Open & Monitored Dynamics

Background

There are two fundamental ingredients to modern quantum theory: unitary evolution and measurement. Unitary evolution refers to the way that isolated (closed) states evolve in time. The constraint that this evolution be unitary means that quantum information cannot be destroyed. Unitary evolution is deterministic, meaning every given input is always mapped to a corresponding output, and reversible. Measurement of a quantum system, by contrast, is a discontinuous, random, and hence irreversible process. That is to say, a quantum state can be used to define a probability distribution of measurement outcomes, but every individual outcome of a given experiment will be random. The state, moreover, changes discontinuously in a way that is directly correlated with the outcome of the measurement. In this way, measurement constitutes a fundamentally distinct dynamical process by which quantum states can evolve.

Open quantum systems are systems in which quantum information is not conserved. One example of open-system dynamics is to consider unitary dynamics over a closed system \(\mathcal{S}\), but to “ignore” some sub-region \(\mathcal{R}\). In that case, quantum information can leak from the observed region into the ignored region, and hence does not appear to be conserved (at least, not “locally”). This is a ubiquitous example as even the most carefully controlled experiments are never perfectly “closed” systems because they are coupled to the surrounding environment. Often we model just the experimental system and include the effects of the environment by considering open-system dynamics. Another example of open-system dynamics arises when one measures the quantum system but “ignores” the measurement outcome. If the outcome was known, then in principle information is conserved; but if we throw away the outcome of the measurement, we explicitly violate conservation of information, thus leading to open-system dynamics.

Research Highlights

Observation of Strong-to-Weak Spontaneous Symmetry Breaking in a Dephased Fermi Gas
Si Wang, Thomas G. Kiely, Dorothee Tell, Johannes Obermeyer, Marnix Barendregt, Petar Bojović, Philipp M. Preiss, Abhijat Sarma, Titus Franz, Matthew P. A. Fisher, Cenke Xu, Immanuel Bloch

Strong-to-Weak Symmetry Breaking in Open Quantum Systems: From Discrete Particles to Continuum Hydrodynamics
Jacob Hauser, Kaixiang Su, Hyunsoo Ha, Jerome Lloyd, Thomas G. Kiely, Romain Vasseur, Sarang Gopalakrishnan, Cenke Xu, Matthew P. A. Fisher

Spin liquid and superconductivity emerging from steady states and measurements
Kaixiang Su, Abhijat Sarma, Marcus Bintz, Thomas G. Kiely, Yimu Bao, Matthew P. A. Fisher, Cenke Xu