TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.7.1.009
TI  - A solvable model for graph state decoherence dynamics
PY  - 2024/02/23
UR  - https://www.scipost.org/SciPostPhysCore.7.1.009
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 7
IS  - 1
SP  - 009
A1  - Houdayer, Jérôme
AU  - Landa, Haggai
AU  - Misguich, Grégoire
AB  - We present an exactly solvable toy model for the continuous dissipative dynamics of permutation-invariant graph states of $N$ qubits. Such states are locally equivalent to an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state, a fundamental resource in many quantum information processing setups. We focus on the time evolution of the state governed by a Lindblad master equation with the three standard single-qubit jump operators, the Hamiltonian part being set to zero. Deriving analytic expressions for the expectation values of observables expanded in the Pauli basis at all times, we analyze the nontrivial intermediate-time dynamics. Using a numerical solver based on matrix product operators, we simulate the time evolution for systems with up to 64 qubits and verify a numerically exact agreement with the analytical results. We find that the evolution of the operator space entanglement entropy of a bipartition of the system manifests a plateau whose duration increases logarithmically with the number of qubits, whereas all Pauli-operator products have expectation values decaying at most in constant time.
ER  -

@Article{10.21468/SciPostPhysCore.7.1.009,
	title={{A solvable model for graph state decoherence dynamics}},
	author={Jérôme Houdayer and Haggai Landa and Grégoire Misguich},
	journal={SciPost Phys. Core},
	volume={7},
	pages={009},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.7.1.009},
	url={https://scipost.org/10.21468/SciPostPhysCore.7.1.009},
}