Màster Oficial - Ciència i Tecnologia Quàntiques / Quantum Science and Technology

URI permanent per a aquesta col·leccióhttps://hdl.handle.net/2445/188101

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Sorting atomic positions in an optical tweezer atom arrays
(2026-09) Volante-Abovich, Matias; Redon, Quentin ; Tarruell Pellegrin, Leticia
In this work we report on the development of a dynamical rearrangement system for optical tweezer atom arrays. This lays the foundation for the Rydberg atom-array experiment at ICFO which aims to simulate lattice gauge theories with strontium-88. The developed system uses acousto-optic deflectors (AODs) to move individually trapped atoms into defect-free target geometries. We focus on the laser source built to feed the AODs, a tapered amplifier at the 813.4nm clock-magic wavelength. Therein, the beam shaping and fiber-coupling optics have been assembled and characterized as part of this thesis project, reaching 58% fiber coupling efficiency. We explore the practical alignment and control of movable tweezers through an independent test setup, specifically characterizing the frequency-dependent diffraction efficiency of the crossed AODs and their single- and multi-tone performance. In addition, we address the need for efficient atom rearrangement by implementing and benchmarking three sorting algorithms of varying computational cost. Finally, we tackle the required scaling analysis by estimating the maximum array size rearrangeable within the atomic trap lifetime, ensuring thereby the suitability of the system for defectfree array assembly and the limits for the current experiment
Bounding Spectral Properties of Many-Body Quantum Systems
(2026-09) Tudurache, Gerard-Constantin; Frías Pérez, Miguel; Farina, Donato; Acín dal Maschio, Antonio
Simulating quantum many-body systems with large size is a considerable challenge in physics. Often, understanding complex many-body phenomena requires information about the spectrum of their Hamiltonian. Apart from performing the exact diagonalisation, which is not possible for systems with tens of particles, there are some scalable methods for obtaining information about specific energy regions (e.g., ground state properties, spectral gap). The main methods that address the problem of characterising properties of the spectrum are variational methods and quantum Monte Carlo methods. These methods were mostly used for low energy states, performing poorly for excited states. On the other hand, semidefinite programming is emerging as a complementary tool, able to yield certified results for quantities of interest. In this thesis, we explore the capabilities of semidefinite programming in the context of quantum many-body systems. Recent works regarding the ground state [WSF+24], [WJF+26] showcased the potential of these programs and we proceed to focus on their performance in the context of highly entangled states. The proposed semidefinite program can determine parts of the spectrum with no eigenstate and provide bounds for the expectation values of a target eigenstate
Creating Non-Equilibrium States with Quantum Generative Models
(2026-09) Ruiz Galindo, Pedro; De Chiara, Gabriele; Domingo Colomer, Laia
Quantum denoising diffusion models (QDDMs) have recently been proposed as generative models for quantum-state distributions, with existing approaches primarily designed for pure or nearly pure-state ensembles. In this work, we develop design strategies to extend QDDMs to complex mixed-state distributions. The main modification to the denoising architecture introduces a Haar-random auxiliary qubit and replaces post-measurement extraction with a partial trace over the auxiliary qubits, naturally enabling mixed-state generation. We investigate different auxiliary-state constructions and two forward diffusion processes based on depolarizing noise and scrambling circuits. The proposed framework is benchmarked on single-qubit distributions and mixed-state ensembles arising from open quantum-system dynamics, including thermal and non-equilibrium steady-state distributions, extending the evaluation to physically motivated ensembles. Across the benchmarks considered, the partial-trace approach generally achieves better reconstruction for single-qubit mixed-state distributions and accurately reproduces the considered steady-state distributions, while post-measurement approach remains advantageous for pure-state ensembles. We further find that the choice of auxiliary states strongly influences the geometry of the generated distributions, whereas no systematic advantage is observed between depolarizing and scrambling diffusion. Finally, we demonstrate the feasibility of implementing the proposed framework on a real quantum processor through an adaptation for IBM Quantum hardware.
Towards a compact and transportable solid-state quantum memory
(2026-09) Ramos Sánchez, José Ernesto; De Riedmatten, Hugues ; Teller, Markus
The distribution of entanglement over long-distance quantum networks requires quantum repeaters placed along the network, since otherwise it is impeded by losses in the quantum channels. A possible implementation of quantum repeaters is based on quantum memories paired with sources of entangled photons. In this thesis, we present the design, construction, and characterization of compact solid-state quantum memory hardware based on a Pr3+:Y2SiO5 crystal. The hardware encompasses an AOM rack for precise optical pulse shaping, a laser system stabilized via the Pound-Drever-Hall (PDH) technique, and a cryogenically cooled Pr3+:Y2SiO5 sample on an optical table setup with small footprint. We measure the efficiency, temporal response, and thermal stability of the AOM rack, and we estimate a stabilized laser linewidth of 2.7(3) kHz. Additionally, we characterize the quantum memory crystal within our setup, measuring an inhomogeneous broadening of 11.2(4) GHz and a coherence time (T2) of 58(11) μs, which corresponds to an homogeneous linewidth of 5.5(10) kHz. This confirms the suitability of the hardware for the implementation of the AFC protocol as a quantum memory protocol. The advancements present in this compact system constitute a key step towards the deployment of rackintegrated quantum repeater nodes for long-distance quantum communication networks.
Optical Engineering of Quantum Materials: Floquet Theory and Beyond
(2026-09) Pérez Checa, Joan Ernest; Martínez Romeral, Jorge; Canonico Armas, Luis M.
In this thesis, the relationship between Floquet theory and a non-equilibrium quantum dynamics simulation in the particular case of graphene irradiated with a laser is studied. First, Floquet theory is applied to identify the quasienergy spectrum of the laser-material system. Next, the electron dynamics of the system are studied in real-time using a non-equilibrium quantum dynamics simulation. Then, the results of both approaches are compared and used to understand the behaviour of electrons in the system. Finally, by using effective models, an analytical expression relating the size of the Floquet dynamical gap with the rate of absorption and emission of photons given by the results of the quantum dynamics simulation is obtained.
On Quantum Reading Capacities
(2026-09) Pascual Abraldes, Víctor; Winter, Andreas; Calsamiglia Costa, John
In this thesis, we investigate the communication scheme known as quantum reading. In this framework, classical information is encoded as a sequence of quantum channels chosen from a memory cell, and the receiver’s goal is to decode the data by solving a quantum channel discrimination problem. We explore existing versions of this scheme, deriving expressions for their capacities or, when exact formulas are unattainable, establishing lower and upper bounds. Furthermore, we introduce a novel protocol involving entanglement-assistance in the encoding, for which we provide a formula for its capacity. We then focus on specific classes of memory cells, namely jointly teleportation-simulable and jointly classical-quantum cells, where capacity computations are greatly simplified. Additionally, we numerically analyze the strict super-additivity exhibited by a memory cell consisting of two unitary channels. Finally, we establish the continuity of the quantum reading capacities and their corresponding upper bounds by employing Alicki–Fannes–Winter continuity bounds on the underlying entropic quantities
Probabilistic Simulation of Deep Quantum Circuits and Applications to Shor’s Algorithm
(2026-09) Monsó Mas, Helena; Jiang, Edward; Heightman, Timothy; Acín dal Maschio, Antonio
The simulation of deep quantum circuits is traditionally bottlenecked by the exponential scaling of the Hilbert space. This thesis presents a classical simulation framework that circumvents this barrier by mapping quantum states to classical probability distributions using informationally complete positive operator-valued measures (IC-POVMs). By leveraging an autoregressive transformer architecture, this work redefines quantum simulation as a highdimensional generative modeling task, utilizing the self-attention mechanism to capture non-local multi-qubit correlations. To rigorously benchmark the model against volume-law entanglement, the circuits are generated dynamically using uncompiled logical primitives, including the Cuccaro ripple-carry adder routed through the Vedral-Barenco-Ekert (VBE) modular exponentiation architecture. Evaluated via a variance-stabilized mixed Monte Carlo framework, the transformer successfully simulated a 25-qubit quantum Fourier transform (QFT) applied to an entangled 1D cluster state, maintaining a classical fidelity of Fc > 0.99 over 325 gates. Furthermore, the model executed the complete, uncompiled Shor’s algorithm to factor N = 15. Across a depth of 301 gates and 22 qubits, the network sustained a classical fidelity of Fc > 0.97. These results demonstrate that attention-based neural networks can robustly track complex, reversible quantum arithmetic without suffering exponential error accumulation, thereby establishing a stricter classical baseline for proving practical quantum advantage.
Universal properties from quantum many-body dynamics
(2026-09) Márquez Olguín, Joaquín G.; Carignano, Stefano
The Loschmidt echo—the amplitude for a quantum state to return to itself—provides a route to the universal properties of a critical many-body system. Continued from real to imaginary time, it becomes the partition function of a conformal field theory on a strip, and its universal data—the central charge and the operator content—are encoded in the spectrum of a transfer matrix, obtained by contracting the space–time tensor network along the space direction. We apply this framework to a transverse-field Ising model extended by a nextnearest-neighbour coupling: a non-integrable chain that remains critical and in the Ising universality class over a wide range of that coupling. After a quench to the critical point, the temporal entanglement that governs the cost of the transverse contraction grows only logarithmically with the evolution time, so the method remains efficient at times where conventional evolution algorithms are limited by the entanglement barrier. We develop a translation-invariant matrix product operator, accurate to second order in the time step, that represents the time evolution of the model, and use two power methods to compute the leading eigenvectors and eigenvalues of the resulting non-Hermitian transfer matrix. Within the accessible time windows, our results are consistent with the central charge and operator content predicted by the Ising universality class.
Entropic Spectroscopy of Spatiotemporal Replica Defects in (1 + 1)D Quantum Ising Dynamics
(2026-09) Majumdar, Avinaba; Bou Comas, Aleix; Tagliacozzo, Luca
Generalised temporal entropies extend entanglement-based diagnostics from spatial subsystems to cuts through real-time quantum evolution. This thesis develops a spatiotemporal Rényi-2 construction that combines a crossed temporal replica geometry with spatial SWAP readouts, and applies it to the finite open one-dimensional quantum Ising chain. A general Boolean/Möbius framework organises replica-defect geometries, while the selected protocol is formulated as a crossed-replica spacetime tensor network. On the integrable transverse-field line h = 0, an exact Gaussian–Pfaffian evaluator is constructed and benchmarked against DMRG/TEBD; the same protocol is then studied at h = 0.5 with TEBD. At g = 0.5, 1.0, 1.5, the integrable entropy dynamics show phase- and geometry-dependent real-space structure within an exactly known ballistic envelope, and site-resolved Fourier analysis resolves the freefermion energy-difference and two-quasiparticle continua. Breaking integrability reorganises these spectra qualitatively: g = 0.5 exhibits confinement-scale localisation and mesonic structure, g = 1.0 develops a finite lowest branch consistent with the lightest magnetic-Ising E8 scale, and g = 1.5 reveals a mobile interacting branch with two-excitation kinematic structure. Complementary symmetric two-region Rényi-2 mutual-information diagnostics are also evaluated for disconnected spatial supports. In the mobile mixed-field cases, fixed local entropies remain bounded and oscillatory over the accessible T = 8 window while their spatial support continues to expand. These results establish spatiotemporal entropy and entropic spectroscopy as controlled probes of locality, integrability breaking, interacting spectral organisation, and dynamical complexity
Calibration of a Double-Loop Galvanic Coupler between Tunable Fluxoniums
(2026-09) Laguna Rueda, Álvaro; Scarpelli, Lorenzo
Analog quantum computing requires independent, in-situ control over every term of the implemented Hamiltonian, including the qubit-qubit couplings. One issue of commonly used galvanic couplers between fluxoniums is the couplerinduced nonlinear crosstalk. The presence of a current circulating in the coupler main loop (the z-loop) generates a flux that shifts, nonlinearly, the degeneracy point of the fluxonium. For precise qubit control, such a crosstalk needs to be compensated. While for a single qubit this can be done accurately, this becomes a highly non-trivial task when multiple qubits are involved. Here we perform preliminary measurements on a double-loop galvanic coupler. Besides the z-loop, we include a DC SQUID as an x-loop. The DC SQUID enables us to tune the coupler susceptibility while keeping the net circulating current in the coupler at zero, therefore eliminating the nonlinear crosstalk. Furthermore, we show that the coupler susceptibility can be tuned through the ferromagnetic, zero and antiferromagnetic coupling regimes using only the SQUID flux, keeping the coupler at its sweet spot and therefore leaving the qubit sweet spots unperturbed. Finally, we measure and fit the spectrum of each qubit with the coupling switched off in order to extract the qubits’ energy parameters, and report a preliminary measurement of the two-qubit spectrum with the coupling turned on
Quantum-to-classical transition of non-Gaussian bosonic systems in non-markovian dynamics
(2026-09) Julián Abós, Iris; Centrone, Federico; Acín dal Maschio, Antonio
Non-Gaussian bosonic states offer resources that are inaccessible to Gaussian states and essential for quantum applications such as quantum computing and error correction. However, their fragility raises the question of whether their key features can survive realistic environments. Reservoirs with memory are promising candidates for state protection, since they can induce revivals of those features. This thesis investigates that mechanism within quantum Brownian motion (QBM), the minimal archetype of a structured bosonic environment and the standard description of a broad range of experimental platforms. QBM has the further advantage of remaining exactly tractable despite describing dynamics that are simultaneously non-Gaussian and non-Markovian. Our main methodological result is a set of closed expressions for the purity, the coherence, the non-Gaussianity and the Wigner function of the cat state and its two squeezed generalisations, valid for any environment of this class. Applying them to a bath with a band gap shows that the structure of the environment, rather than the strength of its coupling, decides what survives: part of the dynamics is trapped in an undamped bound mode–a mechanism already observed experimentally–which generates revivals that keep recurring at arbitrarily long times. However, the protection is only partial, since the gap shields the system from dissipation but not from thermal noise, which still degrades the superposition. Finally, we show that squeezing redistributes robustness among these features, so that no single squeezing is optimal for all of them at once.
The Robustness and Breakdown of Collective Physics in Cavity-coupled Rydberg Arrays
(2026-09) Jiménez Isábal, Albert; Chang, Darrick; Jaworowski, Błażej
Quantized optical cavities naturally mediate long-range and even all-toall interactions between atoms, offering a route towards quantum many-body regimes that are difficult to access in conventional condensed matter systems. Their initial response is typically collective, with the atoms coherently behaving as a macroscopic spin and exhibiting phenomena such as spin squeezing. However, recent work has shown that sufficiently strong cavity interactions can nevertheless drive these systems into highly entangled states with non-trivial local structure, including quantum spin liquids. How a state that initially responds collectively to an all-to-all interaction can evolve into one dominated by local quantum correlations, remains an important question. Focusing on Rydberg atom arrays coupled to a single-mode cavity, we first show that the collective regime is remarkably robust. Even with strong superextensive cavity couplings, finite-momentum correlations vanish in the thermodynamic limit leading to a purely collective description. We develop a nonlinear spin-wave theory that predicts how this collective regime can break down and local correlations build up, but only under an unusual rescaling of the cavity interaction. More broadly, this thesis also highlights the challenges of characterizing long-range interacting quantum systems with standard many-body approaches, such as perturbation theory. Developing new theoretical descriptions for these intrinsically non-local systems may open the way to discovering quantum phases and dynamics beyond those accessible in short-range systems.
The mixed-dimensional quantum MacWilliams identity
(2026-09) González Lociga, David; Ball, Simeon (Simeon Michael)
As emerging quantum architectures evolve into heterogeneous networks combining different physical substrates, such as qubits for logic and higherdimensional qudits for robust communication, the traditional scalar metrics of quantum error correction become insufficient. To address this, we introduce a mathematical framework based on dimension multisets to characterize quantum error-correcting codes (QECC) and absolutely maximally entangled (AME) states in mixed-dimensional Hilbert spaces. By replacing scalar weights with multisets, we accurately capture the exact physical composition of error supports across these diverse systems. Our central result is the mixed-dimensional quantum MacWilliams identity, which establishes the formal algebraic relationship between Shor-Laflamme enumerators and unitary weight enumerators. From this foundation, we deduce the mixed-dimensional shadow identity and derive rigorous, generalized constraints on code parameters, explicitly formulating the mixed-dimensional quantum Hamming, Singleton and Scott’s bounds, and developing a linear program to systematically evaluate code viability. For the Singleton bound, a tighter bound that has no homogeneous analogue is derived for pure mixed-dimensional codes. Finally, we deploy this enumerator machinery to thoroughly analyze AME states, utilizing shadow inequalities to constrain their existence and introducing a combinatorial grid method for the explicit construction of mixed-dimensional tripartite AME states.
Pauli Correlation Encoding for Balanced MinCut with initial testing on VLSI implementations
(2026-09) Enríquez Cantú, Oscar Antonio; Garcia Saez, Artur; Borrallo Rentero, Alejandro
This master thesis centers on solving the balanced MinCut problem for (hyper)graphs via Quantum Variational Algorithms. This is achieved by compressing the binary variables in the problem for various network sizes with few qubits using Pauli Correlation Encoding. We adapt an existing heuristic algorithm for hyperparameter tuning to our problem, showing empirical evidence for convergence on feasible solutions. The thesis explores relevant formulations for the problem that can be translated directly for this specific encoding. We compare our solutions to the ones provided by well known classical methods, and identify future improvements to make this quantum optimization scheme be on par with these refined classical solutions. Finally, we test this methodology on real chip design applications, where we find opportunities for better adaptation in this design problem, so the proposed mechanism can eventually be used to solve real applications in this field.
Entanglement Phase Transition in Monitored Cluster States
(2026-09) Egido Quesada, Mireia; Acín dal Maschio, Antonio; Centrone, Federico
Entanglement scaling reveals how quantum correlations are distributed and how difficult a many-body state is to simulate classically. Since measurements modify quantum states, can random local measurements produce a macroscopic entanglement transition in an already entangled system? We study this question using two-dimensional cluster states, represented as graphs whose vertices are either qubits or harmonic oscillators, and whose edges encode entangling operations. When applied to these states, Pauli-Z and ˆq-homodyne measurements delete vertices and their edges, while other measurement bases can also rewire the surviving graph. For each measurement realisation, we identify the largest connected component (LCC), divide it across a fixed spatial cut, and calculate its von Neumann entropy. Under vertex deletion, the mean LCC entropy obeys a boundary law, scaling linearly with the system size L in the percolating regime, but becomes approximately independent of L once long-range connectivity is lost. Moreover, the critical points and exponents obtained through finite-size scaling agree between the qubit and harmonic-oscillator systems within numerical uncertainty and are consistent with two-dimensional site percolation. These results provide strong evidence for an entanglement phase transition. However, larger systems and improved statistics near the critical point are required before making a definitive claim. For the homodyne measurements with a momentum component considered here, rewiring preserves enough entanglement channels for the entropy to remain approximately proportional to L, and no transition is resolved within the accessible system sizes. These results show that entanglement scaling depends strongly on how measurements transform the underlying graph. Larger simulations and broader ranges of edge weights and measurement angles are needed to determine whether these behaviours persist in the large-system limit.
Simulating the Lindblad Master Equation in Multi-Qubit Phase Space with Deep Learning
(2026-09) Domínguez Ruiz, Isaac; Heightman, Timothy; Jiang, Edward
The cost of simulating an open quantum many-body system is set by the density matrix, which grows exponentially with the number of particles. Phasespace representations replace it with a function, the Q-function, which encodes the state of N spin-1/2 particles as a scalar field on N spheres. The Lindblad master equation then becomes a partial differential equation for that function, on a domain growing linearly with N. This thesis presents a solution that employs a neural network trained on no data. The initial condition is built into the ansatz, and the training signal is the residual of the equation itself, supplemented only by an exact equation of motion for the Pauli moments and a penalty on unphysical harmonic content. On the transverse-field Ising chain under on-site amplitude damping, the reconstructed states reach worst-time fidelities of 0.9994, 0.9970, and 0.9787 at two, three, and four sites against exact integration. The moment equation of motion is decisive: without it, the same field reaches only 0.9801 at three sites. Enforcing it requires phase-space integrals, evaluated here on a quadrature grid whose cost grows exponentially with N. A Monte-Carlo estimator removes that cost but plateaus at 0.9830, limited by a variance intrinsic to the correlators being estimated
A Majorana operator pool for adapt-VQE in nuclear shell model
(2026-09) Del Canto de Guzmán, Daniel; Rios Huguet, Arnau; Gallego Lizarribar, Kerman; Ainaud Fondevila, Joan
Quantum computers can represent a quantum many-body system in a natural way, but the devices available today are noisy, and that is what motivates the hybrid quantum-classical algorithms known as variational quantum eigensolvers. One of them, ADAPT-VQE, builds the trial state one operator at a time, taking at every step the generator with the largest energy gradient out of a predefined pool. That pool is the central design choice of the algorithm, and in this work we test two ways of changing it within the nuclear shell model, in the p shell with the Cohen–Kurath interaction. The first is to replace the usual fermionic double excitations by quartic products of Majorana operators, which map onto a single Pauli string under Jordan–Wigner instead of a sum of eight. The second is to give up the restriction to the physical sector and let the ansatz move through the whole Fock space, adding a quadratic penalty in the proton and neutron numbers. We run classical simulations of seventeen pshell nuclei and compare the pools in convergence and in number of operations. The results obtained with the projected Majorana pool are equivalent to those obtained for the same nuclei with the fermionic one. If the projection onto the physical sector is dropped and the symmetries are imposed through the penalty instead, the cost in operations grows by up to two orders of magnitude, and no convergence is found within the analyzed values of the penalty for nine of the seventeen nuclei.
Full nonlocality beyond maximally entangled scenarios
(2026-09) De Azevedo e Mello, Isadora Regina; Renner, Martin J.; Acín dal Maschio, Antonio
Nonlocality is a quantum phenomenon that enables many different technology applications. Full nonlocality, arguably its strongest form, is of interest. However, identifying exactly which states can exhibit this property remains an open problem. Recent work established a connection between the phenomenon and antidistinguishability. Building upon that result, we propose a specific protocol with particular measurement settings in order to identify states that exhibit full nonlocality extending beyond the maximally entangled scenario. Consequently, this work derives new conditions for a family of non-maximally entangled states in d-dimensions narrowing the discussion to 5-dimensional states when considering explicit measurements
A rack-integrated photon pair source for field deployable quantum internet nodes
(2026-09) Castañeiras Morales, Sergio; De Riedmatten, Hugues ; Gundín Martínez, Manuel
The losses associated with long-range optical fibre communications are a major challenge for establishing large-scale quantum communication networks. Quantum repeaters provide a solution, requiring field-deployable quantum nodes. One possible way of realising a quantum network node is to combine a photon pair source and a quantum memory. For the photon-pair source, stability, compatibility with both the telecommunications band and the quantum memory, and high efficiency are required. In this work, I designed, assembled, and characterised a rack-integrated cavity-enhanced spontaneous parametric downconversion (cSPDC) narrow-linewidth photon-pair source for a field-deployable quantum repeater node. The source generates photon pairs at 606 nm and 1552 nm from a periodically poled KTP crystal, compatible with Pr3+:Y2SiO5 quantum memory and telecommunications networks. In order to make the photons compatible with the quantum memory, their linewidth is narrowed using a 2.2-meter-long bow-tie cavity. Additionally, to make the source truly field-deployable, it is mounted in a standard 19-inch rack drawer together with the optics and lasers required for its operation. The cavity characterization yielded a linewidth of 1.26 ± 0.02 MHz for the signal photons, compatible with a Pr3+:Y2SiO5 solid-state quantum memory. The rack-integrated source maintained a fibre-coupling efficiency of approximately 64% over a 48-hour measurement, demonstrating its stability. I measured a heralding efficiency of 21%, lower than expected from the cavity design. The main limitations were identified as non-optimal pump focusing and photon collection. Overall, the results demonstrate a compact, stable, and rack-integrated cSPDC source. The source is designed to be compatible with a quantum memory setup that constitutes a field-deployable quantum node, contributing to the development of large-scale quantum communication networks
The Quantum Internet: A Complex Network Perspective
(2026-09) Birch Hardwick, Elizabeth; Yehia, Raja; Mariani, Luca; Acín dal Maschio, Antonio
The distribution of entanglement over large distances is fundamentally limited by optical fibre attenuation, necessitating quantum repeaters to realise a global quantum internet. While current theoretical studies often consider repeater performance in linear chains, these models do not capture the more complex topologies of spatially distributed communication networks. In this work, entanglement distribution is simulated across spatially embedded complex networks using a sequential repeater scheduling strategy and a realistic, hardware-aware model based on Nitrogen-Vacancy Centres. The dependence of network performance on spatial node density is first investigated. By applying an elementary link entanglement generation threshold, a percolation transition is identified, determining the critical density at which macroscopic entanglement connectivity emerges. End-to-end entanglement generation rate and fidelity are then analysed to characterise the physical capabilities of the network. Quantum key distribution is subsequently evaluated as a direct application of this distributed entanglement. By analysing the end-to-end secret key rate and network reachability, the operational 90%-reachability density required to establish macroscopic secure communication is determined. Ultimately, the results demonstrate that increasing the spatial density significantly enhances both the fidelity of the distributed entanglement and the resulting cryptographic key rates. Furthermore, the inclusion of multiplexing is shown to provide a substantial advantage across all metrics; it not only increases communication rates, but also dramatically lowers the density thresholds required to achieve both entanglement connectivity and end-to-end security

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