E. Rains, private communication, December 1996. 15 FIGURES 0.095 0.167 0.25 0.5  Home/Search Document Not in Database Summary Related Articles Check |
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Current Fluctuations for the Totally Asymmetric Simple.. - Prähofer, Spohn (2001) (Correct)
....and Rains [5] extend to arbitrary ; and allow for small deviations of the boundary densities as in (5.2) with n replaced by v . Very recently they investigate the case of re ection symmetry relative to the diagonal, in particular = and an extra line density along the diagonal [15]. The particle model behind the Poisson last passage percolation is the PNG model [16, 17, 18] It consists of point particles with velocity 1. They annihilate each other at a collision and are created in pairs with rate 1. If (x; t) is the density of right movers, and (x; t) of left ....
....at the lower edge the w(j; 0) are exponential with rate 1 . By maximizing the passage time on scale n we obtain the same phase diagram as for the critical step. However the uctuations in N t , now the number of particles injected up to time t, are modi ed. In Figure 4 we summarize the ndings [15] which could be written more formally as in Conjecture 7.1. GSE is the distribution of the largest eigenvalue of a symplectic Gaussian random matrix. F 0 is a novel distribution and given by 0 (x) 1 ( v(x) u(x) x 2u (x) 2u(x) F (x)E(x) 7.15) in the notation of [5] So ....
J. Baik, E.M. Rains, private communication
Quantum Stabilizer Codes and Classical Linear Codes - Cleve (1996) (1 citation) (Correct)
....is zero if ffi 1=6 [20] It remains an open question whether the 1 Gamma H(ffi) Gamma ffi log 2 3 bound also applies to degenerate codes. Very recently, it has been announced that the ffi 1=6 threshold bound does extend to nondegenerate codes, and this will be appear in a forthcoming paper [22]. It is interesting to note that there exist some degenerate stabilizer codes that outperform all known nondegenerate codes on the depolarizing channel, for some values of ffi [5] The best lower bound for this channel that we are aware of is 1 Gamma H(2ffi) Gamma 2ffi log 2 3 [8] For the ....
E. Rains, private communication, December 1996. 15
Quantum analog of the MacWilliams identities in classical coding.. - Shor (1997) (10 citations) (Correct)
....which protects 1 qubit of information against 2 errors using n = 9 qubits. A solution of the Macwilliams identities exists for codes mapping 1 qubit into n = 10 qubits; however an extension of the techniques in this paper based on classical shadow code techniques rules this possibility out as well [20]. The smallest possible code protecting against two errors thus would map 1 qubit into n = 11 qubits; such a code was constructed in [15] Both possibilities eliminated above would have required degenerate quantum codes. These might have allowed to find more compact codes than would have been ....
....such a code was constructed in [15] Both possibilities eliminated above would have required degenerate quantum codes. These might have allowed to find more compact codes than would have been expected from an analogy to classical codes. A systematic study of the MacWilliams identities for n 30 [20] shows that this is not the case. The most compact codes appear not to be degenerate. It will be interesting to know if this holds as n 1. In conclusion, we have derived the quantum analog of the MacWilliams identities which give necessary conditions for the existence of codes. We have ....
E. Rains, private communication.
quant-ph/9612048 - Dec Quantum Stabilizer (Correct)
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E. Rains, private communication, December 1996. 15 FIGURES 0.095 0.167 0.25 0.5
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