1,770 research outputs found
Everett's "Many-Worlds" Proposal
Hugh Everett III proposed that a quantum measurement can be treated as an interaction that correlates microscopic and macroscopic systems—particularly when the experimenter herself is included among those macroscopic systems. It has been difficult, however, to determine precisely what this proposal amounts to. Almost without exception, commentators have held that there are ambiguities in Everett’s theory of measurement that result from significant—even embarrassing—omissions. In the present paper, we resist the conclusion that Everett’s proposal is incomplete, and we develop a close reading that accounts for apparent oversights. We begin by taking a look at how Everett set up his project—his method and his criterion of success. Illuminating parallels are found between Everett’s method and then-contemporary thought regarding inter-theoretic reduction. Also, from unpublished papers and correspondence, we are able to piece together how Everett judged the success of his theory of measurement, which completes our account of his intended contribution to the resolution of the quantum measurement problem
Zero-Error Coding for Computing with Encoder Side-Information
We study the zero-error source coding problem in which an encoder with Side
Information (SI) transmits source symbols to a decoder. The decoder
has SI and wants to recover where are deterministic. We
exhibit a condition on the source distribution and that we call "pairwise
shared side information", such that the optimal rate has a single-letter
expression. This condition is satisfied if every pair of source symbols "share"
at least one SI symbol for all output of . It has a practical
interpretation, as models a request made by the encoder on an image ,
and corresponds to the type of request. It also has a graph-theoretical
interpretation: under "pairwise shared side information" the characteristic
graph can be written as a disjoint union of OR products. In the case where the
source distribution is full-support, we provide an analytic expression for the
optimal rate. We develop an example under "pairwise shared side information",
and we show that the optimal coding scheme outperforms several strategies from
the literature
Abstract Hidden Markov Models: a monadic account of quantitative information flow
Hidden Markov Models, HMM's, are mathematical models of Markov processes with
state that is hidden, but from which information can leak. They are typically
represented as 3-way joint-probability distributions.
We use HMM's as denotations of probabilistic hidden-state sequential
programs: for that, we recast them as `abstract' HMM's, computations in the
Giry monad , and we equip them with a partial order of increasing
security. However to encode the monadic type with hiding over some state
we use rather
than the conventional that suffices for
Markov models whose state is not hidden. We illustrate the
construction with a small
Haskell prototype.
We then present uncertainty measures as a generalisation of the extant
diversity of probabilistic entropies, with characteristic analytic properties
for them, and show how the new entropies interact with the order of increasing
security. Furthermore, we give a `backwards' uncertainty-transformer semantics
for HMM's that is dual to the `forwards' abstract HMM's - it is an analogue of
the duality between forwards, relational semantics and backwards,
predicate-transformer semantics for imperative programs with demonic choice.
Finally, we argue that, from this new denotational-semantic viewpoint, one
can see that the Dalenius desideratum for statistical databases is actually an
issue in compositionality. We propose a means for taking it into account
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