Quantum Error Correcting Codes From The Compression Formalism

Details Quantum Error Correcting Codes From The Compression Formalism Quantum Error Correcting Codes From The Compression Formalism

2005-11-10

arxiv.org/abs/quant-ph/0511101v2

Rep. Math. Phys., 58 (2006), 77-91.

Physics

Quantum Physics

8 pages, 2 figures, Rep. Math. Phys., to appear

Scientific paper

10.1016/S0034-4877(06)80041-8

We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and identify correctable codes for Pauli-error models not obtained by the stabilizer formalism. This is accomplished through an application of a new tool for error correction in quantum computing called the ``higher-rank numerical range''. We describe its basic properties and discuss possible further applications.

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