65,077 research outputs found
The structure of degradable quantum channels
Degradable quantum channels are among the only channels whose quantum and
private classical capacities are known. As such, determining the structure of
these channels is a pressing open question in quantum information theory. We
give a comprehensive review of what is currently known about the structure of
degradable quantum channels, including a number of new results as well as
alternate proofs of some known results. In the case of qubits, we provide a
complete characterization of all degradable channels with two dimensional
output, give a new proof that a qubit channel with two Kraus operators is
either degradable or anti-degradable and present a complete description of
anti-degradable unital qubit channels with a new proof.
For higher output dimensions we explore the relationship between the output
and environment dimensions ( and respectively) of degradable
channels. For several broad classes of channels we show that they can be
modeled with a environment that is "small" in the sense . Perhaps
surprisingly, we also present examples of degradable channels with ``large''
environments, in the sense that the minimal dimension . Indeed, one
can have .
In the case of channels with diagonal Kraus operators, we describe the
subclass which are complements of entanglement breaking channels. We also
obtain a number of results for channels in the convex hull of conjugations with
generalized Pauli matrices. However, a number of open questions remain about
these channels and the more general case of random unitary channels.Comment: 42 pages, 3 figures, Web and paper abstract differ; (v2 contains only
minor typo corrections
Maximization of capacity and p-norms for some product channels
It is conjectured that the Holevo capacity of a product channel \Omega
\otimes \Phi is achieved when product states are used as input. Amosov, Holevo
and Werner have also conjectured that the maximal p-norm of a product channel
is achieved with product input states. In this paper we establish both of these
conjectures in the case that \Omega is arbitrary and \Phi is a CQ or QC channel
(as defined by Holevo). We also establish the Amosov, Holevo and Werner
conjecture when \Omega is arbitrary and either \Phi is a qubit channel and p=2,
or \Phi is a unital qubit channel and p is integer. Our proofs involve a new
conjecture for the norm of an output state of the half-noisy channel I \otimes
\Phi, when \Phi is a qubit channel. We show that this conjecture in some cases
also implies additivity of the Holevo capacity
An application of decomposable maps in proving multiplicativity of low dimensional maps
In this paper we present a class of maps for which the multiplicativity of
the maximal output p-norm holds when p is 2 and p is larger than or equal to 4.
The class includes all positive trace-preserving maps from the matrix algebra
on the three-dimensional space to that on the two-dimensional.Comment: 9 page
The standstill luminosity in Z Cam systems
We consider accretion discs in close binary systems. We show that heating of
a disc at the impact point of the accretion stream contributes significantly to
the local energy budget at its outer edge. As a result the thermal balance
relation between local accretion rate and surface density (the `S-curve')
changes; the critical mass transfer rate above which no dwarf nova outbursts
occur can be up to 40% smaller than without impact heating. Standstills in ZCam
systems thus occur at smaller mass transfer rates than otherwise expected, and
are rather fainter than the peak luminosity during the dwarf nova phase as a
result.Comment: 3 pages, 3 figures. Accepted for publication in MNRA
Constructive counterexamples to additivity of minimum output R\'enyi entropy of quantum channels for all p>2
We present a constructive example of violation of additivity of minimum
output R\'enyi entropy for each p>2. The example is provided by antisymmetric
subspace of a suitable dimension. We discuss possibility of extension of the
result to go beyond p>2 and obtain additivity for p=0 for a class of
entanglement breaking channels.Comment: 4 pages; a reference adde
Age structure, dispersion and diet of a population of stoats (Mustela erminea) in southern Fiordland during the decline phase of the beechmast cycle
The dispersion, age structure and diet of stoats (Mustela erminea) in beech forest in the Borland and Grebe Valleys, Fiordland National Park, were examined during December and January 2000/01, 20 months after a heavy seed-fall in 1999. Thirty trap stations were set along a 38-km transect through almost continuous beech forest, at least 1 km apart. Mice were very scarce (nights, C/100TN) along two standard index lines placed at either end of the transect, compared with November 1999 (>60/100TN), but mice were detected (from footprints in stoat tunnels) along an 8 km central section of the transect (stations 14-22). Live trapping with one trap per station (total 317.5 trap nights) in December 2000 caught 2 female and 23 male stoats, of which 10 (including both females) were radio collared. The minimum range lengths of the two females along the transect represented by the trap line were 2.2 and 6.0 km; those of eight radio-tracked males averaged 2.9 ± 1.7 km. Stations 14-22 tended to be visited more often, by more marked individual stoats, than the other 21 stations.
Fenn trapping at the same 30 sites, but with multiple traps per station (1333.5 trap nights), in late January 2001 collected carcasses of 35 males and 28 females (including 12 of the marked live-trapped ones). Another two marked males were recovered dead. The stoat population showed no sign of chronic nutritional stress (average fat reserve index = 2.8 on a scale of 1-4 where 4 = highest fat content); and only one of 63 guts analysed was empty. Nevertheless, all 76 stoats handled were adults with 1-3 cementum annuli in their teeth, showing that reproduction had failed that season. Prey categories recorded in descending frequency of occurrence were birds, carabid beetle (ground beetle), weta, possum, rat, and mouse. The frequencies of occurrence of mice and birds in the diet of these stoats (10% and 48%, respectively) were quite different from those in stoats collected in Pig Creek, a tributary of the Borland River (87%, 5%), 12 months previously when mice were still abundant. Five of the six stoat guts containing mice were collected within 1 km of stations 14-22
Qubit Channels Can Require More Than Two Inputs to Achieve Capacity
We give examples of qubit channels that require three input states in order
to achieve the Holevo capacity.Comment: RevTex, 5 page, 4 figures
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