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Hyper-entanglement between two or more photonic degrees of freedom (DOF) can enhance and enable new quantum protocols by allowing each DOF to perform the task it is optimally suited for. Here we demonstrate the generation of photon pairs hyper-entangled between pulse modes and frequency bins. The pulse modes are generated via parametric downconversion in a domain-engineered crystal and subsequently entangled to two frequency bins via a spectral mapping technique. The resulting hyper-entangled state is characterized and verified via measurement of its joint spectral intensity and non-classical two-photon interference patterns from which we infer its spectral phase. The protocol combines the robustness to loss, intrinsic high dimensionality and compatibility with standard fiber-optic networks of the energy-time DOF with the ability of hyper-entanglement to increase the capacity and efficiency of the quantum channel, already exploited in recent experimental applications in both quantum information and quantum computation.

Efficient distributed computing offers a scalable strategy for solving resource-demanding tasks such as parallel computation and circuit optimisation. Crucially, the communication overhead introduced by the allotment process should be minimised -- a key motivation behind the communication complexity problem (CCP). Quantum resources are well-suited to this task, offering clear strategies that can outperform classical counterparts. Furthermore, the connection between quantum CCPs and nonlocality provides an information-theoretic insights into fundamental quantum mechanics. Here we connect quantum CCPs with a generalised nonlocality framework -- beyond the paradigmatic Bell's theorem -- by incorporating the underlying causal structure, which governs the distributed task, into a so-called nonlocal hidden variable model. We prove that a new class of communication complexity tasks can be associated to Bell-like inequalities, whose violation is both necessary and sufficient for a quantum gain. We experimentally implement a multipartite CCP akin to the guess-your-neighbour-input scenario, and demonstrate a quantum advantage when multipartite Greenberger-Horne-Zeilinger (GHZ) states are shared among three users., Comment: 21 pages, 5 figures

How much information do we need about a process' past to faithfully simulate its future? The statistical complexity is a prominent quantifier of structure for stochastic processes. Quantum machines, however, can simulate classical stochastic processes while storing significantly less information than their optimal classical counterparts. This implies qualitative divergences between classical and quantum statistical complexity. Here, we develop error-tolerant techniques to witness such divergences, enabling us to account for the inevitable imperfections in realising quantum stochastic simulators with present-day quantum technology. We apply these tools to experimentally verify the quantum memory advantage in simulating an Ising spin chain, even when accounting for experimental distortion. This then leads us to observe a recently conjectured effect, the ambiguity of simplicity$\unicode{x2013}$the notion that the relative complexity of two different processes can depend on whether we model the process using classical or quantum means of information processing., Comment: 9 pages, 6 figures

Computer simulation of observable phenomena is an indispensable tool for engineering new technology, understanding the natural world, and studying human society. Yet the most interesting systems are often complex, such that simulating their future behaviour demands storing immense amounts of information regarding how they have behaved in the past. For increasingly complex systems, simulation becomes increasingly difficult and is ultimately constrained by resources such as computer memory. Recent theoretical work shows quantum theory can reduce this memory requirement beyond ultimate classical limits (as measured by a process' statistical complexity, C). Here we experimentally demonstrate this quantum advantage in simulating stochastic processes. Our quantum implementation observes a memory requirement of C_q = 0.05 $\pm$ 0.01, far below the ultimate classical limit of C = 1. Scaling up this technique would substantially reduce the memory required in simulation of more complex systems., Comment: 7 pages, 4 figures

A credit risk monitoring model using Markov Chains was first prescribed by Cyert, Davidson and Thomson (1962) (the CDT model). It is used to monitor transition of a credit account from one performance state to another, as an alternative to scorecard methodologies. The propensity of such transition is called transition probability. Successive variants ofthe CDT model assumed a few outdated assumptions although proper tests had been available. Moreover no solutions were offered despite many had long suspected the dependency oftransition probability on economic conditions. In this empirical research, using real, substantial retail bank data, and adopting the Mover-Stayer notion (Frydman et al, 1985): 1. the unquestioned assumptions are proved invalid; 2. the true functional dependency of a transition probability time series on selected economic indicators is established; 3. the parameter associated to each explanatory variable is estimated using a non linear optimisation technique on the maximum logarithmic likelihood of a transition probability; 4. segments based on different transitional behaviour are identified for the given portfolio; 5. a pilot scorecard scheme is carried out to investigate membership to the segments identified in (4), given existing application and behavioural information.

Entanglement in high-dimensional quantum systems, where one or more degrees of freedom of light are involved, offers increased information capacities and enables new quantum protocols. Here, we demonstrate a functional source of high-dimensional, noise-resilient hyperentangled states encoded in time-frequency and vector-vortex structured modes, which in turn carry single-particle entanglement between polarisation and orbital angular momentum. Pairing nonlinearity-engineered parametric downconversion in an interferometric scheme with spin-to-orbital-angular-momentum conversion, we generate highly entangled photon pairs at telecom wavelength that we characterise via two-photon interference and quantum state tomography, achieving near-unity visibilities and fidelities. While hyperentanglement has been demonstrated before in photonic qubits, this is the first instance of such a rich entanglement structure involving spectrally and spatially structured light, where three different forms of entanglement coexist in the same biphoton state., 5 pages, 4 figures, Supplement: 6 pages, 2 figures