The ability to send quantum information over long distances can enable fundamentally new applications, such as intrinsically secure communication, enhanced metrology, and distributed quantumcomputation. Entangled links serve as powerful resources for sending quantum information between nodes in a quantum network. However, generating entanglement in sufficient quantity and quality across a network, such that they can be used for applications, remains an open challenge.

In this thesis, we explore the use of color centers in diamond as network nodes. Their electron spin serves as a matter qubit with an optical interface, enabling the entanglement of two distant color centers, mediated by photons. The surrounding nuclear spins are used as memory qubits for local computation and entanglement storage. In this thesis, we investigate both the well-established nitrogen-vacancy (NV) center in diamond and the recently discovered tin-vacancy (SnV) center in diamond. The physics and control methods for both types of color centers are discussed in Chapter 2.

Remote entanglement between matter qubits can be achieved with many different entanglement protocols. In Chapter 3, we present a framework that explains and categorizes different protocols and quantum network hardware components. This framework is then used to compare the performance of various protocols while using similar hardware.

There have been many realisations of rudimentary network links between two network nodes using various quantum hardware. In Chapters 4 and 5, we realize the first entanglement-based three-node quantum network employing NV centers in diamond. In this network, we demonstrate fundamental network capabilities such as the creation of a remote three-party Greenberger–Horne–Zeilinger (GHZ) state and entanglement swapping to connect non-neighboring network nodes, as detailed in Chapter 4. These advancements are facilitated by storing an entangled state in a network node while generating a second entangled link. In Chapter 5 we demonstrate quantum teleportation between two non-neighboring network nodes by adding a fifth qubit to the network and utilizing the entangled link generated through the entanglement swapping.

The three-node network experimentswere enabled by the nuclear spin memory, emphasizing the importance of nuclear spin control for quantum networks based on color centers. In Chapter 6, we explore nuclear spin control with the SnV center in diamond. This recently discovered color center promises enhanced entanglement rates compared to the NV center due to its superior optical interface. We control single nuclear spins and show entanglement between the electron and nuclear spin. These experiments provide insights into the challenges and opportunities of controlling nuclear spins using an electron spin-1/2.

The development of a quantum internet is crucial for the advancement of quantum computing, enabling secure and distributed quantum computing capabilities. Despite significant progress in building small-scale quantum networks in lab environments, a fundamental barrier remained: the inability to communicate between quantum computers over metropolitan-scale distances. This thesis tackles this challenge and shows the development of a scalable quantum network hardware platform for long-distance deployment using existing internet fiber connections (Part I). To further widen the understanding of the future implications of a quantum internet, the second part of this thesis explores the social and business implications of future quantum networks (Part II). The results of thesis aim to accelerate the commercialization of a quantum internet and improve our understanding of its implications in business and society.

In modern-day research, magnetometry provides valuable information for a wide range of studies. Among all the different forms of magnetometers, the nitrogenvacancy (NV) lattice defect in diamond has emerged as a powerful magnetic field sensor thanks to the combination of sensitivity, spatial resolution and versatile capabilities. High-fidelity microwave control and optical readout of the NV spin over a wide range of conditions has enabled applications in condensed matter physics, chemistry, biology, geoscience and many more. In particular, its capability of visualizing magnetic phenomena with high spatial resolution has proven to be a powerful tool in both fundamental physics and applied sciences. Advances in NV magnetometry in the past decade have led to numerous breakthroughs, especially in revealing the nanoscale physics of condensed matter systems. However, the free-space optics generally used for optical interrogation of the NV spins are challenging to realize in cryogenic, intra-cellular, or other hard-to-reach environments. As such, realizing robust all-fiber-based NV probes with efficient optical readout could enable new measurements in low-temperature (quantum) or biological systems...

Quantum networks are expected to enable applications that are provably impossible with classical communication alone, such as generation of secret keys for secure communication and high-precision distributed sensing. A fundamental resource needed for many of these applications is shared entanglement among distant parties. Hence, the viability of an application relies on the underlying protocol for entanglement distribution. Existing protocols often suffer from long waiting times, as they rely on the success of multiple random events, each with a low probability of success. Moreover, pre-distribution of entanglement is difficult, since entanglement degrades over time when stored in memory, eventually becoming unusable. In this thesis, we address these challenges by designing efficient entanglement distribution protocols and architectures.

First, we focus on on-demand entanglement distribution, in which the entanglement distribution process is initiated only after some users request it. We find optimal protocols that minimize the waiting time for distributing entanglement among two users that are connected by a chain of two-way quantum repeaters. The performance of these protocols sets a benchmark for on-demand distribution of quantum states. We also study a multi-user network of one-way quantum repeaters, and we conclude that finite waiting times are only achievable when the users are at most a few kilometers apart from each other, irrespective of the number of repeaters available.

Next, we examine protocols for continuous entanglement distribution, in which the distribution process is initiated before any user requests. While these protocols can sometimes lead to resource wastage – as noise in memory renders the entanglement
unusable if distributed too early –, they offer the potential to reduce expected waiting times compared to on-demand methods. Surprisingly, we find that, when the time required to distribute entanglement follows a broad probability distribution, initiating the process preemptively can actually result in longer expected waiting times compared to an on-demand approach.

Lastly, we propose an architecture for buffering high-quality entanglement, ensuring it is readily available for use when needed. A key feature of this system is the use of purification subroutines to prevent the buffered entanglement from degrading over time due to quantum decoherence. Among other findings, we show that maximizing entanglement quality upon consumption requires frequent purification, even if this process often fails and results in the loss of high-quality buffered entanglement. The results presented in this dissertation were obtained mostly analytically, leveraging tools from performance analysis, including queueing theory and renewal theory, and supported by extensive discrete-event simulations. Our theoretical insights provide benchmarks and identify fundamental limitations of quantum networks, offering valuable guidance for the design of reliable entanglement distribution systems.

The Nitrogen-Vacancy (NV) center has demonstrated great potential as a quantum networks platform. While many milestones have been reached, the current hardware implementations have reached their limit in terms of remote entanglement generation rates, which hinders the scalability of the platform. The most dominant limits are that only ∼ 3% of the emission is coherent, and the outcoupling efficiency in state-of-the-art network experiments is ∼ 15%. The coherent emission can be increased via the Purcell effect, which can be achieved by the use of an open Fabry-Pérot microcavity. In such a setup the NV center is embedded in a micrometer-thin diamond membrane, thereby retaining its favourable optical properties. The open microcavity has the ability of in situ spectral and spatial tunability. However, this is accompanied by a high susceptibility to vibrations, which needs to be considered in the experimental design. The goal of this thesis is to simultaneously increase the coherent emission and the outcoupling efficiency by coupling NV centers to an open Fabry-Pérot microcavity. An optimized cavity is found by characterizing different fiber tip mirrors, reaching a bare cavity finesse of 9500. The vibrations in the bare cavity are analyzed, revealing a root mean square cavity length detuning of 22 pm while operating at low temperature. A hybrid cavity is formed with a diamond membrane with NV centers, resulting in cavity with a finesse of 2100, quality factor of 266000, mode volume of 108 λ 3 , and outcoupling efficiency ∼ 30%. Due to a different setup configuration, an increased root mean square cavity length detuning of 190 pm is measured, resulting in a lowered Purcell factor. Off-resonant measurements demonstrate the coupling of NV centers to the cavity. Moreover, excited state lifetimes are measured to obtain a Purcell factor of 2.6 ± 0.5, with a corresponding enhanced coherent emission ratio of 0.07 ± 0.01. This result is in good agreement with simulations that include the effect of vibrations. The ZPL branching ratio and outcoupling efficiency are improved by a factor two compared to state-of-the-art confocal microscope setups. For the first time in open microcavities, the ability to drive the spin of NV centers is shown by an optically detected magnetic resonance measurement with a contrast of (28 ± 2)%. By improving the setup to the already obtained vibration level, and a realistic finesse of 5000, an expected Purcell factor of ∼ 15.7 and outcoupling efficiency of ∼ 80% can be reached, paving the way to the next-generation of quantum network nodes.

Electron-spin qubits associated to solid-state defects can exhibit exceptional optical and spin coherence. Additionally, magnetic interactions with surrounding spins presents a resource for multi-qubit registers. Combined, this makes such solid-state defect systems promising for quantum network applications. In this thesis, we first realize a toolbox to control electron-nuclear spin qubits surrounding an NV-center in diamond and investigate such spins as potential qubits by generating an entangled state shared amongst two spins. Secondly, we improve the robustness of a nuclear-spin memory qubit while emulating remote entanglement generation protocols. Ancillary (spectator) qubits subject to noise correlated to the memory qubit are measured and subsequent feedforward allows to mitigate this noise in real-time. Thirdly, we investigate spectral diffusion dynamics in commercially available silicon carbide and demonstrate (near-)Fourier linewidth limited optical transitions within a broad inhomogeneously broadened spectrum. Finally, an outlook on electron spin clusters and photonic integration of electron spins is presented.

The efforts to bring quantum states, fundamental building blocks of nature, from research labs into the outside world are intensifying. The generation and processing of remote quantum states between nodes in a network would allowfor new applications such as distributed quantum computing, quantumenhanced sensing and quantum communication. Various demonstrations of such a quantum network have been shown in a lab setting, such as the generation of a three node GHZ-state, device-independent quantum key distribution and memory enhanced quantumcommunication. Color centers in diamond have been at the forefront of these developments due to their optically active spin interface, long coherence times and nuclear spin registers. The Nitrogen Vacancy (NV-) center is the color center of choice in this thesis, which we describe in Chapter 2. We explain what an NV-center is, how to control it and how we can use them to generate remote entanglement.

Solid-state defects in diamond and silicon carbide have emerged as a promising platform for exploring various quantum technologies, such as distributed quantum computing, quantum simulations of many-body physics, and nano-scale nuclear magnetic resonance. The noise environment surrounding such defects, consisting of magnetic and electrical impurities, directly impacts the spin and optical coherence, posing a key challenge for advancing quantum technologies. Systematic study of these spins and charges is crucial for mitigating their noise contribution. In some cases, establishing control over the environment can even convert it into a resource, to be used for storing, or processing (quantum) information. In this thesis, we develop experimental and analytical tools that enable a more detailed study of the defect spin and charge environment, and can be exploited to manipulate its microscopic configuration.

For many quantum applications we require high-fidelity entanglement between multiple pairs of solid state qubits at a distance. To achieve a high fidelity, we have to minimize the time during which the generated qubits need to stay coherent. Entanglement protocols often used in practice only generate one qubit at the same time. To generate multiple entangled pairs, the protocol is repeated. However during the time it takes for all pairs to be generated, the memory qubits will dephase. The required coherence time increases with the inverse transmission probability of the photons, which decreases exponentially with distance. This thesis is concerned with entanglement generation protocols that herald multiple entangled pairs simultaneously and in general herald N-dimensional entangled bipartite states. The main advantage of using more than 2 dimensions is that the qudits only dephase during the time in which the protocol executes. With simulations we show that the fidelity of the entangled pairs created with our protocols is higher than the fidelity of pairs created by protocols that heralds one entangled pair for distances L > 10 km. We also show a polynomial relation between the total success probability of the tailored protocol with dimension, which is an exponential improvement with respect to previous works.

The future quantum internet promises to create shared quantum entanglement between any two points on Earth, enabling applications such as provably-secure communication and connecting quantum computers. A popular method for distributing entanglement is by sending entangled photons through optical fiber. However, the probability of successful transmission decreases exponentially with the fiber length. This makes it challenging to realize large fiber-based quantum networks that create shared entanglement, let alone the construction of a quantum internet. Quantum repeaters have been proposed as a solution to mitigate losses by acting as intermediary nodes that divide long optical fibers into smaller segments. The required technology, however, is still under development. In this thesis we aim to expedite the realization of fiber-based quantum networks by identifying shortcuts towards that end.

One way in which we look for shortcuts is by identifying the technological advances that are required to build such networks. To achieve this we translate performance demands on the network to requirements on individual components, such as quantum repeaters. This way we are not only able to indicate how much development current-day technology still requires before functional quantum networks can be built, but also what specific set of improvements could be applied to state-of-the-art hardware to get there as soon as possible.

A specific promising shortcut that we investigate in this thesis is the construction of quantum networks using existing fiber infrastructure. As deploying optical fiber is costly, an economical method for building quantum networks would be to incorporate fiber that has already been placed in the field. Existing infrastructure however imposes restrictions on quantum networks, in particular on the possible locations where quantum hardware could be installed. An important question to answer is then how severe the effects of these restrictions are. We address this question by investigating the performance degradation caused by displacing nodes from their optimal location, and the increase in required technological advances when restrictions are taken into account. Additionally, we provide tools for choosing where to deploy quantum repeaters when subject to placement restrictions.

Finally, we also address the fact that quantum networks may need to provide entanglement to more than just two parties. When a network has many end nodes that require bipartite entanglement between different pairs of them, it is important that it is designed such that every end node is sufficiently connected to every other end node. We provide conditions to judge whether this is the case and a method to ensure the conditions are met. Alternatively end nodes could require multipartite entangled states shared by more than two of them, in which case specialized nodes may need to be included in the network. We investigate what such a node could look like and perform a thorough performance analysis.

Throughout the work, the goal was to develop the physical layer of a quantum network stack. The layer of the network stack connected to the physical layer is the link layer. For entanglement-based quantum networks, we demonstrated the successful operation of a link layer and a physical layer. The physical layer’s entanglement generation procedure—implemented here using two NV center-based quantum network nodes—is abstracted by the link layer into a robust platform-independent service that can be utilized to run quantum networking applications. Other quantum network platforms using the approaches provided here (which are not unique to our diamond devices) will accelerate the development of large-scale and heterogeneous quantum networks.

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A vision is developed on how successful university-industry collaborations can be established in the field of quantum technology development. By looking at the stakeholders, purpose and type of collaboration, and influencing factors, a three-step model is developed to move from awareness to acceptance to collaboration. By overcoming the existing barriers, university-industry collaborations can be successfully realized.

Crucial to the behaviour of a Nitrogen-Vacancy (NV) centre are its excited state cyclicities, determining the ability to perform high fidelity readout, spin-photon entanglement generation or fast spinpumping. This work presents a unified model to predict these excited state cyclicities over a wide range of strain, electric field, magnetic field and temperature, a useful tool for a model based predictive engineering approach towards the development of new NV qubits.
A set of measurements was performed to verify the prediction made by the model and improve the model over a wide range of perpendicular strain up to 7.5 GHz. An automated photon detection efficiency measurement was implemented, showing an average PSB photon detection efficiency of 2.8(3)% in the given setup. The cyclicities of the |Ex⟩ and |Ey⟩ excited states were measured over the given strain range for a single NV centre, showing a severe drop in cyclicity towards higher strain for both transition, a convergence of cyclicities towards zero strain, and a consistently higher cyclicity for |Ex⟩ compared to |Ey⟩, as predicted by the model. However, clear differences were discovered between predictions and measurements, with the recommendation to repeat the measurement at a lower sample temperature of 4K where temperature mixing is negligible. A framework was developed to measure the excited state branching ratios into and out of the singlet states, and were measured for the |E1,2⟩ states, showing that significant singlet branching remains present at high strain. However, a broken optical device prevented accurate measurements.
Furthermore, an optimisation framework was developed, implemented and verified for a mirror coupling light out of a quantum frequency converter into a telecom fibre; one of the final steps towards an operationally autonomous NV quantum network node.

SnV centres in diamond are a promising candidate for quantum internet applications because of their strong spin-photon interface, long spin coherence times, and insensitivity to electric fields. Integrating them in diamond waveguides could strongly improve entanglement rates and could make for a scalable design. In this thesis, we show using simulations that rectangular <110> waveguides are good candidates for high emitter-waveguide coupling, reaching a maximum of 79%. Optimal dimensions are 250 nm x 120 nm (width x height). This also falls inside the single-mode regime for the emitted light. The measured lifetime limits for the linewidth of Γ = 25 MHz, dephasing of Γ_𝑑 = 10 MHz, and >10 seconds long spectral stability in the bulk diamond sample, together with an APD dark count rate of 171 Hz should lead to a transmission dip around resonance of Δ𝑇/𝑇 = 25%, which we predict using a different simulation. The currently obtained taper coupling from diamond waveguide to optical fiber is approximately 10%. This is probably enough to see the transmission dip, but it needs to be improved for future experiments. Post-selecting SnV centres in waveguides and using Purcell enhancement to boost ZPL emission can further improve these results.

A future quantum internet will bring revolutionary opportunities. In a quantum internet, information will be represented using qubits. These qubits obey the rules of quantum mechanics. The possibilities to create superposition and entangled states, and to perform projective measurements give the quantum internet its unique strengths. A quantuminternet will enable fundamentally secure communication, quantumcomputations in the cloud with complete privacy and quantum enhanced sensing. But it is likely that many of its applications are still unknown. A full-scale quantum internet puts demanding requirements on the individual components. In the last decades single nodes and remote entanglement have been explored, but a small-scale prototype quantum network does not yet exist. In this thesis we go beyond single- or two-node experiments and realize the first multi-node quantum network using nitrogen-vacancy centers in diamond. The electron spin of this defect serves as the communication qubit and nearby 13C nuclear spins as memory qubits. We investigate the performance of the network and demonstratemultiple key network-primitive protocols. In addition, we further explore and improve the individual building blocks...

Generation of high fidelity entanglement between quantum nodes is a key component of a future quantum internet. Heralded entanglement generation of two spatially separated qubit nodes can be established by interference and measurement of two photons, each entangled with one qubit state. The two-node entanglement fidelity is limited by the degree of indistinguishability of the photons, which can be measured in a Two-Photon Quantum Interference (TPQI) experiment. In this thesis, a TPQI experiment has been performed with photons emitted by a single Nitrogen-Vacancy (NV) center. This self-interference experiment shows a visibility of V=0.91±0.02 and a photon indistinguishability of J=0.945 in the Monte-Carlo method obtained 1σ-confidence interval of [0.920, 0.966] after correction for system imperfections, demonstrating near-perfect indistinguishability of zero-phonon line photons emitted by a single NV center. Furthermore, an extensive TPQI model was developed that includes possible arrival time- and frequency differences of the photons. This model predicts a dark- and noise count limited V=0.79±0.06 for a future two-node NV TPQI experiment with quantum frequency-converted photons, at a distinguishable photon coincidence rate of 1.2mHz, allowing for an experimentally feasible double-click two-node entanglement fidelity of 0.89±0.03.

In order to create a quantum network for distributed quantum computing and secure communication, quantum nodes are required which can share an entangled state. Colour centres in diamond are a very promising set of nodes that can be used to create entanglement between remote locations. A well-studied colour centre in diamond is the Nitrogen Vacancy (NV) centre. The NV centre is a promising candidate because the electron spin can be readout optically and the spin state can be manipulated using microwaves. Furthermore, the NV-centre can be coupled to closely located nuclear spins, where the nuclear spins grant access to multiqubit protocols and the creation of a linked qubit register. A problematic downside of the NV centre is its entanglement rate which is currently limited to ∼ 39𝐻𝑧. The entanglement rate can be increased by coupling the colour centre to an optical cavity. One approach is to use open fibre-based Fabry-Pérot microcavities, with the advantage that it can be fibre coupled, achieve high quality factors and its spectral tunability. An important downside to the spectral tunability, is its sensitivity to vibrations. Therefore the goal of this thesis is to characterise a novel fibre-based microcavity setup, investigate the vibrations influencing the microcavity and actively reduce the vibrations with a feedback loop. When a stable optical microcavity is established, a diamond membrane can be placed in the microcavity to enhance its coherent emission. The novel setup uses a new, low vibration cryostat design together with a passive vibration isolator to suppress vibrations inducing a change in microcavity length. A moveable mirror coated fibre and a flat mirror form the microcavity, where the transmitted light of the microcavity is collected with an objective. We first show control over the microcavity by measuring the linewidth and the length of the microcavity. With this setup we obtain a typical finesse ∼ 6000 (for a bare microcavity), which results in a quality factor of around 80.000 and a mode volume of 27𝜆 3 for a microcavity length of 5𝜇𝑚. Moreover, we show that the microcavity length dependence on temperature, is roughly 3 1 3 𝜇𝑚 per ℃. And we demonstrate a measurement which allows us to measure the angle of the fibre. The angle of can cause a large decrease in the quality factor and is important for mode coupling. Next, vibrations causing a detuning in microcavity length are characterised. The vibrations can be categorised into multiple frequency ranges which are further analysed. The vibrations for certain frequency ranges can be heavily suppressed by changing the conditions of the passive vibration isolator. By characterising the vibrations, we come to the conclusion that the passive vibration isolation is not optimal, resulting in a high level of vibration. Improving the passive vibration isolation is required in order to proceed to a regime where active feedback can stabilise the microcavity length when the cryostat is on. Finally, we demonstrate active length stabilisation under vacuum at room temperature. The transmitted light of the microcavity is used to actively feedback a voltage to a coarse piezo and a fine piezo. The coarse piezo counteracts microcavity length drifts at lower frequencies and the fine piezo counteracts faster length fluctuations due to vibrations. With this active feedback method, a fundamental mode of the microcavity can automatically be found, and the microcavity length can be locked to that mode. An estimation of the maximum root mean square (RMS) vibration level with the cryocooler off, at room temperature and with active stabilisation is 10𝑝𝑚. This is at least a factor 2 lower than the RMS vibration level without active stabilisation. Multiple suggestions are made to lower the vibration level in the novel setup. For example, how to improve the performance of the passive vibration isolator and how to implement a different active length stabilisation scheme like the Pound-Drever-Hall lock.

Owing to its exceptional spin properties and bright spin-photon interface, the nitrogenvacancy (NV) center in diamond has emerged as a promising platformfor quantum science and technology, including quantum communication, quantum computation and quantum sensing. In this thesis we develop novel methods for atomic-scale imaging and high-fidelity control of complex nuclear-spin systems coupled to the electron spin of an NV center in diamond. This well-controlled quantum system provides new opportunities in quantum sensing, quantum information processing, and may also form the building block of a large-scale quantum network, one of the key goals in quantum technology.

Due to its long spin coherence and coherent spin-photon interface the nitrogen vacancy (NV) center in diamond has emerged as a promising platform for quantum science and technology, including quantum networks, quantum computing and quantum sensing. In recent years larger quantum systems have been demonstrated by using optical entanglement links between distant NV centers. These systems were based on high-quality NV centers that exhibit good optical coherence. State-of-the-art experiments with such systems have shown deterministic delivery of entanglement across a two-node quantum network as well as genuine multi-partite entanglement across a three-node quantum network. The additional capability to create larger quantum registers by direct magnetic coupling between high-quality NV centers and to other nearby defects would provide new opportunities for quantum memories in quantum networks but also for enhanced sensing protocols and spin chains for quantum computation architectures. In this thesis, we investigate methods to create larger quantum registers based on magnetic coupling and develop techniques to address and control individual defects in a system consisting of multiple defects. The results provide new insights for extended quantum registers based on magnetically coupled defects...

In this report we present a model to simulate the performance and robustness of the Charge-Resonance Check (CR-Check) in the Nitrogen-Vacancy (NV) center. The CR-Check is a routine which verifies that the charge state of the NV center is NV$^-$ and that the lasers, addressing the NV center, are on resonance with the optical lines. This is done by shining a red (λ=637 nm) laser on the NV center and measuring the amount of fluorescence photons, since they are dependent on the resonance frequency being near the frequency of the laser. If these counts do not pass the threshold for success, then either a new measurement of the photons is done or the system is repumped with a green (λ=532 nm) high intensity laser if they are below the repump threshold. The most important parameters are the duration of the red laser (dt) and the spectral diffusion of the NV center (sigma), which is an intrinsic property of the NV center. The model was implemented in Python, where also Numba, a high-performance Python compiler was used. An algorithm for finding the optimal values is included, so that different implementations can be compared. Then parameter sweeps were performed to get insight on the effects of the parameters. The distribution of frequency spectrum was investigated, it follows the shape of the Generalized Normal distribution with a disturbance due to the memory parameter. We observed that the mean time till success goes up linearly with the sigma after it is higher than 80 MHz for dt. This effect can be explained by taking into account the Normal distribution which was used to determine the resonance frequency. It became clear that the N_thr_repump and N_thr_success often come as pairs, which have been shown to be linearly dependent on the rate. Also it has been observed that after a certain sigma amount the N_thr_repump and N_thr_success do not change anymore. We noticed that for fixed sigma there is a optimal value of dt. This optimal value of dt is dependent on sigma. Average number of photon counts was nearly independent of sigma and only linearly dependent on dt. This is a sign that the CR-Check can always bring the NV center sufficiently on resonance. It has been observed that when the NV center's spectral diffusion is below 40 MHz, it is significantly faster to use the CR-strategy with dt = 25 μs compared to the standard dt of 50 μs. Lastly new implementations, where p-values are used rather than the measured counts, were shown to be capable of performing a CR-Check procedure. These implementations have used either the cumulative density function (cdf) of the Poisson distribution or the t-test or the Wilcoxon signed-rank test. The test using the cdf performed very similar to the current implementation. The other two test were slower with regards to the mean time till success, as they seem to require a lower spectral diffusion than was mandated.