15,660 research outputs found
Abstract Hodge decomposition and minimal models for cyclic algebras
We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to homotopy
Feynman diagrams and minimal models for operadic algebras
We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of well-known results for A∞-algebras. Furthermore, we show that these results carry over to the case of algebras over modular operads; the sums over trees get replaced by sums over general Feynman graphs. As a by-product of our work we prove gauge-independence of Kontsevich's ‘dual construction’ producing graph cohomology classes from contractible differential graded Frobenius algebras
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Free resolutions of algebras
Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is itself a tensor algebra. The construction rests combinatorially on the set of bracketings that arise naturally in the description of a free contractible differential graded algebra with given generators
Cocommutative coalgebras: homotopy theory and Koszul duality
We extend a construction of Hinich to obtain a closed model category
structure on all differential graded cocommutative coalgebras over an
algebraically closed field of characteristic zero. We further show that the
Koszul duality between commutative and Lie algebras extends to a Quillen
equivalence between cocommutative coalgebras and formal coproducts of curved
Lie algebras.Comment: 38 page
Approximate quantum error correction can lead to better codes
We present relaxed criteria for quantum error correction which are useful
when the specific dominant noise process is known. These criteria have no
classical analogue. As an example, we provide a four-bit code which corrects
for a single amplitude damping error. This code violates the usual Hamming
bound calculated for a Pauli description of the error process, and does not fit
into the GF(4) classification.Comment: 7 pages, 2 figures, submitted to Phys. Rev.
Non-separated states from squeezed dark-state polaritons in electromagnetically-induced-transparency media
Within the frame of quantized dark-state polaritons in
electromagnetically-induced-transparency media, noise fluctuations in the
quadrature components are studied. Squeezed state transfer, quantum
correlation, and noise entanglement between probe field and atomic polarization
are demonstrated in single- and double- configurations, respectively.
Even though a larger degree of squeezing parameter in the continuous variable
helps to establish stronger quantum correlations, inseparability criterion is
satisfied only within a finite range of squeezing parameter. The results
obtained in the present study may be useful for guiding experimental
realization of quantum memory devices for possible applications in quantum
information and computation.Comment: 12 pages, 7 figure
Quantum parallelism of the controlled-NOT operation: an experimental criterion for the evaluation of device performance
It is shown that a quantum controlled-NOT gate simultaneously performs the
logical functions of three distinct conditional local operations. Each of these
local operations can be verified by measuring a corresponding truth table of
four local inputs and four local outputs. The quantum parallelism of the gate
can then be observed directly in a set of three simple experimental tests, each
of which has a clear intuitive interpretation in terms of classical logical
operations. Specifically, quantum parallelism is achieved if the average
fidelity of the three classical operations exceeds 2/3. It is thus possible to
evaluate the essential quantum parallelism of an experimental controlled-NOT
gate by testing only three characteristic classical operations performed by the
gate.Comment: 6 pages, no figures, added references and discussio
Deutsch-Jozsa algorithm as a test of quantum computation
A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a
refined algorithm, which reduces the size of the register and simplifies the
function evaluation, is proposed. The refined version allows a simpler analysis
of the use of entanglement between the qubits in the algorithm and provides
criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful
test of quantum computation.Comment: 10 pages, 2 figures, RevTex, Approved for publication in Phys Rev
Quantum Faraday Effect in Double-Dot Aharonov-Bohm Ring
We investigate Faraday's law of induction manifested in the quantum state of
Aharonov-Bohm loops. In particular, we propose a flux-switching experiment for
a double-dot AB ring to verify the phase shift induced by Faraday's law. We
show that the induced {\em Faraday phase} is geometric and nontopological. Our
study demonstrates that the relation between the local phases of a ring at
different fluxes is not arbitrary but is instead determined by Faraday's
inductive law, which is in strong contrast to the arbitrary local phase of an
Aharonov-Bohm ring for a given flux.Comment: Submitted to Phys. Rev. Let
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