Neutrosophic Quantum Error Correction

Source abstract

Quantum error correction is a fundamental ingredient in the protection of quantum information against decoherence and operational noise. Classical quantum error-correcting codes are normally formulated using completely positive trace-preserving quantum channels, density operators, and binary or finite-alphabet error models. In this paper we introduce a mathematical framework for neutrosophic quantum error correction (NQEC), in which the action of a quantum noise process is accompanied by three-valued degrees describing the available evidence for an error, the indeterminacy of the error description, and the degree of non-error or reliable behavior. The proposed framework does not replace the standard Hilbert-space formalism. Instead, it associates a neutrosophic descriptor (T, I, F) with quantum error events or families of error operators. We formulate neutrosophic quantum channels, neutrosophic error operators, neutrosophic code spaces, and a generalized Knill– Laflamme-type condition. A neutrosophic recovery map is then defined as a completely positive recovery operation supplemented by a consistent neutrosophic error classification. We prove several basic properties, including reduction to ordinary quantum error correction when the indeterminacy component vanishes and the error information becomes classical. Examples based on the bit-flip, phase-flip, depolarizing, and three-qubit repetition codes are given. We also formulate a neutrosophic syndrome formalism and discuss approximate correction, uncertain error probabilities, and possible extensions to stabilizer codes and fault-tolerant quantum computation.