Manipulating biphotonic qutrits

Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement induced non-linearities can be employed to dramatically extend the range of possible transforms on biphotonic qutrits; the three level quantum systems formed by the polarisation of two photons in the same spatio-temporal mode. We fully characterise the biphoton-photon entanglement that underpins our technique, thereby realising the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.Comment: 4 pages, 4 figure

Experimental demonstration of Shor's algorithm with quantum entanglement

Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation and its full realization will have a large impact on modern cryptography. Here we implement a compiled version of Shor's algorithm in a photonic system using single photons and employing the non-linearity induced by measurement. For the first time we demonstrate the core processes, coherent control, and resultant entangled states that are required in a full-scale implementation of Shor's algorithm. Demonstration of these processes is a necessary step on the path towards a full implementation of Shor's algorithm and scalable quantum computing. Our results highlight that the performance of a quantum algorithm is not the same as performance of the underlying quantum circuit, and stress the importance of developing techniques for characterising quantum algorithms.Comment: 4 pages, 5 figures + half-page additional online materia

Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment

We produce and holographically measure entangled qudits encoded in transverse spatial modes of single photons. With the novel use of a quantum state tomography method that only requires two-state superpositions, we achieve the most complete characterisation of entangled qutrits to date. Ideally, entangled qutrits provide better security than qubits in quantum bit-commitment: we model the sensitivity of this to mixture and show experimentally and theoretically that qutrits with even a small amount of decoherence cannot offer increased security over qubits.Comment: Paper updated to match published version; 5 pages, 4 figures, images have been included at slightly lower quality for the archiv

Linear Optical CNOT Gate in the Coincidence Basis

We describe the operation and tolerances of a non-deterministic, coincidence basis, quantum CNOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration.Comment: Submitted to Physical Review

Investigation of two qubit quantum gates in linear optics

We discuss progress towards implementing two qubit quantum gates in optics. We review the operation of an optical quantum gate which performs all the operations of a control-NOT (CNOT) gate in the coincidence basis with two, unentangled photons as the input and discuss its implementation

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.Comment: 5 pages, 4 figure

Biodiversity and species interactions: extending Lotka-Volterra community theory

A new analysis of the nearly century-old Lotka-Volterra theory allows us to link species interactions to biodiversity patterns, including: species abundance distributions, estimates of total community size, patterns of community invasibility, and predicted responses to disturbance. Based on a few restrictive assumptions about species interactions, our calculations require only that the community is sufficiently large to allow a mean-field approximation. We develop this analysis to show how an initial assemblage of species with varying interaction strengths is predicted to sort out into the final community based on the species' predicted target densities. The sorting process yields predictions of covarying patterns of species abundance, community size, and species interaction strengths. These predictions can be tested using enrichment experiments, examination of latitudinal and productivity gradients, and features of community assembly

Simple scheme for expanding a polarization-entangled W state by adding one photon

We propose a simple scheme for expanding a polarization-entangled W state. By mixing a single photon and one of the photons in an n-photon W state at a polarization-dependent beam splitter (PDBS), we can obtain an (n+1)-photon W state after post-selection. Our scheme also opens the door for generating n-photon W states using single photons and linear optics.Comment: 3 pages, 2 figure

Robust decision-making under severe uncertainty for conservation management

In-conservation biology it is necessary to make management decisions for endangered and threatened species under severe uncertainty. Failure to acknowledge and treat uncertainty can lead to poor decisions. To illustrate the importance of considering uncertainty, we reanalyze a decision problem for the Sumatran rhino, Dicerorhinus sumatrensis, using information-gap theory to propagate uncertainties and to rank management options. Rather than requiring information about the extent of parameter uncertainty at the outset, information-gap theory addresses the question of how much uncertainty can be tolerated before our decision would change. It assesses the robustness of decisions in the face of severe uncertainty. We show that different management decisions may result when uncertainty in utilities and probabilities are considered in decision-making problems. We highlight the importance of a full assessment of uncertainty in conservation management decisions to avoid, as much as possible, undesirable outcomes

Entangled Qutrits: Production and Characterisation

We produce and measure entangled qubits and qutrits, two- and three-level quantum systems, realised using transverse spatial modes of the optical field. Photons encoded in these modes are manipulated and analysed by a combination of holograms and single-mode fibres. Using quantum state tomography, we achieve the most complete characterisation of entangled qutrits to date. Ideally, entangled qutrits provide better security than qubits in quantum bit-commitment and coin-flipping protocols: we show that to reach this regime places stringent requirements on the initial state