79,751 research outputs found
Thermal states are vital: Entanglement Wedge Reconstruction from Operator-Pushing
We give a general construction of a setup that verifies bulk reconstruction,
conservation of relative entropies, and equality of modular flows between the
bulk and the boundary, for infinite-dimensional systems with operator-pushing.
In our setup, a bulk-to-boundary map is defined at the level of the
-algebras of state-independent observables. We then show that if the
boundary dynamics allow for the existence of a KMS state, physically relevant
Hilbert spaces and von Neumann algebras can be constructed directly from our
framework. Our construction should be seen as a state-dependent construction of
the other side of a wormhole and clarifies the meaning of black hole
reconstruction claims such as the Papadodimas-Raju proposal. As an
illustration, we apply our result to construct a wormhole based on the HaPPY
code, which satisfies all properties of entanglement wedge reconstruction.Comment: 38 pages, 4 figures, 1 tabl
The Zero-Undetected-Error Capacity Approaches the Sperner Capacity
Ahlswede, Cai, and Zhang proved that, in the noise-free limit, the
zero-undetected-error capacity is lower bounded by the Sperner capacity of the
channel graph, and they conjectured equality. Here we derive an upper bound
that proves the conjecture.Comment: 8 Pages; added a section on the definition of Sperner capacity;
accepted for publication in the IEEE Transactions on Information Theor
On secure network coding with uniform wiretap sets
This paper shows determining the secrecy capacity of a unicast network with
uniform wiretap sets is at least as difficult as the k-unicast problem. In
particular, we show that a general k-unicast problem can be reduced to the
problem of finding the secrecy capacity of a corresponding single unicast
network with uniform link capacities and one arbitrary wiretap link
On Universal Properties of Capacity-Approaching LDPC Ensembles
This paper is focused on the derivation of some universal properties of
capacity-approaching low-density parity-check (LDPC) code ensembles whose
transmission takes place over memoryless binary-input output-symmetric (MBIOS)
channels. Properties of the degree distributions, graphical complexity and the
number of fundamental cycles in the bipartite graphs are considered via the
derivation of information-theoretic bounds. These bounds are expressed in terms
of the target block/ bit error probability and the gap (in rate) to capacity.
Most of the bounds are general for any decoding algorithm, and some others are
proved under belief propagation (BP) decoding. Proving these bounds under a
certain decoding algorithm, validates them automatically also under any
sub-optimal decoding algorithm. A proper modification of these bounds makes
them universal for the set of all MBIOS channels which exhibit a given
capacity. Bounds on the degree distributions and graphical complexity apply to
finite-length LDPC codes and to the asymptotic case of an infinite block
length. The bounds are compared with capacity-approaching LDPC code ensembles
under BP decoding, and they are shown to be informative and are easy to
calculate. Finally, some interesting open problems are considered.Comment: Published in the IEEE Trans. on Information Theory, vol. 55, no. 7,
pp. 2956 - 2990, July 200
New Equations for Neutral Terms: A Sound and Complete Decision Procedure, Formalized
The definitional equality of an intensional type theory is its test of type
compatibility. Today's systems rely on ordinary evaluation semantics to compare
expressions in types, frustrating users with type errors arising when
evaluation fails to identify two `obviously' equal terms. If only the machine
could decide a richer theory! We propose a way to decide theories which
supplement evaluation with `-rules', rearranging the neutral parts of
normal forms, and report a successful initial experiment.
We study a simple -calculus with primitive fold, map and append operations on
lists and develop in Agda a sound and complete decision procedure for an
equational theory enriched with monoid, functor and fusion laws
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