Measurement-induced entanglement transitions in monitored circuits

4 problems

• Universality of the charge-sharpening transition in U(1) monitored circuits

  Open

  When circuits conserve a quantity like total charge, a second transition appears: below it, an observer cannot quickly learn the total charge from the measurements. Which universal class this learning transition belongs to is not settled.

• Universality class of the measurement-induced transition in Haar circuits

  Open

  At the transition, quantities like entanglement follow power laws with universal exponents, as at a boiling point. These exponents and the theory that produces them are not known for ordinary random circuits of qubits.

• Does a critical phase exist for monitored free fermions in one dimension?

  Contested

  For particles that do not interact, some simulations show a whole range of measurement rates with slowly growing entanglement, while a field theory predicts that this range disappears in very large systems. The two pictures disagree.

• Observing the measurement-induced transition without exponential postselection

  Partially resolved

  Seeing the transition directly requires repeating the same random set of measurement outcomes, which happens with exponentially small probability. A way to detect it in generic circuits with resources that grow only polynomially with size is not established.