Temporal correlation beyond quantum bounds in non-hermitian dynamics
arXiv:1907.13400 · doi:10.1088/1751-8121/abde76
Abstract
We study the dynamics of two level systems described by non-hermitian Hamiltonians with real eigenvalues. Within the framework of hermitian quantum mechanics, it is known that maximal violation of Leggett-Garg inequality is bounded by (Luder's bound). We show that this absolute bound can be evaded when dynamics is governed by non-hermitian Hamiltonians. Moreover, the extent of violation can be optimized to reach its algebraic maximum of which is otherwise only feasible when the Hilbert space is infinite dimensional in the hermitian case. The extreme violation of Leggett-Garg inequality is shown to be directly related to the two basic ingredients: (i) The Bloch equation for the two level system has non-linear terms which allow for accelerated dynamics of states on the Bloch sphere exceeding all known quantum speed limits of state evolution; and (ii) We need to ensure that the quantum trajectory of states always lies on a single great circle (geodesic path) on the Bloch sphere at all times.
arXiv commentv2: Includes (a) A numerical comparison of our predictions with existing experimental results (Ref. 44 in the article) ; and (b) An extensive discussion of Leggett-Garg Inequality in the context of possible embedding of the non-hermitian dynamics within a higher dimensional Hilbert space following unitary time evolution and postselection
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