Direct Measurement of a Nonlocal Entangled Quantum State.

Entanglement and the wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using weak values, was demonstrated by Lundeen et al. [Nature 474, 188 (2011)]. However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining weak values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using modular values. The method is experimentally implemented for a photon pair in a hyperentangled state, i.e., entangled both in polarization and momentum degrees of freedom.

Anomalous correlation-induced dynamical phase transitions.

The nonanalyticity of the Loschmidt echo at critical times in quantum quenched systems is termed as the dynamical quantum phase transition, extending the notion of quantum criticality to a nonequilibrium scenario. In this paper, we establish a new paradigm of dynamical phase transitions driven by a sudden change in the internal spatial correlations of the disorder potential in a low-dimensional disordered system. The quench dynamics between prequenched pure and postquenched random system Hamiltonian reveals an anomalous dynamical quantum phase transition triggered by an infinite disorder correlation in the modulation potential. The physical origin of the anomalous phenomenon is associated with the overlap between the two distinctly different extended states. Furthermore, we explore the quench dynamics between the prequenched random and postquenched pure system Hamiltonian. Interestingly, the quenched system undergoes dynamical quantum phase transitions for the prequench white-noise potential in the thermodynamic limit. In addition, the quench dynamics also shows a clear signature of the delocalization phase transition in the correlated Anderson model.

Measuring a dynamical topological order parameter in quantum walks.

Quantum processes of inherent dynamical nature, such as quantum walks, defy a description in terms of an equilibrium statistical physics ensemble. Until now, identifying the general principles behind the underlying unitary quantum dynamics has remained a key challenge. Here, we show and experimentally observe that split-step quantum walks admit a characterization in terms of a dynamical topological order parameter (DTOP). This integer-quantized DTOP measures, at a given time, the winding of the geometric phase accumulated by the wavefunction during a quantum walk. We observe distinct dynamical regimes in our experimentally realized quantum walks, and each regime can be attributed to a qualitatively different temporal behavior of the DTOP. Upon identifying an equivalent many-body problem, we reveal an intriguing connection between the nonanalytic changes of the DTOP in quantum walks and the occurrence of dynamical quantum phase transitions.