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Wolf, Michael M. ; Cubitt, Toby S. ; Pérez García, David | 2011-11-23This 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 t[...]texto impreso
Using tools from classical signal processing, we show how to determine the dimensionality of a quantum system as well as the effective size of the environment's memory from observable dynamics in a model-independent way. We discuss the dependenc[...]texto impreso
Cadarso, Andrea ; Sanz, Mikel ; Wolf, Michael M. ; Cirac, J.I. ; Pérez García, David | American Physical Society | 2013-01Based on the theory of Matrix Product States, we give precise statements and complete analytical proofs of the following claim: a large fractionalization in the magnetization or the need of long-range interactions imply large entanglement in the[...]texto impreso
The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this Letter, we show that, remarkably, identi[...]texto impreso
Fernández González, Carlos ; Schuch, Norbert ; Wolf, Michael M. ; Cirac, J.I. ; Pérez García, David | American Physical Society | 2012-12We study Hamiltonians which have Kitaev's toric code as a ground state, and show how to construct a Hamiltonian which shares the ground space of the toric code, but which has gapless excitations with a continuous spectrum in the thermodynamic li[...]texto impreso
It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality-independent of the state and the measurements chosen at the other site. In this Letter we prove the converse: every pair of incompatible quant[...]texto impreso
This is the supplementary information associated to the article: T.S. Cubitt, D. Perez-Garcia, M.M. Wolf, Undecidability of the spectral gap, Nature 528, 207-211 (2015), doi:10.1038/nature16059texto impreso
The spectral gap-the energy difference between the ground state and first excited state of a system-is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped [...]
