Some applications of the Pohozaev identity
We apply the Pohozaev identity to show the nonexistence of nontrivial solutions to a semilinear equation of the form (H−E)u=f(x,|u|)u, where E is a real constant lying on the essential spectrum ...
We apply the Pohozaev identity to show the nonexistence of nontrivial solutions to a semilinear equation of the form (H−E)u=f(x,|u|)u, where E is a real constant lying on the essential spectrum ...
Duality and integrability: Electromagnetism, linearized gravity, and massless higher spin gauge fields as bi-Hamiltonian systems
In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This...
In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This...
Codeword stabilized quantum codes: Algorithm and structure
J. Math. Phys. 50, 042109 (2009); doi:10.1063/1.3086833
Published 28 April 2009
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The codeword stabilized (CWS) quantum code formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes [IEEE Trans. Inf. Theory 55, 433 (2009)]. This formalism reduces the problem of constructing such quantum codes to finding a binary classical code correcting an error pattern induced by a graph state. Finding such a classical code can be very difficult. Here, we consider an algorithm which maps the search for CWS codes to a problem of identifying maximum cliques in a graph. While solving this problem is in general very hard, we provide three structure theorems which reduce the search space, specifying certain admissible and optimal ((n,K,d)) additive codes. In particular, we find that the re does not exist any ((7,3,3)) CWS code though the linear programming bound does not rule it out. The complexity of the CWS-search algorithm is compared with the contrasting method introduced by Aggarwal and Calderbank [IEEE Trans. Inf. Theory 54, 1700 (2008)].
©2009 American Institute of Physics
| History: | Received 26 November 2008; accepted 30 January 2009; published 28 April 2009 |
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http://link.aip.org/link/?JMAPAQ/50/042109/1 |
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