Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For pt.I see ibid., vol.46, no.3, p.778-88 (2000). In Part I of this paper  formulated the problem of error detection with quantum codes on the depolarizing channel and gave an expression for the probability of undetected error via the ight enumerators of the code. In this part  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 lor (existence) bound is proved for stabilizer codes by a counting argument for classical self-orthogonal quaternary codes. Upper bounds are proved by linear programming. First  formulate two linear programming problems that are convenient for the analysis of specific short codes. Next  give a relaxed formulation of the problem in terms of optimization on the cone of polynomials in the Krawtchouk basis.  present two general solutions of the problem. Together they give an upper bound on the exponent of undetected error. The upper and lor asymptotic bounds coincide for a certain interval of code rates close to 1.
['Alexei E. Ashikhmin', 'Alexander Barg', 'E. Knill', 'Simon Litsyn']
I am writing a research paper on a idea Quantum error detection .II. I am writing a research paper on a idea Bounds
[{"from": "human", "value": "I am writing a research paper on a idea Quantum error detection .II. I am writing a research paper on a idea Bounds"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: For pt.I see ibid., vol.46, no.3, p.778-88 (2000). In Part I of this paper  formulated the problem of error detection with quantum codes on the depolarizing channel and gave an expression for the probability of undetected error via the ight enumerators of the code. In this part  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 lor (existence) bound is proved for stabilizer codes by a counting argument for classical self-orthogonal quaternary codes. Upper bounds are proved by linear programming. First  formulate two linear programming problems that are convenient for the analysis of specific short codes. Next  give a relaxed formulation of the problem in terms of optimization on the cone of polynomials in the Krawtchouk basis.  present two general solutions of the problem. Together they give an upper bound on the exponent of undetected error. The upper and lor asymptotic bounds coincide for a certain interval of code rates close to 1."}]