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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/231691
Entanglement Phase Transition in Monitored Cluster States
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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.
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Màster Oficial de Ciència i Tecnologia Quàntiques / Quantum Science and Technology, Facultat de Física, Universitat de Barcelona. Curs: 2025-2026. Tutors: Antonio Acín, Federico Centrone
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EGIDO QUESADA, Mireia. Entanglement Phase Transition in Monitored Cluster States. [consulted: 3 of October of 2026]. Available at: https://hdl.handle.net/2445/231691