Aspects of mutually unbiased bases in odd prime power dimensions

We rephrase the Wootters-Fields construction [Ann. Phys., {\bf 191}, 363 (1989)] of a full set of mutually unbiased bases in a complex vector space of dimensions $N=p^r$, where $p$ is an odd prime, in terms of the character vectors of the cyclic group $G$ of order $p$. This form may be useful in explicitly writing down mutually unbiased bases for $N=p^r$.Comment: 3 pages, latex, no figure

Probabilistic quantum multimeters

We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant multimeters for a large class of program states, then the universal multimeters for a special choice of program. In both cases we start with deterministic but erroneous devices and then proceed to devices that never make a mistake but from time to time they give an inconclusive result. These multimeters are optimized (for a given type of a program) with respect to the minimum probability of inconclusive result. This concept is further generalized to the multimeters that minimize the error rate for a given probability of an inconclusive result (or vice versa). Finally, we propose a generalization for qudits.Comment: 12 pages, 3 figure

How well can you know the edge of a quantum pyramid?

We consider a symmetric quantum communication scenario in which the signal states are edges of a quantum pyramid of arbitrary dimension and arbitrary shape, and all edge states are transmitted with the same probability. The receiver could employ different decoding strategies: he could minimize the error probability, or discriminate without ambiguity, or extract the accessible information. We state the optimal measurement scheme for each strategy. For large parameter ranges, the standard square-root measurement does not extract the information optimally.Comment: 13 pages, 5 figures, 1 tabl

Optimal Conclusive Discrimination of Two Non-orthogonal Pure Product Multipartite States Locally

We consider one copy of a quantum system prepared in one of two non-orthogonal pure product states of multipartite distributed among separated parties. We show that there exist protocols which obtain optimal probability in the sense of conclusive discrimination by means of local operations and classical communications(LOCC) as good as by global operations. Also, we show a protocol which minimezes the average number of local operations. Our result implies that two product pure multipartite states might not have the non-local property though more than two can have.Comment: revtex, 3 pages, no figur

The contact drag of towed demersal fishing gear components

This study was funded in part by Fisheries Innovation Scotland, project FIS02, and by the FP7 project BENTHIS (312088). It does not necessarily reflect the views of the European Commission and does not anticipate the Commission's future policy in this area.Peer reviewedPostprin

Modelling global-scale climate impacts of the late Miocene Messinian Salinity Crisis

Late Miocene tectonic changes in Mediterranean–Atlantic connectivity and climatic changes caused Mediterranean salinity to fluctuate dramatically, including a ten-fold increase and near-freshening. Recent proxy- and model-based evidence suggests that at times during this Messinian Salinity Crisis (MSC, 5.96–5.33 Ma), highly saline and highly fresh Mediterranean water flowed into the North Atlantic Ocean, whilst at others, no Mediterranean Outflow Water (MOW) reached the Atlantic. By running extreme, sensitivity-type experiments with a fully coupled ocean–atmosphere general circulation model, we investigate the potential of these various MSC MOW scenarios to impact global-scale climate. The simulations suggest that although the effect remains relatively small, MOW had a greater influence on North Atlantic Ocean circulation and climate than it does today. We also find that depending on the presence, strength and salinity of MOW, the MSC could have been capable of cooling mid–high northern latitudes by a few degrees, with the greatest cooling taking place in the Labrador, Greenland–Iceland–Norwegian and Barents seas. With hypersaline MOW, a component of North Atlantic Deep Water formation shifts to the Mediterranean, strengthening the Atlantic Meridional Overturning Circulation (AMOC) south of 35° N by 1.5–6 Sv. With hyposaline MOW, AMOC completely shuts down, inducing a bipolar climate anomaly with strong cooling in the north (mainly −1 to −3 °C, but up to −8 °C) and weaker warming in the south (up to +0.5 to +2.7 °C). These simulations identify key target regions and climate variables for future proxy reconstructions to provide the best and most robust test cases for (a) assessing Messinian model performance, (b) evaluating Mediterranean–Atlantic connectivity during the MSC and (c) establishing whether or not the MSC could ever have affected global-scale climate

Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices

We present reduction theorems for the problem of optimal unambiguous state discrimination (USD) of two general density matrices. We show that this problem can be reduced to that of two density matrices that have the same rank $n$ and are described in a Hilbert space of dimensions $2n$. We also show how to use the reduction theorems to discriminate unambiguously between N mixed states (N \ge 2).Comment: 6 pages, 1 figur