4 papers
Nonbinary Quantum Stabilizer Codes
Alexei Ashikhmin, Emanuel Knill
We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between selforthogonal codes…
Quantum Error Detection II: Bounds
A. Ashikhmin, A. Barg, E. Knill +1
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower…
Quantum Error Detection I: Statement of the Problem
Alexei Ashikhmin, Alexander Barg, Emanuel Knill +1
I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to de…
Remarks on Bounds for Quantum Codes
Alexei Ashikhmin
We present some results that show that bounds from classical coding theory still work in many cases of quantum coding theory.