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Error Avoiding Quantum Codes and Dynamical Stabilization of Grover's Algorithm
An error avoiding quantum code is presented which is capable of stabilizing
Grover's quantum search algorithm against a particular class of coherent
errors. This error avoiding code consists of states only which are factorizable
in the computational basis. Furthermore, its redundancy is smaller than the one
which is achievable with a general error correcting quantum code saturating the
quantum Hamming bound. The fact that this code consists of factorizable states
only may offer advantages for the implementation of quantum gates in the error
free subspace
The AWGN Red Alert Problem
Consider the following unequal error protection scenario. One special
message, dubbed the "red alert" message, is required to have an extremely small
probability of missed detection. The remainder of the messages must keep their
average probability of error and probability of false alarm below a certain
threshold. The goal then is to design a codebook that maximizes the error
exponent of the red alert message while ensuring that the average probability
of error and probability of false alarm go to zero as the blocklength goes to
infinity. This red alert exponent has previously been characterized for
discrete memoryless channels. This paper completely characterizes the optimal
red alert exponent for additive white Gaussian noise channels with block power
constraints.Comment: 13 pages, 10 figures, To appear in IEEE Transactions on Information
Theor
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