Local discrimination of mixed states

We provide rigorous, efficiently computable and tight bounds on the average error probability of multiple-copy discrimination between qubit mixed states by Local Operations assisted with Classical Communication (LOCC). In contrast to the pure-state case, these experimentally feasible protocols perform strictly worse than the general collective ones. Our numerical results indicate that the gap between LOCC and collective error rates persists in the asymptotic limit. In order for LOCC and collective protocols to achieve the same accuracy, the former requires up to twice the number of copies of the latter. Our techniques can be used to bound the power of LOCC strategies in other similar settings, which is still one of the most elusive questions in quantum communication.Comment: 4 pages, 2 figures+ supplementary materia

Making a financial time machine:a multitouch application to enable interactive 3-D visualization of distant savings goals

Financial planning and decision making for the general public continues to vex and perplex in equal measure. Whilst the tools presented by a typical desktop computer should make the task easier, the recent financial crisis confirms the increasing difficulty that people have in calculating the benefits of deferring consumption for future gains (i.e. Saving). We present an interactive concept demonstration for Microsoft SurfaceTM that tackles two of the key barriers to saving decision making. Firstly we show an interface that avoid the laborious writing down or inputting of data and instead embodies the cognitive decision of allocation of resources in a physical gesture based interface, where the scale of the investment or expenditure correlates with the scale of the gesture. Second we show how a fast-forward based animation can demonstrate the impact of small increments in savings to a long term savings goal in a strategy game-based, interactive format. The platform uses custom software (XNATM format) as opposed to the more usual WPFTM format found on Surface applications. This enables dynamic 3-D graphical icons to be used to maximize the interactive appeal of the interface. Demonstration and test trial feedback indicates that this platform can be adapted to suit the narrative of individual purchasing decisions to inform educate diverse user groups about the long term consequences of small financial decisions

On connectivity-dependent resource requirements for digital quantum simulation of dd-level particles

A primary objective of quantum computation is to efficiently simulate quantum physics. Scientifically and technologically important quantum Hamiltonians include those with spin-$s$, vibrational, photonic, and other bosonic degrees of freedom, i.e. problems composed of or approximated by $d$-level particles (qudits). Recently, several methods for encoding these systems into a set of qubits have been introduced, where each encoding's efficiency was studied in terms of qubit and gate counts. Here, we build on previous results by including effects of hardware connectivity. To study the number of SWAP gates required to Trotterize commonly used quantum operators, we use both analytical arguments and automatic tools that optimize the schedule in multiple stages. We study the unary (or one-hot), Gray, standard binary, and block unary encodings, with three connectivities: linear array, ladder array, and square grid. Among other trends, we find that while the ladder array leads to substantial efficiencies over the linear array, the advantage of the square over the ladder array is less pronounced. These results are applicable in hardware co-design and in choosing efficient qudit encodings for a given set of near-term quantum hardware. Additionally, this work may be relevant to the scheduling of other quantum algorithms for which matrix exponentiation is a subroutine.Comment: Accepted to QCE20 (IEEE Quantum Week). Corrected erroneous circuits in Figure

New ventures on the search for viable business models: Taking into account levels of uncertainty / ambiguity.

There exists evidence that most initial selections of business models by new ventures have to be adapted later on and that minor this need for adaptation stems from the high degrees of uncertainty and ambiguity new ventures are confronted with, both on the technology and the market level. The main research question of this paper is whether different levels of uncertainty and ambiguity have an effect on the appropriateness of different search strategies new ventures can use to adapt their business model; and if yes, what this effect is. We first present the relevant literature. We then put forward a simulation model - based on the model developed by Kauffman (1989, 1993) - as a formal basis for addressing our research question and analyze the simulation results. To conclude, these results are discussed in the light of existing research on entrepreneurship and innovation and some limitations of our research methodology are presented.Innovation; Market; Model; Models; Research; Selection; Simulation; Strategy; Technology; Uncertainty;