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We revisit the formulation of quantum mechanics over the quaternions and investigate the dynamical structure within this framework. Similar to standard complex quantum mechanics, time evolution is then mediated by a unitary operator which can be written as the exponential of the generator of time shifts. By imposing physical assumptions on the correspondence between the energy observable and the generator of time shifts, we prove that quaternionic quantum theory admits a time evolution only for systems with a quaternionic dimension of at most two. Applying the same strategy to standard complex quantum theory, we reproduce that the correspondence dictated by the Schrodinger equation is the only possible choice, up to a shift of the global phase.
Entanglement is essential in quantum information science. Typically, the inevitable coupling between quantum systems and environment inhibits entanglement from being created between long-distance subsystems and being maintained for a long time. In th
In this work, a classical-quantum correspondence for two-level pseudo-Hermitian systems is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-Hermitian Hamiltonian if there is a suitable canonica
Providing the microscopic behavior of a thermalization process has always been an intriguing issue. There are several models of thermalization, which often requires interaction of the system under consideration with the microscopic constituents of th
We experimentally study the time-optimal construction of arbitrary single-qubit rotations under a single strong driving field of finite amplitude. Using radiation-dressed states of nitrogen vacancy centers in diamond, we realize a strongly-driven two
The prediction of the response of a closed system to external perturbations is one of the central problems in quantum mechanics, and in this respect, the local density of states (LDOS) provides an in- depth description of such a response. The LDOS is