Scouting Enzyme Behavior

Experimental exploration of enzymatic response in a multi-dimensional context faces the challenge of an explosive number of possible milieu conditions. We address this problem with an evolutionary search strategy that scouts the physiochemical milieu space for unanticipated enzyme behavior and rewards the discovery of experimental conditions that yield surprises

Semibiotic Persistence

From observation, we find four different strategies to successfully enable structures to persist over extended periods of time. If functionally relevant features are very large compared to the changes that can be effectuated by entropy, the functional structure itself has a high enough probability to erode only slowly over time. If the functionally relevant features are protected from environmental influence by sacrificial layers that absorb the impinging of the environment,deterioration can be avoided or slowed. Loss of functionality can be delayed, even for complex systems, by keeping alternate options for all required components available. Biological systems also apply information processing to actively counter the impact of entropy. The latter strategy increases the overall persistence of living systems and enables them to maintain a highly complex functional organisation during their lifetime and over generations. In contrast to the other strategies, information processing has only low material overhead. While at present engineered technology is far from achieving the self-repair of evolved systems, the semibiotic combination of biological components with conventionally engineered systems may open a path to long-term persistence of functional devices in harsh environments. We review nature’s strategies for persistence, and consider early steps taken in the laboratory to import such capabilities into engineered architectures.<br/

Sparse robot swarms: Moving swarms to real-world applications

Robot swarms are groups of robots that each act autonomously based on only local perception and coordination with neighbouring robots. While current swarm implementations can be large in size (e.g. 1000 robots), they are typically constrained to working in highly controlled indoor environments. Moreover, a common property of swarms is the underlying assumption that the robots act in close proximity of each other (e.g. 10 body lengths apart), and typically employ uninterrupted, situated, close-range communication for coordination. Many real-world applications, including environmental monitoring and precision agriculture, however, require scalable groups of robots to act jointly over large distances (e.g. 1000 body lengths), rendering the use of dense swarms impractical. Using a dense swarm for such applications would be invasive to the environment and unrealistic in terms of mission deployment, maintenance and post-mission recovery. To address this problem, we propose the sparse swarm concept, and illustrate its use in the context of four application scenarios. For one scenario, which requires a group of rovers to traverse, and monitor, a forest environment, we identify the challenges involved at all levels in developing a sparse swarm—from the hardware platform to communication-constrained coordination algorithms—and discuss potential solutions. We outline open questions of theoretical and practical nature, which we hope will bring the concept of sparse swarms to fruition

On quaternary complex Hadamard matrices of small orders

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.Comment: 7 page

Multicomplementary operators via finite Fourier transform

A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of dimension d, whenever d is a power of a prime. We discuss a simple construction of d+1 disjoint classes (each one having d-1 commuting operators) such that the corresponding eigenstates form sets of unbiased bases. Such a construction works properly for prime dimension. We investigate an alternative construction in which the real numbers that label the classes are replaced by a finite field having d elements. One of these classes is diagonal, and can be mapped to cyclic operators by means of the finite Fourier transform, which allows one to understand complementarity in a similar way as for the position-momentum pair in standard quantum mechanics. The relevant examples of two and three qubits and two qutrits are discussed in detail.Comment: 15 pages, no figure

From SICs and MUBs to Eddington

This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.Comment: 12 pages; from the Festschrift for Tony Sudber

Affine Constellations Without Mutually Unbiased Counterparts

It has been conjectured that a complete set of mutually unbiased bases in a space of dimension d exists if and only if there is an affine plane of order d. We introduce affine constellations and compare their existence properties with those of mutually unbiased constellations, mostly in dimension six. The observed discrepancies make a deeper relation between the two existence problems unlikely.Comment: 8 page

Quasi-probability representations of quantum theory with applications to quantum information science

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde

Tight informationally complete quantum measurements

We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, "as close as possible" to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows "painless" quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positive-operator-valued measures are both members of this class, the latter being the unique minimal rank-one members. Recast as ensembles of pure quantum states, the rank-one members are in fact equivalent to weighted 2-designs in complex projective space. These measures are shown to be optimal for quantum cloning and linear quantum state tomography.Comment: 20 pages. Final versio