RT Journal Article
T1 Are problems in Quantum Information Theory (un)decidable?
A1 Wolf, Michael M.
A1 Cubitt, Toby S.
A1 Pérez García, David
AB This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of entanglement theory and quantum channels turn out to be decidable via quantifier elimination as long as they admit a compact formulation without quantification over integers. For many asymptotically defined properties which have to hold for all or for one n € N, however, effective procedures seem to be difficult if not impossible to find. We review some of the main tools for (dis)proving decidability and apply them to problems in quantum information theory. We find that questions like ”can we overcome fidelity 1/2 w.r.t. a two-qubit singlet state?” easily become undecidable. A closer look at such questions might rule out some of the “single-letter” formulas sought in quantum information theory.
YR 2011
FD 2011-11-23
LK https://hdl.handle.net/20.500.14352/44449
UL https://hdl.handle.net/20.500.14352/44449
LA eng
NO Comunidad de Madrid
NO Ministerio de Ciencia e Innovación (MICINN)
NO Ministerio de Educación y Ciencia
NO Unión Europea. FP7
NO European CHIST-ERA
NO Unión Europea
DS Docta Complutense
RD 10 abr 2025