1,463 research outputs found
Stabilizer notation for Spekkens' toy theory
Spekkens has introduced a toy theory [Phys. Rev. A, 75, 032110 (2007)] in
order to argue for an epistemic view of quantum states. I describe a notation
for the theory (excluding certain joint measurements) which makes its
similarities and differences with the quantum mechanics of stabilizer states
clear. Given an application of the qubit stabilizer formalism, it is often
entirely straightforward to construct an analogous application of the notation
to the toy theory. This assists calculations within the toy theory, for example
of the number of possible states and transformations, and enables
superpositions to be defined for composite systems.Comment: 7+4 pages, 5 tables. v2: Clarifications added and typos fixed in
response to referee comment
Synthesis and Optimization of Reversible Circuits - A Survey
Reversible logic circuits have been historically motivated by theoretical
research in low-power electronics as well as practical improvement of
bit-manipulation transforms in cryptography and computer graphics. Recently,
reversible circuits have attracted interest as components of quantum
algorithms, as well as in photonic and nano-computing technologies where some
switching devices offer no signal gain. Research in generating reversible logic
distinguishes between circuit synthesis, post-synthesis optimization, and
technology mapping. In this survey, we review algorithmic paradigms ---
search-based, cycle-based, transformation-based, and BDD-based --- as well as
specific algorithms for reversible synthesis, both exact and heuristic. We
conclude the survey by outlining key open challenges in synthesis of reversible
and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table
Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
We propose a family of exactly solvable toy models for the AdS/CFT
correspondence based on a novel construction of quantum error-correcting codes
with a tensor network structure. Our building block is a special type of tensor
with maximal entanglement along any bipartition, which gives rise to an
isometry from the bulk Hilbert space to the boundary Hilbert space. The entire
tensor network is an encoder for a quantum error-correcting code, where the
bulk and boundary degrees of freedom may be identified as logical and physical
degrees of freedom respectively. These models capture key features of
entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi
formula and the negativity of tripartite information are obeyed exactly in many
cases. That bulk logical operators can be represented on multiple boundary
regions mimics the Rindler-wedge reconstruction of boundary operators from bulk
operators, realizing explicitly the quantum error-correcting features of
AdS/CFT recently proposed by Almheiri et. al in arXiv:1411.7041.Comment: 40 Pages + 25 Pages of Appendices. 38 figures. Typos and
bibliographic amendments and minor correction
Existence of an information unit as a postulate of quantum theory
Does information play a significant role in the foundations of physics?
Information is the abstraction that allows us to refer to the states of systems
when we choose to ignore the systems themselves. This is only possible in very
particular frameworks, like in classical or quantum theory, or more generally,
whenever there exists an information unit such that the state of any system can
be reversibly encoded in a sufficient number of such units. In this work we
show how the abstract formalism of quantum theory can be deduced solely from
the existence of an information unit with suitable properties, together with
two further natural assumptions: the continuity and reversibility of dynamics,
and the possibility of characterizing the state of a composite system by local
measurements. This constitutes a new set of postulates for quantum theory with
a simple and direct physical meaning, like the ones of special relativity or
thermodynamics, and it articulates a strong connection between physics and
information.Comment: Published version - 6 pages, 3 appendices, 3 figure
Convertible Codes: New Class of Codes for Efficient Conversion of Coded Data in Distributed Storage
Erasure codes are typically used in large-scale distributed storage systems to provide durability of data in the face of failures. In this setting, a set of k blocks to be stored is encoded using an [n, k] code to generate n blocks that are then stored on different storage nodes. A recent work by Kadekodi et al. [Kadekodi et al., 2019] shows that the failure rate of storage devices vary significantly over time, and that changing the rate of the code (via a change in the parameters n and k) in response to such variations provides significant reduction in storage space requirement. However, the resource overhead of realizing such a change in the code rate on already encoded data in traditional codes is prohibitively high.
Motivated by this application, in this work we first present a new framework to formalize the notion of code conversion - the process of converting data encoded with an [n^I, k^I] code into data encoded with an [n^F, k^F] code while maintaining desired decodability properties, such as the maximum-distance-separable (MDS) property. We then introduce convertible codes, a new class of code pairs that allow for code conversions in a resource-efficient manner. For an important parameter regime (which we call the merge regime) along with the widely used linearity and MDS decodability constraint, we prove tight bounds on the number of nodes accessed during code conversion. In particular, our achievability result is an explicit construction of MDS convertible codes that are optimal for all parameter values in the merge regime albeit with a high field size. We then present explicit low-field-size constructions of optimal MDS convertible codes for a broad range of parameters in the merge regime. Our results thus show that it is indeed possible to achieve code conversions with significantly lesser resources as compared to the default approach of re-encoding
Phylogeographic Relationships of Coereba flaveola and Their Malaria Parasites
This dissertation is broadly focused on elucidating how the geographic structure and demographic changes in host and parasite populations relate to one another, and how such interactions contribute to the generation and maintenance of biological diversity.
I begin by investigating the population structure of the Coereba flaveola (bananaquit) population within Puerto Rico, which is the apparent source of several expansions of the species into the Lesser Antilles. These findings indicate that both island and taxon effects influence the observed demographic changes. Because susceptibility to antagonists is related to both host species-specific characteristics and to geographical location, coevolutionary outcomes of these interactions are suspected to be related to the observed demographic changes. Accordingly, in the second part of this dissertation I investigate an abundant and widespread avian antagonist: avian malaria parasites.
I used contemporary genetic variation of a gene related to host immune evasion to characterize population structure of three mitochondrial lineages of West Indian avian malaria parasites. I found evidence of genetic differentiation in association with a single host genus and among some locations, and evidence of mitochondrial introgression from one lineage into a second lineage. These findings have significant implications for the practice of defining parasite lineages based on mitochondrial genetic variation. Moreover, pairwise comparisons of genetic differentiation illustrate complex patterns of parasite population structure among hosts and locations which are likely influenced by migratory and vector spatial dynamics.
In the final chapter, I return to genetic characteristics of hosts to investigate hemoglobin variation, a component of the host genetic background that has been linked to malaria resistance and tolerance in humans. I assessed genetic variation in αA -globin in C. flaveola populations and tested whether this variation is associated with differences in parasitism. I found no association between αA -globin haplotype and infection by particular parasite lineages among all locations, nor any protective association between globin haplotype frequency and the proportion of individuals infected within populations. However, phylogeographic structure and genetic variation at the αA -globin locus, including a highly variable intron, support it as a locus with potential application in biogeographic analyses
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