On a nonlocal degenerate parabolic problem

Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In particular, the finite time extinction and polynomial decay properties are proved.

An entangling quantum-logic gate operated with an ultrabright single photon-source

We demonstrate unambiguous entangling operation of a photonic quantum-logic gate driven by an ultrabright solid-state single-photon source. Indistinguishable single photons emitted by a single semiconductor quantum dot in a micropillar optical cavity are used as target and control qubits. For a source brightness of 0.56 collected photons-per-pulse, the measured truth table has an overlap with the ideal case of 68.4%, increasing to 73.0% for a source brightness of 0.17 photons- per-pulse. The gate is entangling: at a source brightness of 0.48, the Bell-state fidelity is above the entangling threshold of 50%, and reaches 71.0% for a source brightness of 0.15.

Displacement operator for quantum systems with position-dependent mass

A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique commutation relation for $hat x$ and $hat p_gamma$. Such a formalism naturally leads to a Schrodinger-like equation that is reminiscent of wave equations typically used to model electrons with position-dependent (effective) masses propagating through abrupt interfaces in semiconductor heterostructures. The distinctive features of our approach is demonstrated through analytical solutions calculated for particles under null and constant potentials like infinite wells in one and two dimensions and potential barriers.

Violation of the Leggett-Garg inequality with weak measurements of photons

By weakly measuring the polarization of a photon between two strong polarization measurements, we experimentally investigate the correlation between the appearance of anomalous values in quantum weak measurements, and the violation of realism and non-intrusiveness of measurements. A quantitative formulation of the latter concept is expressed in terms of a Leggett-Garg inequality for the outcomes of subsequent measurements of an individual quantum system. We experimentally violate the Leggett-Garg inequality for several measurement strengths. Furthermore, we experimentally demonstrate that there is a one-to-one correlation between achieving strange weak values and violating the Leggett-Garg inequality.

Experimental quantum computing without entanglement

Entanglement is widely believed to lie at the heart of the advantages offered by a quantum computer. This belief is supported by the discovery that a noiseless (pure) state quantum computer must generate a large amount of entanglement in order to offer any speed up over a classical computer. However, deterministic quantum computation with one pure qubit (DQC1), which employs noisy (mixed) states, is an efficient model that generates at most a marginal amount of entanglement. Although this model cannot implement any arbitrary algorithm it can efficiently solve a range of problems of significant importance to the scientific community. Here we experimentally implement a first-order case of a key DQC1 algorithm and explicitly characterise the non-classical correlations generated. Our results show that while there is no entanglement the algorithm does give rise to other non-classical correlations, which we quantify using the quantum discord - a stronger measure of non-classical correlations that includes entanglement as a subset. Our results suggest that discord could replace entanglement as a necessary resource for a quantum computational speed-up. Furthermore, DQC1 is far less resource intensive than universal quantum computing and our implementation in a scalable architecture highlights the model as a practical short-term goal.

Experimental investigation of the dynamics of entanglement: Sudden death, complementarity, and continuous monitoring of the environment

We report on an experimental investigation of the dynamics of entanglement between a single qubit and its environment, as well as for pairs of qubits interacting independently with individual environments, using photons obtained from parametric down-conversion. The qubits are encoded in the polarizations of single photons, while the interaction with the environment is implemented by coupling the polarization of each photon with its momentum. A convenient Sagnac interferometer allows for the implementation of several decoherence channels and for the continuous monitoring of the environment. For an initially-entangled photon pair, one observes the vanishing of entanglement before coherence disappears. For a single qubit interacting with an environment, the dynamics of complementarity relations connecting single-qubit properties and its entanglement with the environment is experimentally determined. The evolution of a single qubit under continuous monitoring of the environment is investigated, demonstrating that a qubit may decay even when the environment is found in the unexcited state. This implies that entanglement can be increased by local continuous monitoring, which is equivalent to entanglement distillation. We also present a detailed analysis of the transfer of entanglement from the two-qubit system to the two corresponding environments, between which entanglement may suddenly appear, and show instances for which no entanglement is created between dephasing environments, nor between each of them and the corresponding qubit: the initial two-qubit entanglement gets transformed into legitimate multiqubit entanglement of the Greenberger-Horne-Zeilinger (GHZ) type.

Quantum computing using shortcuts through higher dimensions

Quantum computation offers the potential to solve fundamental yet otherwise intractable problems across a range of active fields of research. Recently, universal quantum-logic gate sets - the building blocks for a quantum computer - have been demonstrated in several physical architectures. A serious obstacle to a full-scale implementation is the sheer number of these gates required to implement even small quantum algorithms. Here we present and demonstrate a general technique that harnesses higher dimensions of quantum systems to significantly reduce this number, allowing the construction of key quantum circuits with existing technology. We are thereby able to present the first implementation of two key quantum circuits: the three-qubit Toffoli and the two-qubit controlled-unitary. The gates are realised in a linear optical architecture, which would otherwise be absolutely infeasible with current technology.