SWhat changed
For a unital C*-algebra and a linear map into bounded operators on a Hilbert space, complete positivity is equivalent to representation as the compression V* pi(A) V of a *-representation on a larger Hilbert space. For a unital map the construction can make V an isometry.
Scientific scope
For a unital C*-algebra and a linear map into bounded operators on a Hilbert space, complete positivity is equivalent to representation as the compression V* pi(A) V of a *-representation on a larger Hilbert space. For a unital map the construction can make V an isometry. Ordinary positivity does not suffice for a noncommutative domain; the paper includes a counterexample. The recorded theorem assumes a unital algebra and bounded-operator codomain, not arbitrary nonlinear maps or an unbounded field operator. It is a representation theorem, not a claim that every finite laboratory process has an experimentally certified unitary realization.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. Ordinary positivity does not suffice for a noncommutative domain; the paper includes a counterexample. The recorded theorem assumes a unital algebra and bounded-operator codomain, not arbitrary nonlinear maps or an unbounded field operator. It is a representation theorem, not a claim that every finite laboratory process has an experimentally certified unitary realization.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
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