton decay, see Figure 4.

Figure 3. Optical spectrum of exciton (X) and bi exciton (XX).

Figure 4. De-excitation paths for X and XX. Blue arrows represent the spin of the electrons and green arrows represent the spin of the holes.

### Quantum link for distributing random numbers

The same fiber link is also used to implement a provider-subscriber service to distribute single-photon generated random numbers. The setup for this service is shown in Figure 5. There are two subscribers: one in Stockholm (K), and one in Kista (E) marked on the map with a blue and an orange circle, respectively. Single photons at 1550 nm are generated at the provider in Stockholm using a semiconductor quantum dot. The dot is excited using p-shell excitation. The exciton emission is filtered using a transmission grating (TG) and sent through dedicated fibers of the municipality fiber network to the subscriber in Kista. There, the emission is filtered using a notch filter (NF) in reflection to suppress crosstalk of classical communication signals in the network. The bi-exciton emission is sent through a fiber spool and detected at KTH. At both subscribers, the photons are sent on a fiber beam splitter (BS) and detected using superconducting nanowire single photon detectors (SNSPD).

As a first method, we use the randomness extracted by allocating the bit values 0 and 1 to the respective output ports of a beam splitter. In a second method, we use the time between subsequent photon emissions as the source of randomness.  While our source generated, to a very high degree, pure single photons, the slightly different detection rates on the two channels (1:1.12) caused by an imperfect beam splitter ratio combined with the different detection efficiencies, led to biased random numbers in the first method. The second method allowed us to distribute 19.1kbit/s and 80 kbit/s of unbiased random numbers to two different subscribers. [3]

Figure 5. Image from [3] Metropolitan quantum link in the Stockholm region for quantum random number generation. BS: beam splitter, TG: transmission grating; KTH: Royal Institute of technology; SNSPD: superconducting nanowire single photon detector.; NF: notch filter.

### Quantum link for distributing a time synchronization signal

In another experiment we tested a high accuracy time synchronization method using single photons from a cascaded three-level system self-assembled quantum dots (see Figure 6). This method consists of a central provider with a time reference and one or more subscribers that will receive the high accuracy time synchronization.

This application is composed of two main nodes: master node (KTH) and subscriber node (Kista). The KTH node is the central node where a time reference is provided and sent through deployed fiber to a remote location, Kista. The master node consists of a pulsed laser that drives a quantum dot cascade. The quantum dot produces two triggered photons: exciton (X) and biexciton (XX). One of the single photons is then provisioned to the master clock node (also located in the KTH node) and the other one to the subscriber node (Kista).

The recorded signal from the subscriber node (Kista) and the recorded signal from the provider node (KTH) are cross-correlated and the offset between the two clocks is calculated. Additionally, the return signal X measured at the provider node and the signal XX measured at the provider node are cross correlated, which allows for the calculation of the propagation time within the fiber. These two values can then be used to calculate an absolute offset between the clock at the provider and the subscriber [4].

Figure 6. The Master node at KTH consists of the provider at KTH setup + the time reference setup. The subscriber node, corresponds to the subscriber in kista. BS: Beam splitter, TG: transmission grating, KTH: Kungliga tekniska högskolan, SNSPD: superconducting nanowire single photon detectors, NF: notch filter, R: reflectivity, T: transmission. One photon follows the orange fiber path, the other one the blue fiber path.

### What does it mean for digitalization?

Quantum communication holds the potential to advance digitalization by securing digital transactions between parties, using quantum key distribution, for example. Quantum principles can be applied to develop quantum-resistant cryptographic algorithms to protect against the threats posed by a quantum computer. It holds also the potential to send information using single photons and thus allowing for true ultra-dense WDM networks. By connecting two quantum computers and advanced sensor networks, we can achieve higher sensitivity, accuracy, (for example in time synchronization) and truly distributed computation.

These experiments constitute the basis for building up a quantum communication network that can ultimately support the quantum internet. At the same time, quantum technologies can play an important role in Ericsson’s digitalization journey, contributing to the building of an Enterprise AI engine that delivers business value every day.

#### References

[1] Zeuner, K., Semiconductor Quantum Optics at Telecom Wavelengths, Doctoral thesis, Royal Institute of Technology (KTH), 2020, available at: https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-285782

[2]  Carlnäs, M., 2022, Sharing Quantum Resources Across a Metropolitan Network,  Master thesis, Royal Institute of Technology (KTH), Available at: https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-308989

[3] Gyger, S., Zeuner, K. D., Lettner, T., Bensoussan, S., Carlnäs, M., Ekemar, L., Schweickert, L., Reuterskiöld Hedlund, C., Hammar, M., Nilsson, T., Almlöf, J., Steinhauer, S., Vall-Llosera, G. and Zwiller, V., Metropolitan single-photon distribution at 1550 nm for random number generation, Appl. Phys. Lett. 121, 194003, 2022, https://doi.org/10.1063/5.0112939

[4] Samuel Gyger, Thomas Lettner, Valery Zwiller, Jonas Almlöf, Gemma Vall Llosera, Methods and apparatus for determining an offset for time synchronisation in a communication network. Patent application no.PCT/SE2022/050939

https://www.ericsson.com/en/blog/2023/9/how-a-real-5g-quantum-ai-use-case-could-disrupt-antenna-tilting

https://www.ericsson.com/en/blog/2023/8/building-a-quantum-key-distribution-network-in-sweden

https://www.ericsson.com/en/blog/2023/2/quantum-resistant-algorithms-mobile-networks

https://www.ericsson.com/en/blog/2019/8/introduction-quantum-computing-algorithms-ran

https://www.ericsson.com/en/blog/2019/7/introduction-to-quantum-computer-technology

https://www.ericsson.com/en/blog/2019/9/quantum-computers-future-telecom-infrastructure

https://www.ericsson.com/en/blog/2020/3/post-quantum-cryptography-symmetric-asymmetric-algorithms

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