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Signaled by non-analyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic topological order parameters (DTOPs). In this work, we report the experimental study of DQPTs using discrete-time quantum walks of single photons. We simulate quench dynamics between distinct Floquet topological phases using quantum-walk dynamics, and experimentally characterize DQPTs and the underlying DTOPs through interferencebased measurements. The versatile photonic quantum-walk platform further allows us to experimentally investigate DQPTs for mixed states and in parity-time-symmetric non-unitary dynamics for the first time. Our experiment directly confirms the relation between DQPTs and DTOPs in quench dynamics of a topological system, and opens up the avenue of simulating emergent topological phenomena using discrete-time quantum-walk dynamics.

We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the polarization of the walker photon, which effectively introduces loss to the dynamics. The topological invariant of the nonunitary quantum walk is manifested in the quantized average displacement of the walker, which is probed by monitoring the photon loss. We confirm the topological properties of the system by observing localized edge states at the boundary of regions with different topological invariants. We further demonstrate the robustness of both the topological properties and the measurement scheme of the topological invariants against disorder.

We experimentally simulate non-unitary quantum dynamics using a single-photon interferometric network and study the information flow between a parity-time (PT )-symmetric non-Hermitian system and its environment. We observe oscillations of quantum-state distinguishability and complete information retrieval in the PT -symmetry-unbroken regime. We then characterize in detail critical phenomena of the information flow near the exceptional point separating the PT -unbroken andbroken regimes, and demonstrate power-law behavior in key quantities such as the distinguishability and the recurrence time. We also reveal how the critical phenomena are affected by symmetry and initial conditions. Finally, introducing an ancilla as an environment and probing quantum entanglement between the system and the environment, we confirm that the observed information retrieval is induced by a finite-dimensional entanglement partner in the environment. Our work constitutes the first experimental characterization of critical phenomena in PT -symmetric non-unitary quantum dynamics.

We show that a perfect state transfer of an arbitrary unknown two-qubit state can be achieved via a discrete-time quantum walk with various settings of coin flips and extend this method to the distribution of an arbitrary unknown multiqubit entangled state between every pair of sites in the multidimensional network. Furthermore, we study the routing of quantum information on this network in a quantum-walk architecture, which can be used as quantum information processors to communicate between separated qubits.

We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two periodic revivals of the walker distribution. In our beam-displacer interferometer, the walk corresponds to movement between discretely separated transverse modes of the field serving as lattice sites, and the time-dependent coin flip is effected by implementing a different angle between the optical axis of half-wave plate and the light propagation at each step. Each of the quantum-walk steps required to realize a revival comprises two sequential orthogonal coin-flip operators, with one coin having constant bias and the other coin having a time-dependent ramped coin bias, followed by a conditional translation of the walker. [4][5][6] plus the fundamental interest of being a natural quantized version of the ubiquitous random walk that appears in statistics, computer science, finance, physics, and chemistry. QW research has focused on evolution due to repeated applications of a time-independent unitary step operator U , but a QW with time-dependent unitary steps U (t), with discrete time t ∈ N := {0, 1, 2, . . . }, opens a much richer array of phenomena including localization and quasiperiodicity [7,8]. Here we demonstrate a time-dependent QW and use this technique to demonstrate a revival of the walker's position distribution.Rather than employing direct time-dependent control, we simulate time-dependent coin control by setting different coin parameters for different steps, which are effected in different locations along the longitudinal axis within our photonic beam-displacer interferometer (BDI) [9]. The quantum walker within the BDI is a single heralded photon produced by spontaneous parametric down conversion, and its walking degree of freedom is the set of discretely spaced transverse beam modes. The coin flip is effected by employing quarter-and half-wave plates.Our method for realizing the first time-dependent QW demonstrates the phenomenon of revivals and also opens the door to realizing a multitude of time-dependent QWs experimentally. Compared to prior work employing position-dependent control [10][11][12], our new technique decreases experimental complexity by relaxing the requirement of optical compensation. Our QW revival displays a different characteristic than typical QW properties such as ballistic spreading and localization of the walker distribution.The QW with a coin proceeds as a sequence of coin flips and then walker-coin entangling operations whereby the walker's position is displaced according to the coin state. We explain the QW now in full generality so the coin operator admits both spatial and temporal dependence. Spatially-dependent coin operations have dramatically demonstrated the realization of topological phases by QWs [4][5][6], but the time-dependent QW is, until now, only a theoretical construct and not yet explored experimentally.We employ a two...

Topology in quench dynamics gives rise to intriguing dynamic topological phenomena, which are intimately connected to the topology of static Hamiltonians yet challenging to probe experimentally. Here we theoretically characterize and experimentally detect momentum-time skyrmions in parity-time -symmetric non-unitary quench dynamics in single-photon discrete-time quantum walks. The emergent skyrmion structures are protected by dynamic Chern numbers defined for the emergent two-dimensional momentum-time submanifolds, and are revealed through our experimental scheme enabling the construction of time-dependent non-Hermitian density matrices via direct measurements in position space. Our work experimentally reveals the interplay of symmetry and quench dynamics in inducing emergent topological structures, and highlights the application of discrete-time quantum walks for the study of dynamic topological phenomena.

We perform generalized measurements of a qubit by realizing the qubit as a coin in a photonic quantum walk and subjecting the walker to projective measurements. Our experimental technique can be used to realize photonically any rank-1 single-qubit positive operator-valued measure via constructing an appropriate interferometric quantum-walk network and then projectively measuring the walker's position at the final step.PACS numbers: 42.50. Ex, 42.50.Dv, 03.67.Lx, 03.67.Ac Quantum walks (QWs) exhibit distinct features compared to classical random walks with applications to quantum algorithms [1, 2]. The discrete-time QW is a process in which the evolution of a quantum particle on a lattice depends on a state of a coin, typically a twolevel system, or qubit. Controlling the coin degree of freedom indirectly controls the walker, and, through this indirect control, the walker's state can be measured to infer the coin state. Rigorously speaking, walker-coin entanglement and projective measurement of the walker yields a positive operator-valued measure (POVM) on a single qubit [3]. Furthermore any rank-1 and rank-2 single-qubit POVM can be generated by a judiciously engineered QW. Here we demonstrate experimentally the capability of performing such generalized measurements of a qubit by realizing the walker in the path degree of freedom of a photon and the coin state as polarization and performing optical interferometry with path-based photodetector to perform a POVM on the photon's polarization state.Realizing a POVM is important as a POVM is needed for generalized acquisition of information thereby associated with a multitude of quantum information tasks such as quantum state estimation and tomography [4] Our goal is to realize experimentally a single-qubit POVM and to discriminate between non-orthogonal initial coin states via executing a properly engineered QW whose projective walker measurement is sometimes inconclusive [3]. To achieve a site-specific POVM, we control the internal degree of freedom of the measured twolevel coin. Here we report our successful experimental realization of POVMs, including unambiguous state discrimination of two equally probable single-qubit states and a single-qubit SIC-POVM, via a one-dimensional photonic QW.We focus on rank-1 POVMs, as higher-rank POVMs can be constructed as a convex combination of rank-1 elements [3]. Our experimental technique can be used to realize photonically any rank-1 single-qubit POVM via constructing an interferometric QW and projectively measuring the walker's position at the final step. We characterize experimental performance by the 1-norm distance [18] between the walker distribution obtained experimentally P exp (x) vs theoretically P th (x) over integervalued position x. This distance isand a small distance indicates a successful experimental realization.A standard model of a one-dimensional (1D) discretetime QW consists of a walker carrying a coin that is flipped before each step. In the coin-state basis {|0 , |1 }, the site-dependent coin rotati...