A discrete quantum walk occurs in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons.

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Memristive devices are a class of physical systems with history-dependent dynamics characterized by signature hysteresis loops in their input–output relations. In the past few decades, memristive devices have attracted enormous interest in electronics. This is because memristive dynamics is very pervasive in nanoscale devices, and has potentially groundbreaking applications ranging from energy-efficient memories to physical neural networks and neuromorphic computing platforms. Recently, the concept of a quantum memristor was introduced by a few proposals, all of which face limited technological practicality. Here we propose and experimentally demonstrate a novel quantum-optical memristor (based on integrated photonics) that acts on single-photon states. We fully characterize the memristive dynamics of our device and tomographically reconstruct its quantum output state. Finally, we propose a possible application of our device in the framework of quantum machine learning through a scheme of quantum reservoir computing, which we apply to classical and quantum learning tasks. Our simulations show promising results, and may break new ground towards the use of quantum memristors in quantum neuromorphic architectures.

The study of causal relations, a cornerstone of physics, has recently been applied to the quantum realm, leading to the discovery that not all quantum processes have a definite causal structure. Here, we present the first theory-independent experimental demonstration of entangled temporal orders, resulting in a process with an indefinite causal structure. While such processes have previously been observed, these observations relied on the assumption that experimental operations and systems are described by quantum theory. This opens a 'loophole' wherein the observed process can be explained by an underlying theory with a definite causal structure. To circumvent this, we build a model attempting to describe our experimental data using a large class of general probabilistic theories that are local and have a definite temporal order. We then experimentally invalidate this model by violating a Bell inequality. We therefore conclude that nature is incompatible with theories requiring a local definite temporal order.Bell's theorem revolutionized the foundations of physics, proving that quantum mechanics cannot be described by a local-realist theory, and paving the way for modern quantum information [1,2]. Over the past decades, the theorem has been violated with many different physical systems thereby entangling different observables (such as spin [3][4][5], polarization [6-9], position [10], and energy [11,12]) of two or more particles. However, since there is no observable corresponding to a measurement of the temporal order between events, this theorem had never been applied to causal structures.Typically, in all of our well-established theories, it is assumed that the order between events is pre-defined, precluding the possibility of observing situations where the causal order is genuinely indefinite. Nevertheless, it was recently realized that quantum mechanics predicts the existence of processes that are neither causally ordered nor a probabilistic mixture of causally ordered processes. In other words, these processes cannot be understood as one-way-signalling quantum channels, quantum states, or any convex mixture of them [13][14][15]. More precisely, a quantum process is called causally separable if it can be decomposed as a convex combination of causally ordered processes, otherwise it is causally nonseparable. (Note that the term 'temporal' order is here used to refer to events which cannot be used to receive signalsin particular, to unitary operations -whereas 'causal' or-der refers to more general operations which allow for the exchange of information.) Recently, a method for certifying causal separability, based on 'causal witnesses', was developed [16][17][18], and used to experimentally demonstrate that a certain process -a quantum SWITCH [19] -is causally non-separable [20].In the quantum SWITCH, a qubit is transmitted between two parties, and the order in which the parties receive it is entangled with a second system, which can result in a superposition of temporal orders. The existence of such a super...