Eraseektors

Eraseektors are a theoretical class of information-erasure operations used in speculative discussions of information theory and thermodynamics. An eraseektor formalizes a process that replaces an input state with an erasure symbol while optionally preserving a residual system that captures whatever information remains.

Mathematically, an eraseektor E is described as a linear, completely positive, trace-preserving map that, when applied to a density operator ρ on a finite-dimensional Hilbert space H, yields a joint state on H ⊗ F, where F is an ancillary erasure register carrying a distinguished erasure state |e⟩. In the erasure output, the original content is converted into the erasure flag, and tracing out F recovers a reduced state on H consistent with the erasure event. A central feature is the presence of a designated erasure outcome, often modeled by the state |e⟩ that is orthogonal to usual system states.

Erasure probability can be built into the map, yielding a probabilistic eraseektor: with probability p, the input is replaced by the erasure flag, and with probability 1−p the original state is left intact or partially transformed. As a result, eraseektors generalize simple erasure channels by allowing a coherent residual component in some regimes.

Applications include theoretical analyses of the thermodynamics of information, the cost of erasure per Landauer’s principle, and the study of irreversible information processing in toy models. Because eraseektors are not universally standardized, definitions vary across sources, but the core idea is to model information loss via a distinguished erasure output.

See also: erasure channel, quantum channel, completely positive trace-preserving maps, Landauer's principle.