Matthew FISHER
When a quantum system is coupled to a dissipative environment an initially pure state becomes rapidly mixed as information is lost, and classical behavior invariably follows. Recently, another type of open system dynamics has been explored, when a quantum system is continuously “monitored” by an observer, making a sequence of measurements, and a pure quantum state remainspure. Importantly, the repeated measurements do not simply read out a preexisting unitary dynamics: they yield a new dynamics, which is kind of a random walk thru Hilbert space. The resulting quantum trajectories constitute an ensemble of pure states, which can (in principle) be experimentally accessed in digital quantum simulators. In the many-body context, these quantum trajectories can have a rich entanglement structure, exhibiting - for example - dynamical phase transitions between volume law and area law entanglement, and between phases with or without symmetry breaking and/or topological order. Quantum circuits of qubits provide a setting to theoretically explore such many-body non-equilibrium phenomena, the simplest being a structureless circuit with random two-qubit unitaries and randomly interspersed single qubit measurements but additional structure can be readily included thereby allowing symmetry enriched monitored dynamics. For mixed initial density matrices, monitoring can lead to a plethora of purification transitions, and reveals underlying connections with quantum encoding. Accessing such physics in the lab is challenged by the need for post-selection, which might be circumnavigated by decoding using active error correction. In this talk I will try to give an overview of some topics in such monitored quantum dynamics.