aqora

Quantum Central Limit Theorem for Continuous-Time Quantum Walks on Odd Graphs in Quantum Probability Theory

S. Salimi

arXiv:0710.3043International Journal of Theoretical PhysicsMay 28, 200820 citations

Central Limit Theorems for Open Quantum Random Walks and Quantum Measurement Records

Stéphane Attal, Nadine Guillotin‐Plantard, Christophe Sabot

Annales Henri PoincaréMar 6, 201463 citations

Central Limit Theorems for Open Quantum Random Walks on the Crystal Lattices

Chul Ki Ko, Norio Konno, Etsuo Segawa +1 more

arXiv:1809.10451Journal of Statistical PhysicsMay 22, 20198 citations

Limit Theorems for Open Quantum Random Walks

Norio Konno, Hyun Jae Yoo

arXiv:1209.1419Journal of Statistical PhysicsDec 13, 201251 citations

On a Generalized Central Limit Theorem and Large Deviations for Homogeneous Open Quantum Walks

Raffaella Carbone, Federico Girotti, Anderson Melchor Hernandez

Abstract We consider homogeneous open quantum walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of the quantum trajectories of the walk. We prove that the properly rescaled position process asymptotically approaches a mixture of Gaussian measures. We can generalize the existing central limit type results and give more explicit expressions for the involved asymptotic quantities, dropping any additional condition on the walk. We use deformation and spectral techniques, together with reducibility properties of the local channel associated with the open quantum walk. Further, we can provide a large deviation principle in the case of a fast recurrent local channel and at least lower and upper bounds in the general case.Abstract We consider homogeneous open quantum walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of the quantum trajectories of the walk. We prove that the properly rescaled position process asymptotically approaches a mixture of Gaussian measures. We can generalize the existing central limit type results and give more explicit expressions for the involved asymptotic quantities, dropping any additional condition on the walk. We use deformation and spectral techniques, together with reducibility properties of the local channel associated with the open quantum walk. Further, we can provide a large deviation principle in the case of a fast recurrent local channel and at least lower and upper bounds in the general case.

arXiv:2107.03935Journal of Statistical PhysicsMay 24, 202214 citations

Homogeneous open quantum random walks a lattice

Raffaella Carbone, Yan Pautrat

Abstract. We study open quantum random walks (OQRW) for which the underlying graph is a lattice, and the generators of the walk are translation-invariant. Using the results obtained recently in [5], we study the quantum trajectory associated with the OQRW, which is described by a position process and a state process. We obtain a central limit theorem and a large deviation principle for the position process. We study in detail the case of homogeneous OQRWs on a lattice, with internal space h = C2. 1Abstract. We study open quantum random walks (OQRW) for which the underlying graph is a lattice, and the generators of the walk are translation-invariant. Using the results obtained recently in [5], we study the quantum trajectory associated with the OQRW, which is described by a position process and a state process. We obtain a central limit theorem and a large deviation principle for the position process. We study in detail the case of homogeneous OQRWs on a lattice, with internal space h = C2. 1

Aug 17, 201641 citations

Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum Walks

Related papers

Central Limit Theorem and Large Deviation Principle for Continuous Time Open Quantum Walks

Related papers