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Reform and Representation: A New Method Applied to Recent Electoral Changes
Can electoral reforms such as an independent redistricting commission and the top-two primary create conditions that lead to better legislative representation? We explore this question by presenting a new method for measuring a key indicator of representation - the congruence between a legislator's ideological position and the average position of her district's voters. Our novel approach combines two methods: the joint classification of voters and political candidates on the same ideological scale, along with multilevel regression and post-stratification to estimate the position of the average voter across many districts in multiple elections. After validating our approach, we use it to study the recent impact of reforms in California, showing that they did not bring their hoped-for effects
Inequalities for quantum channels assisted by limited resources
The information capacities and ``distillability'' of a quantum channel are
studied in the presence of auxiliary resources. These include prior
entanglement shared between the sender and receiver and free classical bits of
forward and backward communication. Inequalities and trade-off curves are
derived. In particular an alternative proof is given that in the absence of
feedback and shared entanglement, forward classical communication does not
increase the quantum capacity of a channel.Comment: 8 pages, 4 figures (references updated, minor changes
Quantum information cannot be split into complementary parts
We prove a new impossibility for quantum information (the no-splitting
theorem): an unknown quantum bit (qubit) cannot be split into two complementary
qubits. This impossibility, together with the no-cloning theorem, demonstrates
that an unknown qubit state is a single entity, which cannot be cloned or
split. This sheds new light on quantum computation and quantum information.Comment: 9 pages, 1 figur
Restrictions on Transversal Encoded Quantum Gate Sets
Transversal gates play an important role in the theory of fault-tolerant
quantum computation due to their simplicity and robustness to noise. By
definition, transversal operators do not couple physical subsystems within the
same code block. Consequently, such operators do not spread errors within code
blocks and are, therefore, fault tolerant. Nonetheless, other methods of
ensuring fault tolerance are required, as it is invariably the case that some
encoded gates cannot be implemented transversally. This observation has led to
a long-standing conjecture that transversal encoded gate sets cannot be
universal. Here we show that the ability of a quantum code to detect an
arbitrary error on any single physical subsystem is incompatible with the
existence of a universal, transversal encoded gate set for the code.Comment: 4 pages, v2: minor change
Power of unentangled measurements on two antiparallel spins
We consider a pair of antiparallel spins polarized in a random direction to
encode quantum information. We wish to extract as much information as possible
on the polarization direction attainable by an unentangled measurement, i.e.,
by a measurement, whose outcomes are associated with product states. We develop
analytically the upper bound 0.7935 bits to the Shannon mutual information
obtainable by an unentangled measurement, which is definitely less than the
value 0.8664 bits attained by an entangled measurement. This proves our main
result, that not every ensemble of product states can be optimally
distinguished by an unentangled measurement, if the measure of
distinguishability is defined in the sense of Shannon. We also present results
from numerical calculations and discuss briefly the case of parallel spins.Comment: Latex file, 18 pages, 1 figure; published versio
Clifford Gates by Code Deformation
Topological subsystem color codes add to the advantages of topological codes
an important feature: error tracking only involves measuring 2-local operators
in a two dimensional setting. Unfortunately, known methods to compute with them
were highly unpractical. We give a mechanism to implement all Clifford gates by
code deformation in a planar setting. In particular, we use twist braiding and
express its effects in terms of certain colored Majorana operators.Comment: Extended version with more detail
Quantum computing of delocalization in small-world networks
We study a quantum small-world network with disorder and show that the system
exhibits a delocalization transition. A quantum algorithm is built up which
simulates the evolution operator of the model in a polynomial number of gates
for exponential number of vertices in the network. The total computational gain
is shown to depend on the parameters of the network and a larger than quadratic
speed-up can be reached.
We also investigate the robustness of the algorithm in presence of
imperfections.Comment: 4 pages, 5 figures, research done at
http://www.quantware.ups-tlse.fr
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