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

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

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

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