364 research outputs found
Small sets of complementary observables
Two observables are called complementary if preparing a physical object in an
eigenstate of one of them yields a completely random result in a measurement of
the other. We investigate small sets of complementary observables that cannot
be extended by yet another complementary observable. We construct explicit
examples of the unextendible sets up to dimension and conjecture certain
small sets to be unextendible in higher dimensions. Our constructions provide
three complementary measurements, only one observable away from the ultimate
minimum of two observables in the set. Almost all of our examples in finite
dimension allow to discriminate pure states from some mixed states, and shed
light on the complex topology of the Bloch space of higher-dimensional quantum
systems
Minimal-memory realization of pearl-necklace encoders of general quantum convolutional codes
Quantum convolutional codes, like their classical counterparts, promise to
offer higher error correction performance than block codes of equivalent
encoding complexity, and are expected to find important applications in
reliable quantum communication where a continuous stream of qubits is
transmitted. Grassl and Roetteler devised an algorithm to encode a quantum
convolutional code with a "pearl-necklace encoder." Despite their theoretical
significance as a neat way of representing quantum convolutional codes, they
are not well-suited to practical realization. In fact, there is no
straightforward way to implement any given pearl-necklace structure. This paper
closes the gap between theoretical representation and practical implementation.
In our previous work, we presented an efficient algorithm for finding a
minimal-memory realization of a pearl-necklace encoder for
Calderbank-Shor-Steane (CSS) convolutional codes. This work extends our
previous work and presents an algorithm for turning a pearl-necklace encoder
for a general (non-CSS) quantum convolutional code into a realizable quantum
convolutional encoder. We show that a minimal-memory realization depends on the
commutativity relations between the gate strings in the pearl-necklace encoder.
We find a realization by means of a weighted graph which details the
non-commutative paths through the pearl-necklace. The weight of the longest
path in this graph is equal to the minimal amount of memory needed to implement
the encoder. The algorithm has a polynomial-time complexity in the number of
gate strings in the pearl-necklace encoder.Comment: 16 pages, 5 figures; extends paper arXiv:1004.5179v
On the bulk-skin temperature difference and its impact on satellite remote sensing of sea surface temperature
Satellite infrared sensors only observe the temperature of the skin of the ocean rather than the bulk sea surface temperature (SST) traditionally measured from ships and buoys. In order to examine the differences and similarities between skin and bulk temperatures, radiometric measurements of skin temperature were made in the North Atlantic Ocean from a research vessel along with coincident measurements of subsurface bulk temperatures, radiative fluxes, and meteorological variables. Over the entire 6-week data set the bulk-skin temperature differences (AT) range between -1.0 and 1.0 K with mean differences of 0.1 to 0.2 K depending on wind and surface heat flux conditions. The bulk-skin temperature difference varied between day and night (mean differences 0.11 and 0.30 K, respectively) as well as with different cloud conditions, which can mask the horizontal variability of SST in regions of weak horizontal temperature gradients. A coherency analysis reveals strong correlations between skin and bulk temperatures at longer length scales in regions with relatively weak horizontal temperature gradients. The skin-bulk temperature difference is pararneterized in terms of heat and momentum fluxes (or their related variables) with a resulting accuracy of 0.11 K and 0.17 K for night and daytime. A recommendation is made to calibrate satellite derived SST's during night with buoy measurements and the additional aid of meteorological variables to properly handle AT variations
On the connection between mutually unbiased bases and orthogonal Latin squares
We offer a piece of evidence that the problems of finding the number of
mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS)
might not be equivalent. We study a particular procedure which has been shown
to relate the two problems and generates complete sets of MUBs in
power-of-prime dimensions and three MUBs in dimension six. For these cases,
every square from an augmented set of MOLS has a corresponding MUB. We show
that this no longer holds for certain composite dimensions.Comment: 6 pages, submitted to Proceedings of CEWQO 200
SIC~POVMs and Clifford groups in prime dimensions
We show that in prime dimensions not equal to three, each group covariant
symmetric informationally complete positive operator valued measure (SIC~POVM)
is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover,
the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence,
two SIC~POVMs covariant with respect to the HW group are unitarily or
antiunitarily equivalent if and only if they are on the same orbit of the
extended Clifford group. In dimension three, each group covariant SIC~POVM may
be covariant with respect to three or nine HW groups, and the symmetry group of
the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW
groups respectively. There may exist two or three orbits of equivalent
SIC~POVMs for each group covariant SIC~POVM, depending on the order of its
symmetry group. We then establish a complete equivalence relation among group
covariant SIC~POVMs in dimension three, and classify inequivalent ones
according to the geometric phases associated with fiducial vectors. Finally, we
uncover additional SIC~POVMs by regrouping of the fiducial vectors from
different SIC~POVMs which may or may not be on the same orbit of the extended
Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J.
Phys. A: Math. Theor. 43, 305305 (2010
Gas/particle partitioning and global distribution of polycyclic aromatic hydrocarbons – A modelling approach
The global atmospheric distribution and long-range transport (LRT) potential of three polycyclic aromatic hydrocarbons (PAH) - anthracene, fluoranthene and benzo[a]pyrene - are studied. The model used is a global aerosol-chemistry-transport-model, which is based on an atmospheric general circulation model. The model includes an in-built dynamic aerosol model coupled to two-dimensional surface compartments. Several parameterisations of gas/particle partitioning and different assumptions of degradation in the aerosol particulate phase were tested. PAHs are mostly distributed in the source regions but reach the Arctic and the Antarctic. The Canadian Arctic is predicted to be significantly less affected by mid-latitude PAH emissions than the European Arctic. Re-volatilisation is significant for semivolatile PAHs. Accumulation of semivolatile PAHs in polar regions, however, is not indicated. The model study suggests that gas/particle partitioning in air drastically influences the atmospheric cycling, the total environmental fate (e.g. compartmental distributions) and the LRT potential of the substances studied. A parameterisation which calculates the gas/particle partitioning assuming absorption into organic matter and adsorption to black carbon (soot) agrees best with the observations at remote sites. The study provides evidence that the degradation in the particulate phase must be slower than that in the gas-phase. The predicted concentrations of the semivolatile PAHs anthracene and fluoranthene in near-ground air at remote sites in mid and high northern latitudes are in line with measured concentrations, if adsorption of the substances to soot combined with absorption in particulate organic matter is assumed to determine gas/particle partitioning, but cannot be explained by adsorption alone (Junge-Pankow parameterisation of gas/particle partitioning). The results suggest that PAHs absorbed in the organic matrix of particulate matter is shielded from the gas-phase. (C) 2009 Elsevier Ltd. All rights reserved. [References: 42
Quantum Capacity Approaching Codes for the Detected-Jump Channel
The quantum channel capacity gives the ultimate limit for the rate at which
quantum data can be reliably transmitted through a noisy quantum channel.
Degradable quantum channels are among the few channels whose quantum capacities
are known. Given the quantum capacity of a degradable channel, it remains
challenging to find a practical coding scheme which approaches capacity. Here
we discuss code designs for the detected-jump channel, a degradable channel
with practical relevance describing the physics of spontaneous decay of atoms
with detected photon emission. We show that this channel can be used to
simulate a binary classical channel with both erasures and bit-flips. The
capacity of the simulated classical channel gives a lower bound on the quantum
capacity of the detected-jump channel. When the jump probability is small, it
almost equals the quantum capacity. Hence using a classical capacity
approaching code for the simulated classical channel yields a quantum code
which approaches the quantum capacity of the detected-jump channel
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
Constructing Mutually Unbiased Bases in Dimension Six
The density matrix of a qudit may be reconstructed with optimal efficiency if
the expectation values of a specific set of observables are known. In dimension
six, the required observables only exist if it is possible to identify six
mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard
matrix, we construct all others mutually unbiased to it, using algebraic
computations performed by a computer program. We repeat this calculation many
times, sampling all known complex Hadamard matrices, and we never find more
than two that are mutually unbiased. This result adds considerable support to
the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical
approximations and corrected the number of triples existing for non-affine
families (cf Table 3
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