Open AccessObservation of the dynamics of an ergodic quantum protocol in a photonic realization
Author(s) -
Dengke Qu,
Orsolya Kálmán,
Gaoyan Zhu,
Xiao Liu,
Kunkun Wang,
T. Kiss,
Peng Xue
Publication year - 2021
Publication title -
new journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.584
H-Index - 190
ISSN - 1367-2630
DOI - 10.1088/1367-2630/ac15b4
Subject(s) - physics , qubit , ergodic theory , bloch sphere , statistical physics , ergodicity , quantum state , quantum mechanics , quantum chaos , quantum , realization (probability) , photon , quantum dynamics , mathematical analysis , statistics , mathematics
Iterated quantum protocols with measurement-based selection lead to deterministic chaos for the evolving pure state representing an ensemble of qubits. Deterministic chaos for the pure quantum state may lead to ergodic evolution in the sense that initial states from any small area on the Bloch sphere will cover the whole sphere after a finite number of iterations. We realize two steps of an ergodic protocol in a photonic experiment, where initial qubit states are encoded in the polarization and path degrees of freedom of down-converted photons stemming from a parametric process. We numerically analyze the effect of noise on the time evolution and show that the protocol, described by a Lattès map, remains quasi-ergodic for any initial state if the initial noise is small. Tomographic reconstruction of the quantum states throughout the evolution is consistent with simulations and thus demonstrates ergodicity of the quantum dynamics.