Postselection-Free Entanglement Dynamics via Spacetime Duality

The dynamics of entanglement in hybrid nonunitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply postselection on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of nonunitary circuits by taking advantage of spacetime duality. This method maps the purification dynamics of a mixed state under nonunitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code formed by the mixed phase in this class of hybrid dynamics.

Automated summary

The dynamics of entanglement in hybrid nonunitary circuits involving both unitary gates and quantum measurements have been intensively studied. A proposed method utilizes spacetime duality to overcome the hurdle of postselection on random measurement outcomes in order to prepare output states, mapping the purification dynamics of mixed states onto particular correlation functions in associated unitary circuits. This operational protocol can be implemented on a digital quantum simulator and allows measurement of entanglement phases and subsystem purity.