872 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
Entanglement can completely defeat quantum noise
We describe two quantum channels that individually cannot send any
information, even classical, without some chance of decoding error. But
together a single use of each channel can send quantum information perfectly
reliably. This proves that the zero-error classical capacity exhibits
superactivation, the extreme form of the superadditivity phenomenon in which
entangled inputs allow communication over zero capacity channels. But our
result is stronger still, as it even allows zero-error quantum communication
when the two channels are combined. Thus our result shows a new remarkable way
in which entanglement across two systems can be used to resist noise, in this
case perfectly. We also show a new form of superactivation by entanglement
shared between sender and receiver.Comment: 4 pages, 1 figur
The Absence of Vortex Lattice Melting in a Conventional Superconductor
The state of the vortex lattice extremely close to the superconducting to
normal transition in an applied magnetic field is investigated in high purity
niobium. We observe that thermal fluctuations of the order parameter broaden
the superconducting to normal transition into a crossover but no sign of a
first order vortex lattice melting transition is detected in measurements of
the heat capacity or the small angle neutron scattering (SANS) intensity.
Direct observation of the vortices via SANS always finds a well ordered vortex
lattice. The fluctuation broadening is considered in terms of the Lowest Landau
Level theory of critical fluctuations and scaling is found to occur over a
large H_{c2}(T) range
The concept of the Poverty Datum Line
A book chapter discussing the history of the Poverty Datum Line (PDL) both in the then Rhodesia and elsewhere. The book's preface and introduction are also included.The purpose of this study has been to outline and to cost the minimum consumption needs of urban African families. Research was conducted in Salisbury and Bulawayo, these being the main urban work areas, and Fort Victoria which represents a small Rhodesian town with no one major industry.
After the preliminary research and discussion of the concept of the PDL, costing exercises were carried out in Salisbury in January and in Bulawayo and Fort Victoria in February this year.
Chapter I discusses in some detail the history of the PDL both in this country and elsewhere and explains the assumptions and implications of the concept for the rest of the report. In Chapter II the method of costing is explained and the Salisbury PDL is calculated. Chapters III and IV discuss the PDL for Bulawayo and Fort Victoria respectively. The chapter on the Salisbury PDL is considerably longer than the chapters on Bulawayo and Fort Victoria. This is because much of the methodology used for the Salisbury analysis applies to the studies carried out in the other two towns. Only where significant differences appear is a detailed discussion of method given. Chapter VI summarizes data from chapters II, III and IV, and chapter V makes some final reflections on the project.
As will become clear in the report, this is a need orientated study which attempts to calculate the minimum income required to satisfy the minimum consumption needs of various families. Because of this orientation we have not surveyed the actual living conditions of people. An investigation into actual income and expenditure patterns would be the subject of further research
Compact fermion to qubit mappings
Mappings between fermions and qubits are valuable constructions in physics. To date only a handful exist. In addition to revealing dualities between fermionic and spin systems, such mappings are indispensable in any quantum simulation of fermionic physics on quantum computers. The number of qubits required per fermionic mode, and the locality of mapped fermionic operators strongly impact the cost of such simulations. We present a fermion to qubit mapping that outperforms all previous local mappings in both the qubit to mode ratio and the locality of mapped operators. In addition to these practically useful features, the mapping bears an elegant relationship to the toric code, which we discuss. Finally, we consider the error mitigating properties of the mapping—which encodes fermionic states into the code space of a stabilizer code. Although there is an implicit tradeoff between low weight representations of local fermionic operators, and high distance code spaces, we argue that fermionic encodings with low-weight representations of local fermionic operators can still exhibit error mitigating properties which can serve a similar role to that played by high code distances. In particular, when undetectable errors correspond to “natural” fermionic noise. We illustrate this point explicitly both for this encoding and the Verstraete-Cirac encoding
Improving zero-error classical communication with entanglement
Given one or more uses of a classical channel, only a certain number of
messages can be transmitted with zero probability of error. The study of this
number and its asymptotic behaviour constitutes the field of classical
zero-error information theory, the quantum generalisation of which has started
to develop recently. We show that, given a single use of certain classical
channels, entangled states of a system shared by the sender and receiver can be
used to increase the number of (classical) messages which can be sent with no
chance of error. In particular, we show how to construct such a channel based
on any proof of the Bell-Kochen-Specker theorem. This is a new example of the
use of quantum effects to improve the performance of a classical task. We
investigate the connection between this phenomenon and that of
``pseudo-telepathy'' games. The use of generalised non-signalling correlations
to assist in this task is also considered. In this case, a particularly elegant
theory results and, remarkably, it is sometimes possible to transmit
information with zero-error using a channel with no unassisted zero-error
capacity.Comment: 6 pages, 2 figures. Version 2 is the same as the journal version plus
figure 1 and the non-signalling box exampl
On the dimension of subspaces with bounded Schmidt rank
We consider the question of how large a subspace of a given bipartite quantum
system can be when the subspace contains only highly entangled states. This is
motivated in part by results of Hayden et al., which show that in large d x
d--dimensional systems there exist random subspaces of dimension almost d^2,
all of whose states have entropy of entanglement at least log d - O(1). It is
also related to results due to Parthasarathy on the dimension of completely
entangled subspaces, which have connections with the construction of
unextendible product bases. Here we take as entanglement measure the Schmidt
rank, and determine, for every pair of local dimensions dA and dB, and every r,
the largest dimension of a subspace consisting only of entangled states of
Schmidt rank r or larger. This exact answer is a significant improvement on the
best bounds that can be obtained using random subspace techniques. We also
determine the converse: the largest dimension of a subspace with an upper bound
on the Schmidt rank. Finally, we discuss the question of subspaces containing
only states with Schmidt equal to r.Comment: 4 pages, REVTeX4 forma
Square vortex lattice at anomalously low magnetic fields in electron-doped NdCeCuO
We report here on the first direct observations of the vortex lattice in the
bulk of electron-doped NdCeCuO single crystals. Using
small angle neutron scattering, we have observed a square vortex lattice with
the nearest-neighbors oriented at 45 from the Cu-O bond direction,
which is consistent with theories based on the d-wave superconducting gap.
However, the square symmetry persists down to unusually low magnetic fields.
Moreover, the diffracted intensity from the vortex lattice is found to decrease
rapidly with increasing magnetic field.Comment: 4 pages, 4 Figures, accepted for publication in Phys. Rev. Let
Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0
Complementing recent progress on the additivity conjecture of quantum
information theory, showing that the minimum output p-Renyi entropies of
channels are not generally additive for p>1, we demonstrate here by a careful
random selection argument that also at p=0, and consequently for sufficiently
small p, there exist counterexamples.
An explicit construction of two channels from 4 to 3 dimensions is given,
which have non-multiplicative minimum output rank; for this pair of channels,
numerics strongly suggest that the p-Renyi entropy is non-additive for all p <
0.11. We conjecture however that violations of additivity exist for all p<1.Comment: 7 pages, revtex4; v2 added correct ref. [15]; v3 has more information
on the numerical violation as well as 1 figure (2 graphs) - note that the
explicit example was changed and the more conservative estimate of the bound
up to which violations occur, additionally some other small issues are
straightened ou
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